There are three boys aged 3, 5, and 8, and th… | GMAT Sprint

Free Practice Question

PS · Problem Solving

555-605

Arithmetic

There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by $z$ , what is the difference between the probability that $z$ is even and the probability that $z$ is odd?

Answer Choices

Correct answer marked below

\frac{1}{2}

\frac{1}{3}

\frac{2}{3}

\frac{1}{4}

\frac{1}{9}

Correct

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Explanation

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Official Explanation

Official

To solve the problem, we need to determine the difference between the probability that the sum of the ages of two chosen boys and two chosen girls is even and the probability that it is odd.

Step 1: List the Ages

- Boys' Ages: 3, 5, 8

- Girls' Ages: 4, 7, 10

Step 2: Calculate the Sum of Ages for Boys and Girls

First, we calculate the sum of ages when two boys are chosen and when two girls are chosen.

- Sum of Boys' Ages Taken Two at a Time:

- 3 + 5 = 8

- 3 + 8 = 11

- 5 + 8 = 13

- Sum of Girls' Ages Taken Two at a Time:

- 4 + 7 = 11

- 4 + 10 = 14

- 7 + 10 = 17

Step 3: Determine All Possible Combinations

Next, we consider all possible combinations of the sums of the boys' and girls' ages. There are 3 possible sums for the boys and 3 possible sums for the girls, resulting in a total of

3 \times 3 = 9

combinations.

The possible sums

z

are:

- 8 (boys) + 11 (girls) = 19…

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What this question tests

What it tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Common trap

Applying the order of operations out of sequence or rounding intermediate values before the final step.

There are three boys aged 3, 5, and 8, and three girls aged 4, 7, and 10. If two boys and two girls are chosen at random, and the sum of their ages is denoted by zzz, what is the difference between the probability that zzz is even and the probability that zzz is odd?