On a certain sight-seeing 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 sight-seeing tour?
1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
2) The number of women on the sight-seeing tour was less than 30.
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Patrick_GMATFix
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This is QID 1175 in the GMATFix Solutions Engine. Written and video explanation can be found here.
1) is not sufficient because all we have are ratio values, no concrete number. We could be dealing with very large numbers of people or small numbers.
2) on its own is not helpful because it doesn't tell us anything about men, even when combined with the prompt (which only gives us data on women to children ratio)
Together:
women:children = 5:2. Since there are fewer than 30 women, the numbers of women and children could be
(5, 2) (10, 4) (15, 6) (20, 8) or (25, 10).
Statement (1) tells us that children:men was 5:11, so the actual number of children must be a multiple of 5. Of the possibilities highlighted above, the only working solution is (women, children) = (25, 10). There are 10 children. This along with the known ratio of children:men (5:11) is enough to get the exact number of men (10 children, 22 men).
the statements are sufficient together. Answer is C
1) is not sufficient because all we have are ratio values, no concrete number. We could be dealing with very large numbers of people or small numbers.
2) on its own is not helpful because it doesn't tell us anything about men, even when combined with the prompt (which only gives us data on women to children ratio)
Together:
women:children = 5:2. Since there are fewer than 30 women, the numbers of women and children could be
(5, 2) (10, 4) (15, 6) (20, 8) or (25, 10).
Statement (1) tells us that children:men was 5:11, so the actual number of children must be a multiple of 5. Of the possibilities highlighted above, the only working solution is (women, children) = (25, 10). There are 10 children. This along with the known ratio of children:men (5:11) is enough to get the exact number of men (10 children, 22 men).
the statements are sufficient together. Answer is C
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Patrick_GMATFix
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Brent@GMATPrepNow
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Let W = # of womenSak32 wrote:On a certain sight-seeing 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 sight-seeing tour?
1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
2) The number of women on the sight-seeing tour was less than 30.
Let M = # of men
Let C = # of children
Target question: What is the value of M?
Given: The ratio of the number of women to the number of children was 5 to 2
In other words, W : C = 5 : 2
Statement 1: On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
In other words, C : M = 5 : 11
Let's combine this ratio with the given ratio (W : C = 5 : 2)
To do so, we'll find some EQUIVALENT RATIOS such that they both share a term.
Take 5 : 2 and multiply both terms by 5 to get 25 : 10
So, W : C = 25 : 10
Now take 5 : 11 and multiply both terms by 2 to get 10 : 22
So, C : M = 10 : 22
At this point, we can combine the ratios to get W : C : M = 25 : 10 : 22
As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of M
Consider these three conflicting possibilities:
Case a: W : C : M = 25 : 10 : 22
Case b: W : C : M = 50 : 20 : 44
Case c: W : C : M = 75 : 30 : 66
etc.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The number of women on the sight-seeing tour was less than 30.
There's no information at all about the men so statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 essentially tells us that W : C : M = 25 : 10 : 22, so with each ratio that's equivalent to 25 : 10 : 22, we can a different value of M
So, we could have W : C : M = 25 : 10 : 22
or W : C : M = 50 : 20 : 44
or W : C : M = 75 : 30 : 66
etc.
Statement 2 reduces the possible number of women (W).
If W < 30, then there's only ONE possible ratio that works. That is W : C : M = 25 : 10 : 22
This means that there MUST be 22 men
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
