In a group, the ratio of the number of women to the number of children

I took my time with this question. I'd be really grateful if anyone could spill some secrets on how they did it under 2 minutes. MartyTargetTestPrep avigutman VeritasKarishma Bunuel

So:
Info:
women to the number of children/ W:C = 7:2

(1) The ratio of the number of children to the number of men is 3:5.
C:M = 3:5
we are given more ratio information w/o any absolute values, so insufficient. (Eliminate A,D)
(2) The number of children in the group is between 10 and 15.
The number of children is either 11,12,13, or 14
but from the info of the question, we know that the children are 2x. This means we can eliminate the odd numbers (i.e. 11,13)
here we are can solve no. of children to be either 6 or 7.
Insufficient as we are not getting a certain answer. Eliminate B.

Combining 1&2:
C:M = 3:5
No of children = 12 or 14

solving for both:
3x = 12
x= 12/3=4 (valid)

3x=14 (not divisible)

So the number of children is 12 and the multiplying factor is 3.

Do let me know if there is any error/disconnect. Thanks!

“Between 10 and 15” may or may not include 10 and 15. The fact that they didn’t bother stating “inclusive” or “exclusive” implies that in this case it’s irrelevant. You’re correct that odd values can be eliminated. But a faster way to rule out sufficiency with this statement is the fact that we have no info about men, and the question is asking about men. I get the sense that you may have forgotten what exactly the question asked for.


We now have children represented by 2 ratio units in the free info and by 3 ratio units in statement 1, so we can conclude that the actual number of children is a multiple of 6. There’s only one multiple of 6 between 10 and 15, so we can now find any actual number we want. Men, women, or children.

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avigutman, Thank you for replying! It makes sense to me now. It's great getting your input especially after binging your videos on Ratios haha!

W:C = 7:2
We need the number of men.

(1) The ratio of the number of children to the number of men is 3:5.

C:M = 3:5.
This tells us that W:C:M = 21:6:10
But it doesn't give us the actual number of men. So not sufficient alone.

(2) The number of children in the group is between 10 and 15.
No info on men.

Using both, W:C:M = 21:6:10 and number of children is between 10 and 15. From the ratio, we know that number of children must be a multiple of 6. There is only one value that is a multiple of 6 between 10 and 15 and that is 12. So number of children must be 12. So multiplier will be 2 and number of men will be 20.
Answer (C)

Check this video: https://www.youtube.com/watch?v=5ODENGG5dvc
and this post: https://anaprep.com/arithmetic-ratios-t ... ll-starts/
for a discussion on ratios.

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