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Basic Algebra
1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?
1 page ------->p min.;
x pages ------>5 min.;
The answer is A. 5/p
Just set up a cross multiplication problem and sub in any number you want for p. When you cross multiply you will realize that number will be on the denominator when you divide. Hence, the answer must have p on the bottom;
2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?
(1/4)x+(1/6)x=1;
multiply both sides by 12;
3x+2x=12;
5x=12x=2.4 hours or 2 hours and 24 minutes;
3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?
Take off 15% of the original $450 which is $67.50;
Discount= $382.50;
Take off a further 20% of that discounted price of $382.50;
Which is another $76.50;
Discount = $306;
4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?
Original Price = Sales Price divided by (1 minus discount rate)
Original Price = $12,590 divided by (1 minus 20%)
Original Price = $12,590 divided by 80%;
Original Price = $15,737.50;
Final Answer: $15, 737.50;
Proof: $15,737.50 multiply by 80% equals $12,590;
5. Solve the following equation for A : 2A/3 = 8 + 4A?
Multiply both sides by 3; 2A=24+12Athen ; -24=10Athen A=-2.4;
6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?
S=L-6
J=L+5
L+(L-6)+(L+5) = 41
3L-1= 41
3L=42
L=14;
7. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive? Simple Interest = Principle x Rate x YearswherePrinciple = 4000Rate = 6% = 0.06Years = 5Simple Interest = 4,000 x 0.06 x 5= 1200;
8. Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?
Let x be the original amount.To that you add 35% of x --> 0.35xThe new amount is $670Write an equation:
x + (0.35)x = 670
(1 + 0.35)x = 670
1.35x = 670
x = 670/1.35
x ≈ 496.30;
9. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him?
0.3% is .003
$55 X .003 = $.165;
10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes:
a 2 hour credit art,
a 3 hour credit history,
a 4 hour credit science course,
a 3 hour credit mathematics course, and
a 1 hour science lab. He received
a “B” in the art class, an “A” in the history class,
a “C” in the science class,
a “B” in the mathematics class, and
an “A” in the science lab.
What was his GPA if the letter grades are based on a 4 point scale?
(A=4, B=3, C=2, D=1, F=0).
You have to add up the total number of hours that each class is worth. If a class is longer, it will be worth more points.
Art: 2 Hrs, B = 2x3= 6
History: 3 Hrs, A = 3x4=12
Science:4 Hrs, C= 4x2= 8
Math: 3 Hrs, B = 3x3= 9
Lab: 1 Hr, A = 1x4= 4
Total Hours= 13,
Total Credits= 39
Credits/Hours=3Final GPA: 3.0;
11. Simon arrived at work at 8:15 A.M. and left work at 10: 30 P.M. If Simon gets paid by the hour at a rate of $10 and time and ½ for any hours worked over 8 in a day. How much did Simon get paid?
8:15-12.00pm is 3 hours 45 mins
1200pm-1030pm is 10 hours 30 mins
He worked 14 hour and 15 mins
He worked 8 normal 8 hours and 6 hours and 15 mins over time.
So he gets piad 10 dollars an hour so $80.00 for 8 hours.
So he gets paid 15 dollars an hour so $93.75 for his 6 1/4 hour overtime.
He gets paid $173.75 total;
12. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
If she take 12 she will run out of red and green jellybeans; Answer: 8+4+1=13;
13. If r = 5 z then 15 z = 3 y, then r = ?
15z = 3y
Divide each side of the equation by three.
5z = y
Since you already know that r = 5z, you can substitute r for 5z. Therefore:r = y;
14. If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
300 jellybeans cost x dollars
300/x jellybeans cost one dollar
(300/x)/2 = 150/x jellybeans costs fifty cents;
15. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make;
132 / 22 = $6 per hour.
So multiply 15 x 6 and you get $90;
16. If 8x + 5x + 2x + 4x = 114, the 5x + 3=?
8x+5x+2x+4x =19x = 114
114/19= 6 = x
5(6) +3 = 33;
17. You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?
Sales Tax will be $6.60:0.0825 x $80.00 = $6.60
Add that to the sale price:80.00 + 6.60 = 86.60
Make the change from $100 bill:$100 - $86.60= $13.40;
18. You purchase a car making a down payment of $3,000 and 6 monthly payments of $225. How much have you paid so far for the car?
$3,000.00 + (6 x $225) is:
$3,000.00 + $1,350.00 =$4,350.00 paid so far;
19. Your supervisor instructs you to purchase 240 pens and 6 staplers for the nurse's station. Pens are purchased in sets of 6 for $2.35 per pack. Staplers are sold in sets of 2 for 12.95. How much will purchasing these products cost?
(240/6)*$2.35 + (6/2)*$12.95 =40*$2.35 + 3*$12.95 =$94 + $38.85 =$132.85;
20. If y = 3, then y^3(y^3-y)= ?
y^3 = 27
27(27-3) =(27)(24)= 648;
Advanced Algebra
1. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?
(x+y+z)/3=v
x+y+z=3v
x=3v-y-z
2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?
The first cyclist has a 3 hour head start--and in those three hours, has traveled 3 * 6 = 18 miles.
The question now is: how long will it take for the second cyclist to travel 18 miles more than the first cyclist. The second cyclist will gain 10 - 6 = 4 miles / hour.
so 18 / 4 = 4.5 hours.
the second cyclist will catch up in 4.5 hours after starting.
with equation goodness:
distance = speed * time (where t is time after the second cyclist starts.
18 = 10t - 6t = 4t
18/4 = t = 4.5
3. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?
If Jim can fill a pool in 30 minutes, he fills 1/30 of a pool in 1 minute. Sue fills 1/45 of a pool in 1 minute. Tony fills 1/90 per minute.
1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 per minute.
Since they do 6/90 of the job in one minute, they do the full ("1") job in 6/90 * 90/6 minutes.
So the full job would take 90/6 = 15 minutes.
4. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?
E. t - 2t - 3t = 32, t = 8
8-2*8-3*8=8-16-24=-32
5. What simple interest rate will Susan need to secure to make $2,500 in interest on a $10,000 principal over 5 years?
Simple Interest can be solved very easily with an easy formula.
I = PRT
where...
I = Interest earned
P = Principal amount
R = Interest Rate
T = Time
In this case, we want the Interest rate! So rearrange the formula to find R:
I = PRT
R = I/PT
Then just substitute the values in. Easy as that
R = I/PT
R = 2500/(10000*5)
R = 2500/50000
R = 0.05
WHICH IS A INTEREST RATE OF 5%.
6. Which of the following is not a rational number?
A. -4
B. 1/5
C. 0.8333333...
D. 0.45
E. sqrt( 2 )
sqrt(2)
Any number that cannot be written as a fraction is irrational.
7. A study reported that in a random sampling of 100 women over the age of 35 showed that 8 of the women were married 2 or more times. Based on the study results, how many women in a group of 5,000 women over the age of 35 would likely be married 2 or more times?
8/100=x/5000
cross multiply and solve for x.
8. John is traveling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
x=vt
x= 28 miles
t= 30 min = 0.5 h
so, v= 28/0.5 = 56 miles/hour (minimum).
