PICAT EXAM STUDY GUIDE
ARITHMETIC REASONING
EXAM WITH CORRECT
ANSWERS 2025
Karen is 6 years older than her sister Michelle, and Michelle is 2 years
their
youngerbrother
thanDavid. If the sum of their ages is 62, how old is ( corre
Michelle? answers ) Answer: 18 ct
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 =
54barista
A / 3 x =averages
18 making 16 coffees per hour. At this rate, how many hours
Thisitistake
will Michelle's age.made 1,200 coffees?
until she's ( correct 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 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
pays 6% forsales
an answer.
tax on the purchase, how much does ( correct
she pay? Answer: $40.69 answers )
Camille
First, uses a the
compute 20%price
off coupon when buying
of the sweater a sweater that costs $47.99. If
after the
she also Discounted price of the sweater:
discount:
(100% - 20%)($47.99) = 80%($47.99)
.80(47.99) = $38.39
GRADED
A+
, Second, add the sales tax:
Total amount paid:
$38.39 + $38.39(6%)
38.39 + 38.39(6%)
38.39 + 2.30 = $40.69
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? ( correct
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? ( correct 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? ( correct 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.
This gives us 8 tests with a score of 91
each. 91 x 8 = 728
To get new average after the 9th test,
use the same formula:
728 + = = 89.5
Since there are 2 answer choices that are very close to this, and you don't
know which way the .5 will be rounded, extend the division another place
by adding a 0 to the dividend, then divide.
You find that the answer is now 89.55, which rounds up to 89.6. Therefore,
you now know that 89.5 would not be correct. Always extend the decimal
places when 2 answer choices are as close as these and you don't know
which one is correct.
89.6%
Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her
GRADED
candy away, which amount of candy could have been the amount she
A+
distributed? ( correct
answers ) Answer: 161
The problem states that all of Julie's friends received 7 pieces each. There is
no mention about the number of friends Julie gave the candies to. But no
matter how many
ARITHMETIC REASONING
EXAM WITH CORRECT
ANSWERS 2025
Karen is 6 years older than her sister Michelle, and Michelle is 2 years
their
youngerbrother
thanDavid. If the sum of their ages is 62, how old is ( corre
Michelle? answers ) Answer: 18 ct
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 =
54barista
A / 3 x =averages
18 making 16 coffees per hour. At this rate, how many hours
Thisitistake
will Michelle's age.made 1,200 coffees?
until she's ( correct 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 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
pays 6% forsales
an answer.
tax on the purchase, how much does ( correct
she pay? Answer: $40.69 answers )
Camille
First, uses a the
compute 20%price
off coupon when buying
of the sweater a sweater that costs $47.99. If
after the
she also Discounted price of the sweater:
discount:
(100% - 20%)($47.99) = 80%($47.99)
.80(47.99) = $38.39
GRADED
A+
, Second, add the sales tax:
Total amount paid:
$38.39 + $38.39(6%)
38.39 + 38.39(6%)
38.39 + 2.30 = $40.69
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? ( correct
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? ( correct 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? ( correct 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.
This gives us 8 tests with a score of 91
each. 91 x 8 = 728
To get new average after the 9th test,
use the same formula:
728 + = = 89.5
Since there are 2 answer choices that are very close to this, and you don't
know which way the .5 will be rounded, extend the division another place
by adding a 0 to the dividend, then divide.
You find that the answer is now 89.55, which rounds up to 89.6. Therefore,
you now know that 89.5 would not be correct. Always extend the decimal
places when 2 answer choices are as close as these and you don't know
which one is correct.
89.6%
Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her
GRADED
candy away, which amount of candy could have been the amount she
A+
distributed? ( correct
answers ) Answer: 161
The problem states that all of Julie's friends received 7 pieces each. There is
no mention about the number of friends Julie gave the candies to. But no
matter how many
