PICAT 1 FINAL PAPER 2026 FULL QUESTIONS
AND SOLUTIONS ALREADY GRADED A+
● A barista averages making 16 coffees per hour. At this rate, how many
hours will it take until she's made 1,200 coffees? Answer: 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 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? Answer: 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
● 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? Answer:
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? Answer: 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? Answer: 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%
AND SOLUTIONS ALREADY GRADED A+
● A barista averages making 16 coffees per hour. At this rate, how many
hours will it take until she's made 1,200 coffees? Answer: 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 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? Answer: 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
● 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? Answer:
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? Answer: 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? Answer: 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%