9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
Steven makes 20/5 = 4 drinks per minute
Sue makes 20/10 = 2 drinks per minute
Jack makes 20/15 = 4/3 drinks per minute
4 + 2 + 4/3 = 7 1/3 drinks per minute
20 / (7 1/3) = 20/ (22/3) = 20 * 3 / 22 = 60/22 = ~2.73 minutes~2.73 minutes or ~2 minutes
43.6 seconds.
10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
rate * time = progress. sure, abstract but you get the idea.
sam's rate is 1/4, lisa's is 1/6 and tom's is 1/2. that is, to get a 1 unit of progress done, time must be 2 for tom so that rate is forced to be 1/2.
then the total rate is simply the sum of the 3:
(1/4 + 1/6 + 1/2) * time = progress. again, the job is 1 unit of progress so we simply need to know time. this will be 1 / (1/4 + 1/6 + 1/2).
we can find a common denominator for this expression:
1 / ( 3/12 + 2/12 + 6/12) = 1 / (11/12) = 12/11
now, that has units of days. So, it should take sam, lisa, and tom about 1.09 days to do this job if they work together.
11. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?
A. 3 feet
B. 3 ¾ feet
C. 3 ½ feet
D. 3 ¼ feet
E. 2 ½ feet
36 inch waist + 4 inches = 40 inches
36 inch + 6 inches = 42 inches
So the string must be between 40 inches and 42 inches
36 inches = 3 feet
so... 40 inches = 3 feet, 4 inches = 3 4/12 = 3 1/3 feet
42 inches = 3 feet, 6 inches = 3 1/2 feet
The only one that is between 3 1/3 and 3 1/2 is: C. 3 1/2 feet.
12. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?
a 58.3% increase
7 more cars sold so,
7/12 = 58.3% increase as a percentage of last weeks sales.
13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
www.milearn.com/fileup/Math%20Problems_A.pdf
The north bound plane traveled 150x2 = 300 miles (north)
The west bound plane traveled 200x2 - 400 miles (west)
The distance between them is the length of the hypotenuseof the right triangle formed by the their travel. You shouldrecognize it is in the same ratio as a 3-4-5 right triangle, sothe distance will be 500 miles. Or, just use the Pythagorean theorem:
a^2 + b^2 = c^2 ==> 300^2 + 400^2 = c^2 ==> c^2 = 250,000==>c = 500
14. During a 5-day festival, the number of visitors tripled each day. If the festival opened on a Thursday with 345 visitors, what was the attendance on that Sunday?
345*3=1035 (fri)
1035*3=3105 (sat)
3105*3=9315(sunday
Averages and Rounding
1. Round 907.457 to the nearest tens place.
907.457 rounded off to nearest tens place is 910. If it were asked to round off to nearest "tenths" place, it would have been 907.5
2. At a certain high school, the respective weights for the following subjects are: Mathematics 3, English 3, History 2, Science 2 and Art 1. What is a student's average whose marks were the following: Geometry 89, American Literature 92, American History 94, Biology 81, and Sculpture 85?
Since the subjects are weighted, look at it like this:
Math is worth 3x; (89 x 3 = 267)
Lit is worth 3x; (92 x 3 = 276)
History is worth 2x; (94 x 2 = 188)
Science is worth 2x; (81 x 2 = 162)
Art is worth 1x ;(85 x 1 = 85)
So, 11x = 978
x = 88.909; Round to 88.9
3. Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $3.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?
Add all them up then divide them by the number of days. So:
5.43 + 3.54 + 3.54 + 7.89 = 20.4
20.4/5 = 4.08
So the average daily cost was $4.08
(A lot of people are getting this wrong, because they think she spent $5.43 on both Monday and Thursday, but actually she spent that on both of those days combined.)
4. What is 1230.932567 rounded to the nearest hundredths place?
www.tutorcentral.net/QuizManager/displayquiz.asp?FormID=145
www.wdeptford.k12.nj.us/.../2.%20%20Averages%20and%20Rounding.pdf
hubpages.com/hub/Wonderlic-Personnel-Test-Questions
jsbursch.net/.../pte/docs/ACC-GED-Math-WordProblems-Simple.doc
1230.93
For hundredths, think of it as money.
5. Subtract the following numbers rounded to the nearest tenths
www.wdeptford.k12.nj.us/.../2.%20%20Averages%20and%20Rounding.pdf
subtraction:
134.679-(-45.548)-(-67.8807)=248.11 (rounded to 10th place)
6. What is the absolute value of -9?
9
7. What is the median of the following list of numbers? 4, 5, 7, 9, 10, 12
(7+9)/2 = 8
The median of a set having an even number of elements is the average of the middle two when they are sorted into order.
8. What is the mathematical average of the number of weeks in a year, seasons in a year, and the number of days in January?
jsbursch.net/.../pte/docs/ACC-GED-Math-WordProblems-Simple.doc
www.testmyhead.com/Assessment/Testing.aspx?TestId=54408f89-fec3-4374-8b50-3de76c43c7f5
jsbursch.net/.../pte/docs/ACC-GED-Math-WordProblems-Simple.doc
www.tutorcentral.net/QuizManager/displayquiz.asp?FormID=145
For simplicity, let's assume that leap years occur every 4 years.
Year X contains 365 days
Year X+1 contains 365 days
Year X+2 contains 365 days
Year X+3 contains 366 days and so forth (the cycle repeats itself)
a) average weeks is given by the weighted average.
probability of non-leap year = p(non-leap)=3/4.
probability of leap year = p(leap)=1/4.
weeks in non-leap year, w(non-leap)= 365/7.
weeks in leap year, w(leap) = 366/7.
Therefore, the weighted average = w(leap)*p(leap)+w(non-leap)*p(non-leap)
b) define "season", question is unclear.
c) always 31 days in january
9. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; history is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology.
This is a "weighted" average. Multiply your grades by theweights, sum that up, and divide by the sum of the weights:
The C in trig gets you 2 for the C and a weight of 3 since its math
B in history gets you 3 points with a weight of 2
A in botany gets you 4 points with a weight of 4
B in microbiology gets you 3 points with a weight of 4
so sum1 = 2x3 + 3x2 + 4x4 + 3x4 = 40
sum2 = 3 + 2 + 4 + 4 = 13
The GPA is then 40/13 = 3.08
10. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day?
http://siliconinvestor.advfn.com/readmsg.aspx?msgid=21455460
www.wdeptford.k12.nj.us/.../2.%20%20Averages%20and%20Rounding.pdf
If the week is just the work week, then 28.49/5 = 5.698 or 5.70 per day.Over the entire week, divide by seven to get 4.07 per day.
11. A roast was cooked at 325° F in the oven for 4 hours. The internal temperature rose from 32° F to 145° F. What was the average rise in temperature per hour
If the internal temp. rose from 32 °F to 145 °F over the course of 4 hours, the average rise =(145-32)/4 °F.
12. In the number 743.25 which digit represents the tenths space?
The tenths is always the number right after the decimal point. Thus, the answer is 2.
The hundredTHS is 5.
In contrast, the tens ( note no -ths suffix) is 3. the hundreds is 4 and the thousands is 7.
You do not have a thousanths digit in the given.
