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ASVAB - Arithmetic Reasoning/Mathematics Knowledge TestExam/ Actual Exam Questions with Correct Detailed Answers
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From 1980 through 1990, the population of Country X increased by 100%. From 1990 to
2000, The population increased by 50%. What was the continued increase for the
period 1980-2000?
(a) 150%
(b) 166 2/3%
(c) 175%
(d) 200% - ANSWER - (d) 200%
Be careful with combined percent increase. You cannot just add the two percents,
because they're percents of different bases. In this instance, the 100% increase is
based on the 1980 population, but the 50% increase is based on the larger 1990
population. If you just added 100% and 50% to get 150%, you would have chosen the
wrong answer.
The best way to do a problem like this one is to pick a number for the original whole and
just see what happens. The best number to pick here is 100. (That may be a small
number for the population of a country, but reality is not important - all that matters is the
math.)
If the 1990 population was 100, then a 100% increase would put the 1990 population at
200. And a 50% increase over 200 would be 200 + 100 = 300.
Since the population went from 100 to 300, that's a percent increase of 200%.
pg. 1
,300 - 100/100 x 100% = 200/100 X 100% = 200%
If a man earns $200 for his first 40 hours of work in a week and then is paid one-and-
one-half times his regular rate for any additional hours, how many hours must be work
to make $230 in a week?
(a) 43
(b) 44
(c) 45
(d)46 - ANSWER - (b) 44
To learn the man's overtime rate of pay, first figure out his regular rate of pay. Divide the
amount of money made, $200, by the time it took to make it, 40 hours.
$ hours = $5 per hour. That is the normal rate. The man is paid 1 1/2 times his
regular rate during overtime, so when working more than 40 hours he makes 3/2 x $5
per hour = $7.50 per hour. Now figure out how long it takes the man to make $230. It
takes him 40 hours to make the first $200. The last $30 are made at the overtime rate.
Since it takes the man one hour to make $7.50 at this rate, you can figure out the
number of extra hours by dividing $30 by $7.50 per hour. $30 / $7.50 per hour = 4
hours. The total time needed is 40 hours plus 4 hours, or 44 hours.
If 50% of (x) is 150, what is 75% of (x)?
(a) 225
(b) 250
(c) 275
(d) 300 - ANSWER - (a) 225
The calculations aren't too bad on this one. The most important thing to keep in mind is
that you're solving for 75% of (x) and not for (x) itself. First, you are told that 50% of (x)
is 150. That means that half of (x) is 150, and that (x) is 300. So 75% of (x) = 0.75 x 300
= 225.
pg. 2
,The total fare for two adults and three children on an excursion boat is $14. If each
child's fare is one half of each adult's fare, what is the adult fare?
(a) $2.00
(b) $3.00
(c) $3.50
(d) $4.00 - ANSWER - (d) $4.00
This question where Backsolving (plugging in an answer choice to see if it's correct) can
save you a lot of time. Let's start with choice (b) and see if it works. If (b) is correct, an
adult's ticket would cost $3.00, and a child's ticket would cost $1.50. The total fare
you're asked for is for two adults and three children. If an adult's fare was $3.00, that
total fare would be 2($3.00) + 3($1.50) = $6.00 + $4.50 = $10.50. That's too low since
the question states that the total fare is $14.00.
Now see what happens if an adult fare was more expensive. If (d) was correct, an
adult's ticket would cost $4.00 and a child's ticket would cost $2.00. The total fare would
equal
2($4.00) + 3($2.00) = $8.00 + $6.00 = $14.00.
That's the total fare you're looking for, so (d) is correct.
What is the prime factorization of 140?
(a) 2 x 70
(b) 2 x 3 x 5 x 7
(c) 2 x 2 x 5 x 7
(d) 2 x 2 x 2 x 5 x 7 - ANSWER - (c) 2 x 2 x 5 x 7
To find the prime factorization of a number, find one prime that will go into the number
(here 2 is a good place to start). Express the number as that prime multiplied by some
other number.
pg. 3
, 140 = 2 x 70
Then keep breaking down the larger factor until you are left with only prime numbers.
140 = 2 x 2 x 35
140 = 2 x 2 x 5 x 7
A painter charges $12 an hour while his son charges $6 an hour. If the father and son
worked the same amount of time together on a job, how many hours did each of them
work if their combined charge for their labor was $108?
(a) 6
(b) 9
(c) 12
(d) 18 - ANSWER - (a) 6
John bought a camera on sale that normally costs $160. If the price was reduced 20%
during the sale, what was the sale price of the camera?
(a) $120
(b) $124
(c) $128
(d) $140 - ANSWER - (c) $128
This question asks you to determine the sale price of a camera that normally sells at
$160 and is discounted 20%. To solve, determine what 20% of $160 equals. Rewrite
20% as a decimal.
20% = 0.20. So 20% of $160 = 0.20 x $160 = $32.
pg. 4
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