Data Sufficiency

On a certain sightseeing tour the ratio of the number of children to the number of women was 2 to 5. What is the number of men on the tour?

1. On the tour, the ratio of number of children to number of men was 5 to 11
2. The number of women on the tour was less than 30

Each statement is definitely not enough in itself to solve the problem.

Even when taken together, I think we cannot determine the number of men, because the second statement just says that W < 30 but not equal to. Hence my answer was E.

However GMAT preps answer was C. That is it claims that both statements together are sufficient. Am I missing anything or is the GMAT prep wrong?

This is the trap of GMAT !!

The ans is absolutely correct...

From q and stem 1 we can get a ratio of W/M=25/22

And from stem 2 : W<30

That gives the limit of women and from ratio we can get no. of men as
22.(If you make the women no. more than 25 say 50 the no. of Men would be 44 but it can't be more than 30)

Hope you understand.

So, sufficient !!

Amit

Thanks Amit for the reply.

I think I never solved the first expression to arrive at the ratio 22/25

Since 22 and 25 are co-primes and since W < 30, W has to be 25.

I am sorry how do you get 25/22. I am pretty clueless on how you gusy solved this problem still please break it down for me
Thanks

W:C => 5:2

Statement I
C:M => 5:11

Therefore, W:C:M => 25:10:12 (this you can calculate if you know ratios, let me know if you cant.)

Anyways here it is, Let total number of women and children be 70, I chose 70 for easier calculations. We will have 50 women and 20 children according to the ratio 5:2.

C:M => 5:11

There are 20 children, you can calculate the combined ratio by following method:

20/x = 5/11
x = 24

Combined ratio W:C:M => 50:20:44=> 25:10:22 (

Statement II

Women are less than 30

Combining I & II

Women will always be in multiple of 25.

Therefore, there are 25 women, 10 children & 22 men.

Hence C.

How did you get W:C:M => 25:10:12; i don't know how to calculate this.
Can you explain please?

C:W:M
2 5
5 W 11


the ratio of 2/5=5/W

25=2W

W=25/2

C : W : M
5 25/2 11

We can't have a fraction of people, so we mutiply the whole ratio by 2.

C : W : M
10 25 22


I hope this helps, please correct me if I made a mistake.