Arithmetic
1. Add 0.98 + 45.102 + 32.3333 + 31 + 0.00009
31.00000
00.98000
45.10200
32.33330
00.00009
=
109.41539
2. Find 0.12 ÷ 1
.12
3. (9 ÷ 3) x (8 ÷ 4) =
6
4. 6 x 0 x 5
0
5. 7.95 ÷ 1.5
79.5/15=5.3
75
____
45
45
____
0
6. -32 + 7 equals:
-25
7. -37 + -47 equals:
-84
8. 41% equals:
.41
Commas
1. For the Thanksgiving reunion, relatives were sitting in the dining room, on the porch, and in the carport.
No error
http://shec.hcs.k12.nc.us/www/SHEC_HCS/site/hosting/Accuplacer/296,7,Slide 7
2. Lydia seems to be a kind, considerate girl.
No error
3. This fishing pole Nathan, has seen better days.
Pole, Nathan,
4. My cousin has moved to 56 Central Street Narragansett, Rhode Island 02882.
Central Street,
5. The badger, a shy animal sometimes makes friends with a coyote.
A shy animal,
6. After the death of Blackbeard, the famous pirate, piracy disappeared from the coast of the American colonies.
No error
7. “Silent Night” was written by two men from the village of Oberndorf Austria.
Oberndorf, Austria
8. On November 19, 1929 Admiral Richard E. Byrd flew the Floyd Bennett to the base of the Queen Maud Mountains.
1929,
9. Oh I forgot to bring the cookies
Oh,
10. “The boy in the kayak,” whispered Sue “is the new football captain."
No error
Estimation and Sequences
1. Describe the following sequence in mathematical terms. 144, 72, 36, 18, 9
Descending arithmetic sequence
2. Which of the following is not a whole number followed by its square?
A. 1, 1
B. 6, 36
C. 8, 64
D. 10, 100
E. 11, 144
11, 144
3. A nurse has to record her temperatures in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7° F. What is the temperature in °C?
5/9 ( 100.7-32)C=38.1666C=38.2 C
4. Art realized that he had 2 more quarters than he had originally thought in his pocket. If all of the change in his pocket is quarters and it totals to $8.75, how many quarters did he originally think were in his pocket?
http://home.earthlink.net/~djbach/lessons.html
(8.75-.50)/.25=X = 33 or second option:
Divide 875 by 25, then subtract two from your answer.
5. There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket?
Let x+12=apples
Let x =oranges
so (x)+(x+12)=36
2x +12=36
2x=24
x=12 which was oranges
and we let x+12=apples; so12+12 = 24 apples
6. Which of the following correctly identifies 4 consecutive odd integers where the sum of the middle two integers is equal to 24?
A. 5, 7, 9, 11
B. 7, 9, 11, 13
C. 9, 11, 13, 15
D. 11, 13, 15, 17
E. 13, 15, 17, 19
C
7. What is the next number in the sequence? 6, 12, 24, 48, ___
96
8. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?
A. 0
B. 1
C. 2.33
D. -3
E. none of the above
B. 1
9. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___
1/16
10. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies
A. degrees Celsius
B. milliliters
C. quarts
D. kilograms
E. cups
E
Exponents
1. 10^4 is not equal to which of the following?
100,000
2. Multiply 10^4 by 10^2
10^6
3. Divide x^5 by x^2
x^3
4. Find 8.23 x 10^9
8230000000
5. 83,000 equals:
8.3 x 10^4
6. .00875 equals:
8.75 x 10^-3
Fractions and Square Roots
1. What is the improper fraction or mixed number represented by the following figure?
www.testprepreview.com/modules/fractionsandsquareroots.htm
2. Which of the following fractions most correctly depicts the shaded area of the circle below?
http://www.testprepreview.com/modules/fractionsandsquareroots.htm
3. Which of the following is not a fraction equivalent to 3/4?
A. 6/8
B. 9/12
C. 12/18
D. 21/28
E. 27/36
12/18
4. Solve: 0.25 + 0.65
9/10
5. Which of the following statements is false?
Ten thousandths place is located 5 places to the right of the decimal
6. Find the square of 25/9
(25/9)² = 625 / 81 and just in case:-√ (25 / 9) = 5 / 3
7. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need
Sarah need 3/8+3/5 for both cake & cookies
So she needs 39/40 cups of sugar. That means 78/80 cups
She having 15/16 cups of sugar. That means 75/80 sups
So she need additional 78/80 - 75/80 = 3/80 cups
8. There are 8 ounces in a 1/2 pound. How many ounces are in 7 3/4 lbs?
8 oz = 0.5 lb
x oz = 7.75 lbs
Then you cross multiply
(0.5)(x) =(8)(7.75)
0.5x = 62 ....divide by 0.5,
then you getx = 124 oz
9. If the value of x and y in the following fraction are both tripled, how does the value of the fraction change? XZ/Y http://school.discoveryeducation.com/quizzes32/al3xy/Fractions.html
remains the same
10. Which of the following fractions is the equivalent of 0.5%
Well, what is a percent? A percent is a fraction when the denominator is 100. Percent literally means per hundred.
So, 0.5% means 0.5/100.
Of course, you can't have 0.5 in the numerator.
To get rid of that, the easiest way is to multiply by 2 (since 0.5 = 1/2)
0.5*2/100*2= 1/200
11. Which of these numbers is a factor of 21
A. 2
B. 5
C. 7
D. 42
E. 44
7
12. If the average person drinks 8, (8oz) glasses of water per day, a person who drinks 12.8 oz of water after a morning exercise session has consumed what fraction of the daily average?
The average person drinks 8 X 8 oz. of water or 64 oz. per day. (12.8/64 ) X 100= % of daily average.If the average person consums 8(8 oz) = 64 oz daily. The exerciser drinks 12.8 oz. To find the percent you divide the total daily oz by the exercier's consumed total 12.8/64=.2 which equals 20%.
13. You need 4/5 cups of water for a recipe. You accidentally put 1/3 cups into the mixing bowl with the dry ingredients. How much more water in cups do you need to add?
You need to convert 1/3 and 4/5 into ?/15...
1/3 = 5/15
4/5 = 12/15
so you need to add .... 12-5 = 7/15 cups !!!
Bit tricky to measure 7/15 cups, but its pretty much half a cup
14. ¾ - ½ =
3/4 - 2/4=1/4
15. 7 1/2 - 5 3/8 =
60/8 - 43/8 = 17/8=2 1/8
Geometry - www.testprepreview.com/modules/geometry.htm
Basic Grammar - www.testprepreview.com/modules/grammarpart1.htm
Intermediate Grammar - www.testprepreview.com/modules/englishgrammarpart_2.htm
Advanced Grammar - www.testprepreview.com/modules/grammarpart3.htm
Graphs - www.testprepreview.com/modules/graphs.htm
1. In the following figure, what is the area of the shaded circle inside of the square?
The diameter of the circle = 4 cm
so the radius = 2 cm
Area of the shaded circle = (pi)r^2
A shade circle = 3.14(2^2)A = 3.14*4 = 12.56
2. In the figure below, determine the area of the shaded region of the figure.
The diameter of the circle = 7 cm
so the radius = 3.5 cm
Area of the shaded region = Area of square - Area of circle
A shade = LW - (pi)r^2
A = 7^2 - 3.14(3.5^2) = 10.52
.
.
