3. On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5:2. What was the number of men on the sight-seeing?
1) The ratio of the number of children to the number of men was 5:11
2) The number of women on sight-seeing was less than 30
GMAT Prep Question # 5
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Let W = # of womenOn 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
Cheers,
Brent
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Given:C Okigbo wrote:3. On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5:2. What was the number of men on the sight-seeing?
1) The ratio of the number of children to the number of men was 5:11
2) The number of women on sight-seeing was less than 30
Women:Children = 5:2
Let us assume.
M = No. of Men,
W = No. of Women
C = No. of Children
Question:
Number of men (M)
Statement 1:
C:M = 5:11
Till now all the information we have is about the ratios,
We do not have any information about the Total or for the individual numbers of M, W and C
So we can easily say that this information will not give us the Number of men
Statement 2:
W < 30
This does not gives us any information about the number of men.
So this statement is also not sufficient.
Combining both 1 and 2:
We know that W:C = 5:2 and C:M = 5:11
So we can find the equivalent ratios to be
W:C:M = 25:10:22.
We can find it by making the base same, which in this case is C.
After this, taking the information from the second stataement.
We know W < 30
This can be possible only for one case, when
W = 25, C = 10 and M = 22
Hence we can find the number of men by combining both equations.
Thus C is the answer
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