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Bunuel
Ratio of boys to the girls in a class is 6 : 7. Which of the following cannot be the number of students in the class ?

(A) 26
(B) 52
(C) 104
(D) 675
(E) 1300

IMO D

7x : girls
6x : boys

13x = total students

So total students should be a factor of 13. All options give remainder zero when divided by 13 except 675

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The ratio is 6:7 [6+ 7 = 13 parts]

The number not divisible by 13 is 675.

Answer D
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Bunuel
Ratio of boys to the girls in a class is 6 : 7. Which of the following cannot be the number of students in the class ?

(A) 26
(B) 52
(C) 104
(D) 675
(E) 1300
Solution:

If the number of boys and girls in the class are 6x and 7x, respectively, where x is a positive integer, then the total number of students in the class is 13x. In other words, the number of students in the class is a multiple of 13. Of all the given choices, we see that 675 is not a multiple of 13 since 675/13 = 51 R 12.

Answer: D
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