7. If XYZ Auto Company sold 23,000 vehicles in 1999, how many were SUV's?
Since there were 23000 total vehicles, we know that 13% of these are SUVs. Thus, 13% of 23000 are SUVs, thus there are .13*23000=2990 SUVs
8. If 7,650 trucks were sold in 1999, how many total vehicles were sold in 1999 by XYZ Auto Company?
Say that there are x total vehicles. There are 7650 trucks, thus 17 percent of x is 7650. Therefore, .17x=7650. We find that x=45000, so there are 45000 total vehicles
9. If 3,750 2-door sedans were sold in 1999, then how many 4-door sedans were sold in 1999 by XYZ Auto Company?
Say that there are x total vehicles. Thus, we have that 25% of x is 3750, so .25x=3750. We find that x=15000. Now, 33% of the total vehicles are 4-Door Sedans. Thus, 33% of 15000 is the number of 4-Door Sedans. Thus, we have that there are .33(15000)=4950 4-Door Sedans.
10. How much did the infant gain in the first month of life?
may-kid weighs 9lbs 4oz
april -kid weighs 8lbs 8oz
subtract,but when you borrow you are borrowing 16oz. add to 4 oz = 20 oz
20 - 8 = 12 oz
Basic Math
1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?
Let x = original cost
Let .90x = the amount the student pays (100%-10% = 90%)
Let .85(.90x) = the sales price (100%-15%=85%)
If the sales price = 306, then
.85(.90x)=306
.765x=306
x=$400
So the original cost was $400
This makes sense because $40 was taken off for the student discount, bringing the sales price to $360 and an additional 15% of 360 = $54, so $360-$54 = $306
2. If y(x-1)=z then x= www.algebra.com/?
yx-y=z
yx=z+y
x=(z+y)/y
3. Which of the following values is NOT equal to 34(58+9)?
A. 34 x 67
B. 58(34+9)
C. 34 x 58 + 34 x 9
D. 1,972 + 306
E. (9 + 58) 34
Try calculating each of these yourself: First, 34(58 + 9) = 34(67) = 2278
A. 34 x 67 = 2278
B. 58(34 + 9) = 58(43) = 2494
C. 34 x 58 + 34 x 9 = 34 x (58 + 9) = 34 * 67 = 2278
D. 1,972 + 306 = 307,972
E. (67)34 = 2278
So the answer is B and D are not equal to 34(58 + 9).
4. Two angles of a triangle measure 15° and 85 °. What is the measure for the third angle?
The sum of the measures of the angles in any triangle in the plane is 180 degrees. If two angles are 15 and 85 then their sum is 100 degrees and 180-100=80 degrees
5. If 5 ounces is equal to 140 grams, then 2 pounds of ground meat is equal to how many grams?
32 ounces (since 1 Pound = 16 ounces).
5 oz ---> 140 gr
32 oz ---> x gr
5x = 140*32
x=(32*140)/5 = 896
.
.
12. How many cubed pieces of fudge that are 3 inches on an edge can be packed into a Christmas tin that is 9 inches deep by 12 inches wide by 8 inches high with the lid still being able to be closed?
Given these dimensions, 24 cubed pieces of fudge will fit into this pan, and still allow the lid to be closed.They will be in two layers of 12 (in 3 by 4 rows). (drawing is needed)
13. Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
Let age of brother = x
Age of Sarah = 2x
According to given condition
2x - x = 15
x = 15 So, her younger brother is 15 years old.
14. Which of the following fractions is equal to 5/6?
A. 20/30
B. 15/24
C. 25/30
D. 40/54
E. 2/7
25/30
15. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile cost $8.91 per square yard?
Kitchen is 12 x 20 which is 240 sq ft.
9sq ft = 1sq yd
240sq ft/9sq ft = 26.6667 sq yds
26.6667 sq yds x $8.91 per sq yd = $237.60
16. In a writing competition, the first place winner receives ½ of the prize money. The second runner up receives ¼ of what the winner won. What was the total amount of prize money distributed if the winner receives $6,000
Winner recieves 1/2 of the prize money and he received 6,000 $. So total prize money= 12,00$
17. You are lying 120 ft away from a tree that is 50 feet tall. You look up at the top of the tree. Approximately how far is your hear from the top of the tree in a straight line?
x = sq root(120^2 + 50^2) = 130
18. A cyclist bikes x distance at 10 miles per hour and returns over the same path at 8 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?
total distance = 2x
Time on the way there is (x miles)/(10 miles/hour)= x/10 hours
Time on the way back is (x miles)/(8 miles/hour)= x/8 hours
Total time=(x/10)+(x/8)=(9x/40) hours
Average rate=(total distance)/(total time)
x is a dummy variable and will cancel out
Average rate=(2x)miles/(9x/40)hour= 80/9 mph=8.9 mph D
19. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?
19. If edging cost $2.32 per 12-inch stone, and you want a double layer of edging around your flower bed that is 6 yards by 1 yard. How much will edging you flower bed cost?
convert the flower bed from yardage to feet by multiplying by 3 (3 feet in a yard)
Length = 6*3 or 18 feet
Width = 1*3 or 3 feet
then use the formula:
Perimeter = 2*length + 2*width
Perimeter = 2(18)+2(3)
perimeter = 36+6
Perimeter = 42 feet
But you want a double layer of edging, so you will need:
2*42 feet of edging84 feet of edging.
If edging costs 2.32 per foot (12"stone = 1 foot)
84 feet*$2.32=$194.88 total
20. If 3x=6x-15 then x + 8=
3X=6X-15
3X-6X=-15
-3X=-15
X=-15/-3
X=5 ANSWER.
5+8=13 ANSWER.
21. The number of milliliters in 1 liter is
1,000
22. The cost to ride on a ferry is $5.00 per vehicle and driver with an additional cost of 50 cents per passenger. If the charge to get on the ferry is $6.50, how many people were in the vehicle?
6.50 - 5 = 1.50/50 = 3 + driver = 4.
23. What is 1/9 of 9?
(1/9) * 9 = 0.11 * 9 = 0.99 = 1
24. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
I'd say 9. Even if he gets all the green ones and all the blue ones before he gets a single red one, at 8 he will run out of greens and blues. The next one has to be red
25. Which fraction is equal to 0.20%
0.20% = 0.0020 = 20/10,000 = 1/500
26. Find the missing term in the following sequence: 4, 9, 19, __, 79
39
(double the previous number and add 1)
27. How much money did Jessica's budget allow for housing in April of 2001?
25% of 2490 = 622.5
28. What was the average amount of money that Jessica's budget allowed for clothing the first six months of 2001
(2 578 + 2 432 + 2 668 + 2 490 + 2 622 + 2 555) / 6 = 2 557.5
10% of 2 557.5 = 255.75
29. If Jessica only spent 20% instead of the 25% allotment for food in May of 2001, how much did she save?
20% of 2622 = 524.4
25% of 2622 = 655.5
655.5-524.4 = 131.10
30. Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Jon types at 1/2 pages per minute, Susan at 2/3 pages per minute and Jack in 5/6 pages per minute.
Each minute the three of them can complete 3/6 + 4/6 + 5/6 of a page = 2 pages.
That's ten minutes to complete 20 pages.
31. Of the following fractions, which is less than 2/3?
A. 7/8
B. 5/6
C. 3/4
D. 3/5
E. 5/7
Multiply numerator of first fraction and denominator of second fraction.
Multiply denominator of first fraction and numerator of second fraction.
If first product is larger, first fraction is larger.
