In a class, the number of boys is 4 times the number of girls. From the…
2019
In a class, the number of boys is 4 times the number of girls. From the numbers below, which one can represent the total number of students in the class?
Answer: D. 65 — ConceptWhen one group is a whole-number multiple of another, the total is the sum of both groups, and that sum is forced to be a multiple of a fixed number.…
- A.
66
- B.
54
- C.
56
- D.
65
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Show answer & explanation
Correct answer: D
Concept
When one group is a whole-number multiple of another, the total is the sum of both groups, and that sum is forced to be a multiple of a fixed number. If a quantity equals an integer multiplied by 5, then the total must be divisible by 5 (i.e. it must end in 0 or 5). A candidate that is not divisible by 5 can never be such a total.
Application
Let the number of girls = x. Then the number of boys = 4x.
Total students = girls + boys = x + 4x = 5x.
Since x is a whole number, the total 5x must be a multiple of 5, so it must end in 0 or 5.
Test each candidate for divisibility by 5: 66 (no), 54 (no), 56 (no), 65 (yes, 65 = 5 × 13).
Cross-check
If x = 13 girls, then boys = 4 × 13 = 52, and total = 13 + 52 = 65, which matches. The other values give a non-whole number of girls (e.g. 66 ÷ 5 = 13.2), so they are impossible.
Answer: 65.