ISEE Lower Level Quantitative Reasoning Quiz: Variables In Context

What this quiz covers

This quiz focuses on Variables In Context, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Quantitative Reasoning.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. f - 50 + n + 75 (correct answer)
2. f + 50 + n - 75
3. f + n - 50 + 75
4. (f + n) - 50 + 75

Explanation: The new number of fiction books is $f - 50$. The new number of non-fiction books is $n + 75$. The new total number of books is the sum of these two amounts, which is $(f - 50) + (n + 75)$. By the commutative property of addition, this is the same as $f - 50 + n + 75$. The other options incorrectly group the operations.

Question 2

1. g + 4 + 3
2. 4(g + 3)
3. g/4 + 3
4. 4g + 3 (correct answer)

Explanation: To find the total number of quarts, we must first convert the gallons to quarts. Since there are 4 quarts in a gallon, g gallons is equal to $4 \times g$, or $4g$ quarts. Then, we add the 3 additional quarts. The correct expression for the total number of quarts is $4g + 3$.

Question 3

1. The total cost of the job in dollars.
2. The flat fee for any job in dollars.
3. The number of hours the job takes.
4. The cost per hour of work in dollars. (correct answer)

Explanation: In the expression $100 + 30h$, the total cost is calculated by adding a fixed amount (100) to an amount that changes with the number of hours worked. The term $30h$ means that for every hour h, the cost increases by $30. Therefore, 30 represents the cost per hour, or the hourly rate.

Question 4

1. p = 7s + 4 (correct answer)
2. p = 4s + 7
3. p = 7s - 4
4. p = 7(s + 4)

Explanation: The total number of pencils, p, must account for the pencils given to the students and the pencils left over. If each of the 7 students receives s pencils, the total number of pencils given out is $7 \times s$, or $7s$. Since there are 4 pencils left over, the original total p must be the sum of those given out and those left over: $p = 7s + 4$.

Question 5

1. T = 12(8) + 4s (correct answer)
2. T = 12s + 8(4)
3. T = 12 + 8 + 4 + s
4. T = (12 + 4)s + 8

Explanation: The total number of chairs, T, is the sum of the chairs at the large tables and the chairs at the small tables. The number of chairs at the 12 large tables is $12 \times 8$. The number of chairs at the s small tables is $4 \times s$, or $4s$. Adding these together gives the total: $T = 12(8) + 4s$.

Question 6

1. c - 5 + 3
2. c + 5 - 3
3. c - (5 + 3) (correct answer)
4. c + (5 + 3)

Explanation: To find the number of treats left, we must subtract the total number of treats given away from the starting amount, c. The total number of treats given away is the sum of the morning treats (5) and evening treats (3), which is $(5 + 3)$. Therefore, the expression representing the remaining treats is $c - (5 + 3)$.

Question 7

1. 200 - c - 8 = 24 (correct answer)
2. 200 + c - 8 = 24
3. 200 - c + 8 = 24
4. c - 200 - 8 = 24

Explanation: The number of cupcakes at the end of the day is the starting amount minus the cupcakes sold and minus the cupcakes thrown away. This can be represented as: Starting Amount - Sold - Thrown Away = Left. Plugging in the numbers gives the equation $200 - c - 8 = 24$.

Question 8

1. 150 + p + 12
2. 150 - p + 12 (correct answer)
3. 150 - p - 12
4. p - 150 + 12

Explanation: The truck begins with 150 packages. Delivering p packages means subtracting p from the total, resulting in $150 - p$. Picking up 12 new packages means adding 12 to the new total. Therefore, the expression is $150 - p + 12$.

Question 9

1. (100 - 20m) / 10 (correct answer)
2. 100 - 20m - 10
3. (100 + 20m) / 10
4. 100 / (20m + 10)

Explanation: First, calculate the money Sam earns from mowing lawns, which is (20m). The remaining money he needs to earn is $100 - 20m$. Since he earns $10 for each car wash, we divide the remaining amount by 10 to find the number of cars he must wash. The correct expression is $(100 - 20m) / 10$.