If second product is larger, second fraction is larger
2/3 and 7/8
2 X 8 = 16
3 X 7 = 21
16 < 6 =" 12" 5 =" 15" 4 =" 8" 3 =" 9" 5 =" 10" 3 =" 9"> 9
3/5 is less than 2/3
2/3 and 5/7
2 x 7 = 14
3 x 5 = 15
14 < 3000 =" 360" 90 =" 450" perimeter =" width" feet =" width" feet =" width" feet =" width" feet =" width;" 15000=" 2250;" 2250 =" 17250;" 000 =" 0.0015" 750 =" 0.0026;" 000 =" 0.0017;" 462 =" 0.0014;" 500 =" 0.002;" 4 =" ="" 5x =" -8," 1 =" 8x" x =" -1;" 1 =" 0;" 120 =" 60;" href="http://www.testprepreview.com/modules/mathematics2.htm">Intermediate Math - www.testprepreview.com/modules/mathematics2.htm
1. Two angles of a triangle each measure 70°. What is the measure of the third angle in degrees?
180 - (70 + 70) = 40;
2. If Jack needs 2 ½ pints of cream to make a dessert. How many pints will he need to make 3 desserts?
1 dessert = 2.5 pints; 3 desserts = (3 x 2.5) = 7.5 pints;
3. A discount store takes 50% off of the retail price of a desk. For the store's holiday sale, it takes an additional 20% off of all furniture. The desk's retail price was $320. How much is the desk on sale for during the holiday sale?
Desk's Retail Price - Discount= Discount Price;
320 - 0.5*320 = DP;
320 - 160 = DP;
$160=DP
For holiday Sale:
Discount Price-Holiday discount= Holiday Sale;
160 - o.20 * 160 = HS;
160 - 32 = HS;
$128=HS, Price during Holidays;
4. Which vacation destination is most common for the students? (Look at the Chart)
Beach.
5. If 500 students attend Washington Middle School, how many are going to the mountains for vacation? (Look at the Chart)
12% of 500 = 60;
6. If a ¼ of a teaspoon is 1 ml, then how many milliliters are in 6 teaspoons?
1 teaspon = 4 ml;
6 teaspons = 24 ml;
7. Which of the following is the correct graph for x≥3 or x≤ -2? ( Look at the Chart)
Line D.
8. A scale on a map states that every ¼ of an inch represents 20 miles. If two cities are 3 ½ inches apart, how many miles are actually between the two cities?
1 inch = 80 miles;
3 1/2 inches = 3 * 80 + (1/2 * 80) = 280;
9. Michelle wants to expand her flowerbed by increasing the length and width each by 2 ft. What will the new area of the flowerbed be, if L and W represent the original dimensions of the flowerbed's length and width?
(L+2) (W+2) ;
10. Melinda's lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?
9; If 7 - she will run out of black and white socks; If 8 - she will run out of red and white socks;
11. Which of the following fractions are correctly placed from the least in value to the greatest in value?
A. 1/4, 17/25, 3/4, 11/16
B. 17/25, 1/4, 11/16, 3/4
C. 1/4, 17/25, 11/16, 3/4
D. 1/4, 17/25, 3/4, 11/16
E. 3/4, 17/25, 11/16, 1/4
A. 1 / 4 = 0.25; 17 / 25 = 0.68; 3/4 = 0.75; 11 / 16 = 0.6875;
B . 17 / 25 = 0.68; 1/4 = 0.25; 11/16 = 0.6875; 3/4 = 0.75;
C. 1/4 = 0.25; 17/25 = 0.68; 11/16 = 0.6875; 3/4 = 0.75; is the answer;
D. 0.25; 0.68; 0.75; 0.6875;
E. 0.75; 0.68; 0.6875; 0.25;
12. What is the mathematical average of the number of days in a typical year, the number of days in a week, and the number of hours in a day?
(365 + 7 + 24)/3 = 132;
13. 1.75 x 10^5=
1.75 * 100000 = 175000;
14. The electric company charges 3 cents per kilowatt-hour. George used 2800 kilowatt-hours in April, 3200 kilowatt-hours in May, and 3600 kilowatt-hours in June. What was his average cost of electricity for the 3 months
(2800 * 3 + 3200 * 3 + 3600 * 3) /3 = 9600 cents = $96;
15. On a map, 1/3 inch equals 15 miles. The distance between two towns on a map is 3 2/3 inches. How many miles are actually between the two towns?
1 inch = 15 * 3 = 45; 3 * 45 + 2/3 * 45 = 135 + 30 = 165;
16. James invested $4,000 at 5% interest per year; how long will it take him to earn $200 in simple interest?
4,000 * 0.05 = $200 per yar;
17. John pays $650 in property tax. What is the assessed value of his property if property taxes are 1.2% of assessed value?
1.2% *x = 650;
0.012 * x = 650; x = 650/0.012 = 54 166.67;
18. A lamp is marked with a sale price of $23.80, which is 15% off of the regular price. What is the regular price?
0.85 = 23.80;
1 = x; now, just cross multiply:
x = (23.80 * 1)/0.85 = 28;
19. A mattress store sells their stock for 15% off of retail. If someone pays cash, they take an additional 10% off of the discounted price. If a mattress's retail price is $750, what is the price after the store discount and the cash discount?
15% of 750 = 112.5; 750 - 112.5 = $637.5 after the store discount;637.5 - 63.75 = 573.75;
20. 85% of what number is 136?
A. 160
B. 170
C. 180
D. 190
E. 220
0.85 * x = 136; x = 136/0.85 = 160;
21. A building that is 150 ft tall casts a shadow of 20 feet long. At the same time a tree casts a shadow of 2 ft. How tall is the tree?
shadow is 20/150ths of the length of the building;
A 150 foot building casts a 20 foot shadow. This means that the sun angle causes the shadow to be 20/150 the length of the object casting it.The tree's shadow is 2 feet tall. Multiply 2 feet by 150/20 (inverting the fraction because we're going the other way) and we get 15 feet;
22. Which of the following is a true statement?
A. The product of two negative numbers is negative.
B. The product of one negative and one positive number is positive.
C. When dividing a positive number by a negative number, the results are negative.
D. When dividing a negative number by a positive number, the results are positive.
E. When dividing a negative number by a negative number the results are negative.
C.
23. What is the fractional equivalent of 12.5%?
12.5% = 0.125; (125/1000) = 1/8;
24. Change 4 3/5 to an improper fraction.
4 3/5 = 23/5;
25. The fine for a driver riding in the carpool lane without any passengers is $133. A driver is issued a bench warrant for $2,294.25, which includes a 15% fee for late charges and court costs. How many tickets has the driver not paid?
The $2294.25 that the driver is charged for fines also includes the 15% late charge. So, in order to find out how much the driver was actually charged for ticket fines, we can do the following: x=Amount driver was charged for ticket fines;
1.15x=2294.25;
x=1995;
1995/133= The total amount of tickets received= 15;
Another Solution: (how do you get the 1.15);
Divide $2294.25 by 1.15 to get the total charges without the late fee. Then divide by $133 to get the number of tickets.
2294.25/1.15=1995;
1995/133=15the 1.15 is just an easier way to calculate pre late fee amount with the percentage. if you divided $2294.25 by .15 (the 15% in decimal form) you would have to do another calculation to get the $1995. It works the other way too: If you had $1995 and wanted to know how much it was with the late fee you could multiply $1995 *.15 (=299.25) and then add $1995 + $299.25 (=2294.25) or multiply $1995 by 1.15 (=2294.25) which preforms the multiplication and addition in one step
26. Brett started a race at 6:30 A.M., and he did not cross the finish line until 1:05 P.M. How long did it take for Brett to finish the race?
