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ratio of women

by lukaswelker » Thu Apr 17, 2014 9:14 am
Hey Guys

Can seem to understand the answer behind the following question.

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.

How can the second one be sufficient also?

Many thanks
Lukas
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by Brent@GMATPrepNow » Thu Apr 17, 2014 9:40 am
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
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by Brent@GMATPrepNow » Thu Apr 17, 2014 9:44 am
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

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by amitmj » Fri Apr 18, 2014 2:06 am
Hi Brent,

For the statement 2, can we have Men = 0 as a scenario too ???
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by GMATGuruNY » Fri Apr 18, 2014 3:56 am
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.
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by Brent@GMATPrepNow » Fri Apr 18, 2014 5:21 am
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 :-)

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