The ratio of boys to girls in a class is 7 to 3. Among the options below, an…
2021
The ratio of boys to girls in a class is 7 to 3.
Among the options below, an acceptable value for the total number of students in the class is:
- A.
21
- B.
37
- C.
50
- D.
73
Attempted by 152 students.
Show answer & explanation
Correct answer: C
Key idea: the total number of students must be a multiple of 10 because 7 + 3 = 10.
Explanation: Let k be a positive integer. If boys:girls = 7:3 then boys = 7k, girls = 3k, and total = 10k. Therefore any acceptable total must be divisible by 10.
21: Not acceptable — 21 ÷ 10 = 2.1 gives non-integer counts.
37: Not acceptable — 37 ÷ 10 = 3.7 gives non-integer counts.
50: Acceptable — 50 = 10 × 5, so k = 5, boys = 7 × 5 = 35 and girls = 3 × 5 = 15.
73: Not acceptable — 73 ÷ 10 = 7.3 gives non-integer counts.
Conclusion: 50 is the only acceptable total among the given choices.
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