6 hours and 35 minutes ;
27. What is the fraction equivalent of the shaded region in the following circle?
2/3; (Look at the Chart);
28. Multiply 2.345 x 0.023
2.34500 x 0.023 = 0.053935;
29. A men's basketball team won 24 games and lost 32. What is the ratio of games lost to the number of games played?
32/56 = 4/7;
30. Which of the following choices is equivalent to 5/6
A. 5/12
B. 10/6
C. 20/30
D. 15/24
E. 15/18
E. 15/18 = (5/6) *3;
31. Jill earns $120 for 8 hours of work. At the same pay rate, how much will she earn for 15 hours of work?
120 8
x 15
x = (120 * 15) / 8 = 225;
32. Which two years were the least number of tires sold?
B. 1998 and 2000 (Look at the Chart);
33. Which year did the store sell 1/3 more tires than the year before?
1999; (Look at the Chart);
34. What was the average number of tires sold by the store from 1998 to 2001?
9,375;
35. A salesman sold 20 cars in the month of July, and 40 cars the month of August. What is the percent increase in the number of cars the salesman sold?
100%;
36. If one side of a square is 5 units, what is the area of the square?
25;
37. If 8x + 5 = 21, then 3 x + 4 =
8x + 5 = 21; x = (21 - 5)/8 = 2; 3*2 + 4 = 10;
38. In triangle ABC, AB=BC and (C's measure is 65°.) What is the measure of angle B?
The geometry concept being test here is:
"If a triangle has two sides that are equal, the two angles opposite those sides are also equal."
If AB = BC, then the angles opposite those two sides are equal, namely angle C and angle A.
Since angle C is 65 degrees, angle A is also 65 degrees.
Angle B is then 180 - 65 - 65 = 50;
39. If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?
(8 + 12 + 15 + 21 + x + 11)/ 6 = 17;
8 + 12 + 15 + 21 + x + 11 = 102;
x = 102 - (8 + 12 + 15 + 21 + 11);
x = 102 - 67;
x = 35;
40. Sarah has a 20 dollar bill and a 5 dollar bill. If she purchases two items, one for $11.23 and the other for $8.32, then how much money does she have left over?
(20 + 5) - (11.23 + 8.32) = 25 - 19.55 = 5.45;
Advanced Math - www.testprepreview.com/modules/mathematics3.htm
1. How long will Lucy have to wait before for her $2,500 invested at 6% earns $600 in simple interest?
the simple interest equation is i=prt I is interest is principal or original amount and r is rate in a decimal. substitute it in ---> 600 = 2500*0.06*t ---> 600 = 150t ---> 4=T ---> so 4 months/years..however long it takes to get the 6% probably annually so 4 years;
2. Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
It's a trick question. If grace wants one of each color, she will want 3 jelly beans. So, if she takes out 16-3=13 jelly beans, she will have in her bag, 3 jelly beans;
3. If r = 5 z then 15 z = 3 y, then r =
15 * r/5 = 3y; 3r = 3y; r = 3y/3 = y;
4. What is 35% of a number if 12 is 15% of a number?
15% of X = 12 therefore X = 80 so 35% of X = 28;
Another Solution:
To solve this, we need to first calculate what the unknown number is. We know that 12 is equivalent to 15 % of the number. Let the unknown number = X
This means that 12 is to X as 15 is to 100
12/x = 15/100
X = (12 × 100)/15
X = 80
So the number is 80. Now we need to find the 35 % of that number. This will be done is follows: 35 . × 80 = 28;
5. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price?
1600/x = 80/100, because you know 1600 is 80% of the total (x);
Cross-multiply: 160000 / 80x;
Divide 16000 by 80 = 2000 which is x;
6. A car dealer sells a SUV for $39,000, which represents a 25% profit over the cost. What was the cost of the SUV to the dealer
Price of SUV = $39,000;
Cost of SUV:
[25 (C)]/100 + C = 39,000;
(25C + 100C)/100 = 39,000;
125C = 39,000(100);
125C = 39, 00, 000;
C = 39,00,000/125;
C = $31200;
7. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for?
10% 0f 49000 = 4900;
20% 0f 49000 = 9800;
49000 - 9800 = 39200;
8. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
x(1/4 + 1/2 + 1/6) = 1; Lowest common denominator (LCD = 12);
11x = 12;
x = 12/11 = 1 1/12 = 1.09 days;
9. Find 0.12 ÷12;
0.12 ÷ 12 = 12/1200 = 0.01;
10. Divide x^5 by x^2;
x^5 - X^2 = x^(5-2) = x^3;
11. Which of the following numbers could be described in the following way: an integer that is a natural, rational and whole number?
1;
12. Find the mode of the following list of numbers: 2, 4, 6, 4, 8, 2, 9, 4, 3, 8
Mode which is the most frequently occurring number in a group of numbers. So that,in this list of numbers, the mode is 4;
13. In the fraction 3/x, x may not be substituted by which of the following sets?
A. {1, 2, 4}
B. {-2,-3,-4}
C. {1, 3, 7}
D. {0, 10, 20}
E. {1.8, 4.3}
D. {0, 10, 20}----------Ideas: When x = 0; 3/x is undefined;
14. Sarah needs to make a cake and some cookies. The cake requires 3/8 cup of sugar and the cookies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?
She needs 3/8 + 3/5 = 39/40 cups of sugar.
She has 15/16th cup of sugar.
as 39/40>15/16
she requires: 39/40 - 15/16 cups o sugar = 0.0375 ~ 3/80 of a cup of sugar;
15. At a company fish fry, 1/2 in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?
One half of X are employees.One third of X are employee's spouses.
We add one half PLUS one third:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Then we subtract that fraction from one whole, or 1,to see what fraction is left. That is, we say
1 minus 5/6 which is 1 - 5/6
Now write 1 as 6/6
6/6 - 5/6
We get 1/6
So 1/6 is left. Now we need to make that intoa percent by multiplying it by 100 and tacking on a "%"
1/6 × 100
1/6 × 100/1
50/3
16 2/3 %
So 16 2/3 % of the people in attendance are neither employees nor employee's spouses. Now let's check:
1/2 are employees. That's 50%
1/3 are employee's spouses. That's 33 1/3%;
15 2/3 % are neither employees nor employee's spouses;
Add them up:
50 %
33 1/3 %
16 2/3 %
--------
99 3/3 %
And 99 3/3% = 100;
16. In a college, some courses contribute more towards an overall GPA than other courses. For example, a science class is worth 4 points; mathematics is worth 3 points; History is worth 2 points; and English is worth 3 points. The values of the grade letters are as follows, A= 4, B=3, C=2, D=1, F=0. What is the GPA of a student who made a “C” in Trigonometry, a “B” in American History, an “A” in Botany, and a “B” in Microbiology?
