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## The ratio of the number of women to the number of men

tagged by: M7MBA

This topic has 1 expert reply and 0 member replies

### Top Member

M7MBA Moderator
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#### The ratio of the number of women to the number of men

Sat Dec 02, 2017 5:43 am
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.

The OA is D.

I don't know how to prove that each statement is sufficient.

Can you Experts help me here please. I would be thankful.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
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GMAT Score:
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Sat Dec 02, 2017 8:05 am
M7MBA 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

Cheers,
Brent

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