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ARITHMETIC REASONING PICAT EXAM STUDY GUIDE
EXAM WITH CORRECT QUESTIONS AND CORRECTRY
ANALYZED ANSWERS (ACTUAL EXAM) ALREADY
GRADED A+ LATEST 2025 – 2026
Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger
than their brother David. If the sum of their ages is 62, how old is Michelle? -
...(ANSWERS)....Answer: 18
Let: x = Michelle's age
x + 6 = Karen's age
x + 2 = David's age
State the problem in an equation:
x + x + 6 + x + 2 = 62
3x + 8 = 62
3x + 8 - 8 = 62 - 8
3x = 54
3x /(the slash means divide) 3 =
x = 18
This is Michelle's age.
A barista averages making 16 coffees per hour. At this rate, how many hours will
it take until she's made 1,200 coffees? - ...(ANSWERS)....Answer: 75 hours
To solve the problem, simply set up a proportion using what you know and using x
for what you don't know:
16 coffees / 1 hour = 1200 coffees / x hours
, 2
Cross-multiply, and you have:
16x = 1200
Divide both sides by 16 to isolate x and you have:
x = 75
You may be able to set up this problem in your head by just dividing 1200 by 16.
You will get the same answer, but it's important to know how to use a proportion
since these problems are not always this simple. Using a proportion also helps you
to reason why you need to do the final operation and this will help on some of the
newer tests where you may be asked the reason for an answer.
Camille uses a 20% off coupon when buying a sweater that costs $47.99. If she
also pays 6% sales tax on the purchase, how much does she pay? -
...(ANSWERS)....Answer: $40.69
First, compute the price of the sweater after the discount:
Discounted price of the sweater:
(100% - 20%)($47.99) = 80%($47.99)
.80(47.99) = $38.39
Second, add the sales tax:
Total amount paid:
$38.39 + $38.39(6%)
38.39 + 38.39(6%)
38.39 + 2.30 = $40.69
, 3
At Michael's smoothie shop smoothies cost $3.50 during the week and $4.00 on
weekends. If Jonathan bought a smoothie every day except Saturday how much
did he spend on smoothies that week? - ...(ANSWERS)....Answer: $21.50
Compute the total amount paid for smoothies bought from Monday to Friday (5
days) at $3.50 / smoothie:
5 x $3.50 = $17.50
Add this to the amount paid for the smoothie bought on Sunday at $4.00 /
smoothie:
$17.50 + $4.00 = $21.50
In a classroom of 32 students, 14 are male. What percentage of the class is
female? - ...(ANSWERS)....Answer: 56%
First, solve how many females are in the class:
Number of females = 32 − 14 = 18
To compute for the percentage of females in the class:
Percentage = ()(100%) = 56.25% = 56%
Cory's average score after 8 tests is 91%. If he gets a 78% on his 9th test, what will
his new average be? - ...(ANSWERS)....Answer: 89.6%
The formula for average is:
sum of all values given / number of all values given
For the 8 tests, the average is presented as 91. While we don't know the exact
score on each test, you have to use the information that is given. Since the
average of all previous scores is 91, assign the score of 91 to each of the 8
previous tests.
ARITHMETIC REASONING PICAT EXAM STUDY GUIDE
EXAM WITH CORRECT QUESTIONS AND CORRECTRY
ANALYZED ANSWERS (ACTUAL EXAM) ALREADY
GRADED A+ LATEST 2025 – 2026
Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger
than their brother David. If the sum of their ages is 62, how old is Michelle? -
...(ANSWERS)....Answer: 18
Let: x = Michelle's age
x + 6 = Karen's age
x + 2 = David's age
State the problem in an equation:
x + x + 6 + x + 2 = 62
3x + 8 = 62
3x + 8 - 8 = 62 - 8
3x = 54
3x /(the slash means divide) 3 =
x = 18
This is Michelle's age.
A barista averages making 16 coffees per hour. At this rate, how many hours will
it take until she's made 1,200 coffees? - ...(ANSWERS)....Answer: 75 hours
To solve the problem, simply set up a proportion using what you know and using x
for what you don't know:
16 coffees / 1 hour = 1200 coffees / x hours
, 2
Cross-multiply, and you have:
16x = 1200
Divide both sides by 16 to isolate x and you have:
x = 75
You may be able to set up this problem in your head by just dividing 1200 by 16.
You will get the same answer, but it's important to know how to use a proportion
since these problems are not always this simple. Using a proportion also helps you
to reason why you need to do the final operation and this will help on some of the
newer tests where you may be asked the reason for an answer.
Camille uses a 20% off coupon when buying a sweater that costs $47.99. If she
also pays 6% sales tax on the purchase, how much does she pay? -
...(ANSWERS)....Answer: $40.69
First, compute the price of the sweater after the discount:
Discounted price of the sweater:
(100% - 20%)($47.99) = 80%($47.99)
.80(47.99) = $38.39
Second, add the sales tax:
Total amount paid:
$38.39 + $38.39(6%)
38.39 + 38.39(6%)
38.39 + 2.30 = $40.69
, 3
At Michael's smoothie shop smoothies cost $3.50 during the week and $4.00 on
weekends. If Jonathan bought a smoothie every day except Saturday how much
did he spend on smoothies that week? - ...(ANSWERS)....Answer: $21.50
Compute the total amount paid for smoothies bought from Monday to Friday (5
days) at $3.50 / smoothie:
5 x $3.50 = $17.50
Add this to the amount paid for the smoothie bought on Sunday at $4.00 /
smoothie:
$17.50 + $4.00 = $21.50
In a classroom of 32 students, 14 are male. What percentage of the class is
female? - ...(ANSWERS)....Answer: 56%
First, solve how many females are in the class:
Number of females = 32 − 14 = 18
To compute for the percentage of females in the class:
Percentage = ()(100%) = 56.25% = 56%
Cory's average score after 8 tests is 91%. If he gets a 78% on his 9th test, what will
his new average be? - ...(ANSWERS)....Answer: 89.6%
The formula for average is:
sum of all values given / number of all values given
For the 8 tests, the average is presented as 91. While we don't know the exact
score on each test, you have to use the information that is given. Since the
average of all previous scores is 91, assign the score of 91 to each of the 8
previous tests.
