Data Sufficiency

lukaswelker wrote: The ratio of the number of women to the number of men to the number of children in a room is 5:2:7, respectively. What is the total number of people in the room?

(1) the total number of women and children in the room is 12.
(2) there are fewer than 4 men in the room.

Target question: What is the total number of people in the room?

Given: women : men : children = 5:2:7
So, there are many possible scenarios where the ratio is 5:2:7. Let's LIST a few:
Scenario #1: 5 women, 2 men, 7 children
Scenario #2: 10 women, 4 men, 14 children
Scenario #3: 15 women, 6 men, 21 children
Scenario #4: 20 women, 8 men, 28 children
.
.
.
and so on

Okay, now let's examine the statements:

Statement 1: the total number of women and children in the room is 12.
Let's check some of the scenarios that we LISTED.
Scenario #1: total number of women and children = 12 (NICE!)
Scenario #2: total number of women and children = 24 (no)
Scenario #3: total number of women and children = 36 (no)
...and so on.
We can see that ONLY scenario #1 fits the information in statement 1.
So, there MUST be 5 women, 2 men, and 7 children
In other words, the total number of people in the room MUST equal 14
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are FEWER THAN 4 men in the room.
When we check some of the scenarios that we LISTED, we see that ONLY scenario #1 fits the information in statement 2.
So, there MUST be 5 women, 2 men, and 7 children
In other words, the total number of people in the room MUST equal 14
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

I should point out that this question relies on our ability to recognize that in this REAL WORLD problem, we must use only positive integers.

So, while 0.5 : 0.2 : 0.7 is equivalent to the ratio 5:2:7, we cannot consider this scenario, since we cannot have 0.5 women, 0.2 men, and 0.7 children

Cheers,
Brent

GMATGuruNY wrote:

amitmj wrote:Hi Brent,

For the statement 2, can we have Men = 0 as a scenario too ???

On the GMAT, problems about ratios are restricted to POSITIVE VALUES.
As Brett has mentioned, this particular problem is further constrained to POSITIVE INTEGERS.

Well said, Midge

Cheers,
Brent - now with 50% less "t"