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 Post subject: GMAT Number Theory (Data Sufficiency)Posted: Fri Feb 24, 2012 4:38 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
If 4 students were added to a dance class, would the teacher be able to divide her students evenly into one or more dance teams of 8?
(1) If 12 students were added, the teacher could divide the students evenly into teams of 8.
(2) The number of students in the class is currently not divisible by 8.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(A) To divide the class evenly into teams of 8, we would need the number of students in the class to be a multiple of 8.
Statement (1) is sufficient. If adding 12 students allows the teacher to make even teams of 8, then adding 4 students will allow her to do so as well . There will just be 1 fewer team if 4 are added than if 12 are added.

Statement (2) alone tells us very little about the composition of the class, because it only tells us that the number of students currently in the class is not a multiple of 8. Adding 4 students may or may not allow the teacher to create even groups of 8. Therefore, Statement (2) is insufficient.

Be careful: although both statements combined are sufficient to answer the question, Statement (1) is sufficient alone. Therefore, the correct answer is choice (A).
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A statement should be added saying that the current number of students is non-zero. If the current number is zero then adding 4 would be different than adding 12.

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 Post subject: Re: t.1, qt. 10: number properties, division with a remaindePosted: Fri Feb 24, 2012 4:48 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
A statement should be added saying that the current number of students is non-zero. If the current number is zero then adding 4 would be different than adding 12.
If you have 4 or 12 students in the class, you are still NOT able to divide them into teams of 8. Only classes, where the number of students is a multiple of 8, can be divided into such groups: 8 (1 team), 16 (2 teams), 24 (3 teams), etc.

There could not be 0 students in the class initially, because it would contradict either statement.

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 Post subject: Re: t.1, qt. 10: number properties, division with a remaindePosted: Fri Feb 24, 2012 4:55 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
I did not really understand the explanation for why statement 1 is sufficient to answer the question. I do understand that we need a number of students that is a multiple of 8, but why if adding 12 students allows the teacher to make even teams of 8 then adding 4 will allow her to do the same?

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 Post subject: Re: t.1, qt. 10: number properties, division with a remaindePosted: Fri Feb 24, 2012 5:06 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
If 12 students are added, then we can think of them as 1 team of 8 students plus 4 students. So current students + 4 students must be divisible into groups of 8, otherwise current students + 12 students would not be divisible into groups of 8.

In other words:
We are told that adding 12 students allows the teacher to divide the class into teams of 8. Suppose there were x students. Then after we add 12, we have (x + 12), which is a multiple of 8. It can be written as (x + 4) + 8. Therefore (x + 4) must be a multiple of 8.

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 Post subject: Re: GMAT Number Theory (Data Sufficiency)Posted: Fri Nov 30, 2012 5:39 pm

Joined: Thu Dec 06, 2012 5:19 pm
Posts: 9
What if there are already 0 students in the dance class? Adding 4 will not make it divisible by 8.
0 is divisible by 8.

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 Post subject: Re: GMAT Number Theory (Data Sufficiency)Posted: Fri Nov 30, 2012 5:43 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
clover wrote:
What if there are already 0 students in the dance class?
This contradicts either statement. So such situation is NOT possible.

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