Trignometry "C" = 2 (category Mathematics worth 3 points)
American History "B" = 3 (category History worth 2 points)
Botany "A" = 4 (category Science worth 4 points)
Microbiology "B" = 3 (category Science worth 4 points)
1) Multiple grades with category points and add them all as shown below:
2*3+3*2+4*4+3*4 = 6+6+16+12 = 40
2) Add all the category points as shown below:
3+2+4+4 = 13
Now to get the GPA, divide the answer from step 1 with answer from step 2 as shown:
GPA = 40/13 = 3.08;
17. There are 8 ounces in a ½ pound. How many ounces are in 7 3/4 lbs
8 oz = 1/2 a pound
16 oz = 1 pound
to calculate how many ounces there are in 7 3/4 pounds:
16 oz x 7 = 112 oz
3/4 of 16oz = 12 oz
112 oz + 12 oz = 124 ounces;
18. If the value of x and y in the fraction XZ/Y are both tripled, how does the value of the fraction change?
(3X)Z / (3Y)
Cancel the 3s to get:
XZ/Y
which is just what we started with, so the answer is:
E. remains the same;
19. What is the next number in the following pattern? 1, 1/2, 1/4, 1/8, ___
1/16;
20. Of the following units which would be more likely used to measure the amount of water in a bathtub?
liters;
21. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following?
There are 12 inches in a foot, so:
.17 feet x 12 = 2.04 inches; (2 3/4 inch lipstick);
22. Which of the following fractions is the equivalent of 0.5%?
Best Answer - Chosen by Voters
to change percent into fraction, take out the percent symbol and divide it by 100.
so: .5% becomes .5/100
Now, move the decimal place to the right in the numerator and the denominator until you have rid the fraction of decimals.
so: .5/100 becomes 5/1000
The number of times you move the decimal place in the numerator is equal to the number of zeros you add in the denominator.
then reduce: 5/1000 = 1/200(divide both numerator and denominator by common factor 5);
23. In the graph below, no axes or origin is shown. If point B's coordinates are (10,3), which of the following coordinates would most likely be A's?
(6, 8) ;
24. Over the course of a week, Fred spent $28.49 on lunch. What was the average cost per day?
$28.49/7=$4.07;
25. Of the following units, which would be most likely to measure the amount of sugar needed in a recipe for 2 dozen cookies?
cups;
26. Jim has 5 pieces of string. He needs to choose the piece that will be able to go around his 36-inch waist. His belt broke, and his pants are falling down. The piece needs to be at least 4 inches longer than his waist so he can tie a knot in it, but it cannot be more that 6 inches longer so that the ends will not show from under his shirt. Which of the following pieces of string will work the best?
36" = 3 x 12 = 3 feet
4" = 4/12 foot = 1/3 foot
6" = 6/12 foot = 1/2 foot
Want something between:
36" + 4" = 3 1/3 feet
36" + 6" = 3 1/2 feet
3 4/5 > 3 ½
3 2/3 > 3 ½
3 3/8 < -------- bingo
3 1/4 < 3 1/3
2 1/2 < 3 1/3;
27. After purchasing a flat screen television for $750, John realizes that he got a great deal on it and wishes to sell it for a 15% profit. What should his asking price be for the television?
Buying Price + 15% mark-up = Selling Price;
750 + (750 x 0.15) = 750 + 112.50 = 862.50;
28.If 300 jellybeans cost you x dollars. How many jellybeans can you purchase for 50 cents at the same rate?
Doing this as similar ratios:
300 ... n
----- = ---
..x .....0.50
Cross multiplying you get:
150 = nx
n = 150/x
It depends on x, but you can buy 150/x jellybeans for 0.50.
For example if you could buy 300 jellybeans for 5 dollars, you could buy (150/5) = 30 jellybeans for 0.50.
You can buy 30 jelly beans for $0.50;
29. If 6 is 24% of a number, what is 40% of the same number?
6/24 = x/40
x = (6*40)/24 = 240/24 = 10;
Another Solution:
0.24x = 6; x = 600/24 = 25;
0.4x = N; N = 0.4*25 = 10;
30. Lee worked 22 hours this week and made $132. If she works 15 hours next week at the same pay rate, how much will she make?
Lee earns $132/ 22 = $6 per hour
for 15 hours = $6 * 15 = $90;
31. The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?
7 more cars sold. So 7/12= 58.3% increase
32. If 8x + 5x + 2x + 4x = 114, the 5x + 3 =
x(8+5+2+4) = 114; x = 114/19 = 6;
5*6 + 3 =33;
33. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
Plane A travels 2 hours @ 150 MPH which is 300 miles.
Plane B travels 2 hours @ 200 MPH which is 400 miles.
Since they're travelling at 90° with respect to each other, the difference separating them is:
Sqrt(300^2+400^2) or 500 miles;
34. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?
1 Yard = 3 Feet
L yards = 3L feet
W yards = 3W feet
Area = 3L*3W = 9LW
The cost was 0.1 * 9LW = 0.9*LW
35. Find 8.23 x 10^9
8230000000
37. Which of the following has the least value?
A. 0.27
B. 1/4
C. 3/8
D. 2/11
E. 11%
E . 11% = 0.11;
38. How many boys attended the 1995 convention? (See the graph)
50% of 716 = 358;
39. Which year did the same number of boys and girls attend the conference?
1995;
40. Which two years did the least number of boys attend the convention?
1995 and 1996 ;
Measurement - www.testprepreview.com/modules/measurement.htm
1. What will it cost to carpet a room with indoor/outdoor carpet if the room is 10 feet wide and 12 feet long? The carpet costs 12.51 per square yard.
Total cost = (10/3) x (12/3) x 12.51 = $166.80;
2. If the perimeter of a rectangular house is 44 yards, and the length is 36 feet, what is the width of the house?
Length = 36 feet = 36(1/3 yard) = 12 yards
Perimeter = 2(Length + Width)
P = 2(L + W)
44 = 2(12 + W)
44 = 24 + 2W
44 - 24 = 2W
20 = 2W
10 = W;
3. What is the volume of the following cylinder? (Look at the Graph)
www.testprepreview.com/modules/measurement.htm
The volume of a cylinder is V=PI*r^2*h
V = PI*(3cm)^2*(8cm)
V = 3.14*72=226.08;
4. What is the volume of a cube whose width is 5 inches?
The volume of a cube is the cube of the edge length. (5 in)^3 = 5^3 in^3 = 125 in^3;
5. Sally has three pieces of material. The first piece is 1 yd. 2 ft. 6 in. long, the second piece is 2 yd. 1 ft. 5 in long, and the third piece is 4 yd. 2ft. 8in long. How much material does Sally have?
1 Yard = 3 ft;
1 ft = 12 in;
If you add up the pieces you'll get:
7 yrd, 5 ft, 19 in ; (19in = 1ft,7in);
7 yrd, 6 ft, 7 in ; (6ft = 2yrd);
9 yrd,7 in;
6. A can's diameter is 3 inches, and its height is 8 inches. What is the volume of the can?
pi *( r squared )* height;
3.14 * (1.5^2) * 8 = 56.52;
7. If the area of a square flowerbed is 16 square feet, then how many feet is the perimeter of the flowerbed?
16 square feet = 4 feet on each side. (4 feet * 4 feet = 16 square feet.)
Then just add up the sides: 4 feet + 4 feet + 4 feet + 4 feet = 16 feet.