Question 10

1. m/2 + 5 (correct answer)
2. (m + 5) / 2
3. m - 2 + 5
4. 2m + 5

Explanation: First, calculate the amount of money Jamal had after buying the book. Spending half of his money means dividing his initial amount m by 2, which is $m/2$. Then, he received $5, so we add 5 to this new amount. The correct expression is $m/2 + 5$.

Question 11

1. 40 + 15 + n + 3
2. 40n + 15(3) (correct answer)
3. 40(3) + 15n
4. (40 + 15)(n + 3)

Explanation: The total cost is the sum of the cost of the new games and the cost of the used games. The cost of n new games at $40 each is $40 \times n$, or $40n$. The cost of 3 used games at $15 each is $15 \times 3$. Therefore, the total cost is represented by the expression $40n + 15(3)$.

Question 12

1. 3(25 + 2g) (correct answer)
2. 3(25) + 2g
3. 25 + 2(3g)
4. 3(25g + 2)

Explanation: The cost for one month is the base fee ($25) plus the data cost ($2g$), which is represented by the expression $25 + 2g$. To find the total cost for 3 months, this entire monthly cost must be multiplied by 3. The correct expression is $3(25 + 2g)$.

Question 13

1. 12d - 40 (correct answer)
2. d - 40
3. 12(d - 40)
4. d/12 - 40

Explanation: First, find the total number of individual muffins the baker made. Since d represents the number of dozens, the total number of muffins is $12 \times d$, or $12d$. He sold 40 muffins, so we subtract 40 from the total. The correct expression is $12d - 40$.

Question 14

1. s/4 - 2
2. (s - 2) / 4 (correct answer)
3. s / (4 - 2)
4. 4s - 2

Explanation: First, find the number of students remaining. If 2 students leave from the original group of s students, there are $s - 2$ students left. This new total is then divided into 4 equal teams. Therefore, the number of students on each team is represented by $(s - 2) / 4$.

Question 15

1. 400 - 55h (correct answer)
2. 400 + 55h
3. 55h - 400
4. 400 / 55h

Explanation: The distance the bus has traveled is its speed (55) multiplied by the number of hours (h), which is $55h$. The remaining distance is the total distance (400) minus the distance already traveled. Therefore, the expression is $400 - 55h$.

Question 16

1. s + 1
2. s - 1
3. (3/2)s (correct answer)
4. (2/3)s

Explanation: The ratio of flour to sugar is 3 to 2, which can be written as the fraction 3/2. This means for every 1 cup of sugar, you need 3/2 (or 1.5) cups of flour. To find the amount of flour needed for s cups of sugar, you multiply s by this ratio. The correct expression is $(3/2)s$.

Question 17

1. 2(y - 5)
2. 5 - 2y
3. y + 2 - 5
4. 2y - 5 (correct answer)

Explanation: First, find twice Leo's age, which is $2 \times y$, or $2y$. Then, to find the aunt's age, subtract 5 from that amount. The correct expression is $2y - 5$.

Question 18

1. 24b - 30(2) (correct answer)
2. b - 30(2)
3. 24b + 30(2)
4. 30(2) - 24b

Explanation: First, find the total number of crayons Ms. Davis has, which is the number of boxes b times 24 crayons per box, or (24b). Next, find the number of crayons she gives away, which is 30 students times 2 crayons each, or $30(2)$. To find the number left, subtract the amount given away from the total amount she has: $24b - 30(2)$.

Question 19

1. t - 3(4) (correct answer)
2. t + 3(4)
3. 4t - 3
4. t - 4 - 3

Explanation: The total number of tickets used is the cost per game (3) multiplied by the number of times played (4), which is $3 \times 4$. To find the remaining tickets, this total must be subtracted from the starting number of tickets, t. The correct expression is $t - 3(4)$.

Question 20

1. (P - 50) / 2
2. P - 100
3. (P - 100) / 2 (correct answer)
4. P / 2 - 50

Explanation: The formula for the perimeter of a rectangle is $P = 2l + 2w$. We know the length l is 50, so $P = 2(50) + 2w$, which simplifies to $P = 100 + 2w$. To find the width w, we first subtract 100 from the perimeter: $P - 100 = 2w$. Then, we divide by 2: $w = (P - 100) / 2$.