Data Sufficiency

Hi all,

Couldn't figure out this one. Would really appreciate a brief explanation. thanks!

Q) On a tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the tour?

1) The ratio of the number of children to the number of men was 5 to 11.

2) The number of women on the tour was less than 30.

IMO it is E

Women:Children::5:2.

Nothing but, women=5x and children=2x

1. Children:Men::5:11

Combining ratios, W:C:M::25:10:22. From this you really cannot find the number of men. We do not know the total of women, children and men. Insufficient.

2. women < 30
5x < 30
x < 6

We don't know anything about men here. Insufficient.

Combined, you only know a range of values for men from the given ratios and eqn (x<6). You still don't know the total of women, children and men. Insufficient.

i Believe the answer is C

here is why....

Problem lets us Women to Children is 5:2

1) Certainly Insufficient but added info Children to Men is 5:11
2) Certainly Insufficient

Combined:

We must set up a ratios so that the children are the same value

5 (5:2) = 25:10 2(5:11) = 10:22

therefore we get women:children:men = 25:10:22

This is the lowest form because 25 and 10 is not divisible by 11

Now add the new info

women < 30

since we cannot simplify anymore the amount of women will be 25 and the amount of men will be 22
here is why...

we cannot have a fraction of a person so we must get an integer
try for 15 women

25x:10x:22x

multiply each party by 15/25 (or 3/5ths)

then we get
15: 150/25 : 165/25

men are not divisible

qazpt-you are correct! the answer is C. My problem was getting the children ratios to match.

So I'm assuming the key is similar to finding the least common multiple and then multiplying both ratios by that number?

thanks again!

qazpt wrote: Now add the new info

women < 30

since we cannot simplify anymore the amount of women will be 25 and the amount of men will be 22
here is why...

we cannot have a fraction of a person so we must get an integer
try for 15 women

25x:10x:22x

multiply each party by 15/25 (or 3/5ths)

then we get
15: 150/25 : 165/25

men are not divisible

I don't understand this part. Can you pls explain this part elaborately?

pkw209 wrote:Hi all,

Couldn't figure out this one. Would really appreciate a brief explanation. thanks!

Q) On a tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the tour?

1) The ratio of the number of children to the number of men was 5 to 11.

2) The number of women on the tour was less than 30.

papgust, one key was this:

we cannot have a fraction of a person so we must get an integer

1) The ratio of the number of children to the number of men was 5 to 11.

Clearly insufficient as there is no info about numbers.

2) The number of women on the tour was less than 30.

Clearly insufficient as there is no info about men.

(1) + (2):

From (1), we know that there are at least 11 men. This is because we cannot further divide 5:11 without cutting at least one kid and one man in half. For example, if we were to divide the ratio 5:11 by 2, we would have: 2.5: 5.5, meaning we would have two and a half children and five and a half men. From (1), we also know that the number of men is a multiple of 11.

And from the stem, we know that the ratio of women to children is 5:2. Because children is the variable that shows up in both ratios, let's think about them. From (1), we know that the number of children is a multiple of 5; from the stem, we know that the number of children is a multiple of 2. Therefore, the number of children must be a multiple of both 2 and 5. The least common multiple here is 10. So, there are at least 10 children. If there are ten children, then there are 2.5 x as many women (w/c = 5/2), so there would be 25 women. And the number of men is 11/5 * the number of children, so 11/5 * 10 = 22.

So, from (1) and the stem, the minimal ratio of w:c:m is: 25: 10: 22. This is the minimal ratio because if we were to simplify it further, we would have non-integers, and we would be cutting people into pieces. At this point (ie, before including (2)'s info), you could have that many number of women, children, and men, or 50 women, 20 children, 44 men, and so on.

In other words, there are at least 25 women, and the number of women must be a multiple of 25. And, from (2), we know that the number of women is less than 30. There is only one (positive) multiple of 25 less than 30. Therefore, we have 25 women, 10 children, and 22 men, and choose C.

_____

Suppose the ratio of women to men at a conference was 3:2. This means that the number of women will always be a multiple of 3, the number of men always a multiple of 2, and, because 3 + 2 = 5, the total number always a multiple of 5:

W M T
3 2 5
6 4 10
9 6 15

This is a key concept when moving from part to part to part to whole ratios. Children was the variable that was involved in both of our ratios. w:c = 5:2, therefore number of children a multiple of 2. Children to men was 5: 11, therefore the number of children also a multiple of 5. This is the key deduction that allowed qazpt to set up the ratio of w:c:m = 25:10:22.

Another important (and closely related) point is that when dealing with ratios of objects and people, you are always dealing with positive integers because in most of these problems it would be absurd to divide or cut up the object or the person.

Wonderful explanation! Thanks testluv..!

pkw209 wrote:qazpt-you are correct! the answer is C. My problem was getting the children ratios to match.

So I'm assuming the key is similar to finding the least common multiple and then multiplying both ratios by that number?

thanks again!

Yes, that was the key. As discussed in qazpt's and my posts, we focussed on children b/c they showed in both ratios. And, we know we have at least ten (least common multiple) of them b/c the number of them must be a multiple of both 5 and 2.

thanks Testluv. you all have been very helpful and I appreciate it very much!