It's just a coincidence that both answers are 16;
if the area of the flowerbed was 9 square feet, the perimeter would be 12 feet;
8. Of the following units which would be more likely used to measure the amount of water in a bathtub?
liters;
9. If a match box is 0.17 feet long, what is its length in inches the most closely comparable to the following?
There are 12 inches in a foot, so:
.17 feet x 12 = 2.04 inches (2 3/16 inch staple remover)
10. What is the cost in dollars to steam clean a room W yards wide and L yards long it the steam cleaners charge 10 cents per square foot?
Multiply W times L to get total square yards. Then divide by 12 to get total square feet, then multiply by 10 to get total cost:
W*L ---> yds^2;
WL/12 ---> ft^2;
WL/12 * 10 = 0.83WL ~ 0.9WL;
11. Once inch equals 2.54 cm, How many centimeters tall is a 76- inch man?
76 * 2.54 = 193.04 sm;
12. A room measures 11 ft x 12 ft x 9 ft. What is the volume?
11 * 12 * 9 = 1 188;
13. A vitamin's expiration date has passed. It was supposed to contain 500 mg of Calcium, but it has lost 325 mg of Calcium. How many mg of Calcium are left?
500 - 325 = 175 mg;
14. You have orders to give a patient 20 mg of a certain medication. The medication is stored 4 mg per 5-mL dose. How many milliliters will need to be given?
This is cross multiplication;
20mg/x = 4mg/5ml; 4x = 20*5; x = (20*5)/4 = 25ml;
If each teaspoonful (5ml) contains 4mg then 4x=20...... x = 5!
5 teaspoonfuls or 25ml would bring you to your dose;
15. You need exactly a 1680 ft^3 aquarium for your fish. At the pet store you see four choices of aquariums, but the volume is not listed. The length, width, and height are listed on the box. Which of the following aquariums would fit your needs?
A. 12 ft x 12 ft x 12 ft
B. 13 ft x 15 ft x 16 ft
C. 14 ft x 20 ft x 6 ft
D. 15 ft x 16 ft x 12 ft
E. 15 ft x 12 ft x 12 ft
A= 1728
B= 3120
C= 1680; 14 x 20 x 6 = 1680;
16. One slice of bread is 80 calorie. Approximately how many calories are in 2 ½ slices of bread?
2.5 * 80 = 200;
Nouns - www.testprepreview.com/modules/nouns.htm
Percents and Ratios
1. If a discount of 20% off the retail price of a desk saves Mark $45, how much did he pay for the desk?
Algebra..you know that $45 is 20% of the original price, so set an equality...

$45/X = 20/100 where X is the original price;
x= (100*45)/20;
x= 225 - 45 = $180;
2. A customer pays $1,100 in state taxes on a newly purchased car. What is the value of the car if state taxes are 8.9% of the value?
.089X=1100;
X=1100/.089;
X=$12,359.55 PRICE OF THE CAR;
3. How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest?
Interest = principle * interest rate * time,
then:
210 = 3000 * 0.07 * time
or:
time = 210/(3000 * 0.07) = 210/210 = 1 year;
4. Sabrina's boss states that she will increase Sabrina's salary from $12,000 to $14,000 per year if she enrolls in business courses at a local community college. What percent increase in salary will result from Sabrina taking the business courses?
Use this formula: increase/original price x 100;
So, 14,000 - 12,000 = 2,000 increase;
So, 2,000/12,000 = .167;
So, .167 x 100 = 16.7%;
5. 35% of what number is 70?
.35 x = 70;
x = 70/.35 = 200;
6. What number is 5% of 2000?
10% = 200;
5% = 100;
7. What percent of 90 is 27?
Divide 27 by 90 to get .3 then u move the decimal 2 places. 27 is 30% of 90;
8. Jim works for $15.50 per hour for a health care facility. He is supposed to get a 75 cent per hour raise at one year of service. What will his percent increase in hourly pay be?
You simply have to find what percent 75 cents is out of $15.50. Make a proportion; remember that percentages are out of a hundred:
0.75/15.5 = x/100 (cross multiply)
75 = 15.5x (divide both sides by 15.5)
4.84 = x;
9. If 45 is 120% of a number, what is 80% of the same number
x times 1.20 = 45
x = 45/1.20
x = 37.5
80% of 37.5 is:
37.5 x .80 = 30 <===your answer;
10. How long will Lucy have to wait before her $2,500 invested at 6% earns $600 in simple interest?
the simple interest equation is
i=prt
I is interest is principal or original amount and
r is rate in a decimal.
substitute it in --->
600 = 2500*0.06*t --->
600 = 150t --->
4=T ---> so 4 months/years..however long it takes to get the 6% probably annually so 4 years
11. What is 35% of a number if 12 is 15% of a number?
15% of X = 12 therefore X = 80 so 35% of X = 28;
12. A computer is on sale for $1600, which is a 20% discount off the regular price. What is the regular price?
1600/x = 80/100, because you know 1600 is 80% of the total (x)
Cross-multiply: 160000 / 80x
Divide 16000 by 80 = 2000 which is x;
13. A car dealer sells a SUV for $39,000, which represents a 25% markup over the dealer's cost. What was the cost of the SUV to the dealer?
Dealer_cost*125% = $39,000
dealer_cost = $39,000/125% = $39,000/1.25 = $31,200;
14. After having to pay increased income taxes this year, Edmond has to sell his BMW. Edmond bought the car for $49,000, but he sold it for a 20% loss. What did Edmond sell the car for?
10% = 4900;
20% = 9800;
49000 - 9800 =$39200;
15. At a company fish fry, ½ in attendance are employees. Employees' spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are not employees or employee spouses?
the percentage of people who are NOT employees or employee spouses, is 1-(1/3+1/2)
1/3+1/2 converting to common denominator, is 2/6+3/6 =5/6. Therefore there is 1/6 people who are not employees or spouses. 1/6 is 16.7%;
16. If 6 is 24% of a number, what is 40% of the same number?
6/24 = x/40;
x=(40*6)/24=10;
17. 25% of 400 =
10% 0f 400=40;
5% of 400=20
25% of 400 =100;
18. 22% of $900 =
10% of 900 = 90;
2% of 900 = 18;
22% of 900 = 198;
19. Which of the following percentages is equal to 0.45?
A. 0.045%
B. 0.45%
C. 4.5%
D. 45%
E. 0.0045%
D. 45%;
20. Which of these percentages equals 1.25?
A. 0.125%
B. 12.5%
C. 125%
D. 1250%
E. 1250.5%
C. 125%
Basic Reading Comprehension - www.testprepreview.com/modules/reading1.htm
Reading for the Main Idea - www.testprepreview.com/modules/readingmainidea.htm
Advanced Reading Comprehension - www.testprepreview.com/modules/readingtest2.htm
Reading Vocabulary - www.testprepreview.com/modules/readingvocabulary.htm
Sentence Correction - www.testprepreview.com/modules/sentencecorrectiont.htm
Sentence Flow - www.testprepreview.com/modules/sentenceflowt.htm
Usage Test 1 - www.testprepreview.com/modules/usagetest.htm
Usage Test 2 - www.testprepreview.com/modules/usagetest2t.htm
Usage Test 3 - www.testprepreview.com/modules/usage_test_3.htm
Verbs - www.testprepreview.com/modules/verbs.htm
Writing Section 1 -www.testprepreview.com/modules/writing1section1.htm
Writing Section 2 - www.testprepreview.com/modules/writing1section2.htm
Self Improvement Directory - www.testprepreview.com/selfimprovementdirectory.htm