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 W = # of women
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
