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## Is 4+n/6 an integer?

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 2 member replies
raj44 Senior | Next Rank: 100 Posts
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#### Is 4+n/6 an integer?

Tue Aug 12, 2014 12:41 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Good Day,

The question is as follows:

Is 4+n/6 an integer?

1. n is a multiple of 3
2. n divided by 6 has a remainder of 0

Though the problem looks pretty straight forward, it underlines a very imp fact regarding Data Sufficiency YES/NO questions and this fact I want to be cleared!

Now, if we look at the individual statements, obviously we choose values and evaluate the Question Stem.

1. n is a multiple of 3

we can select n to be 3, in which the answer is NO and we can select n as 6 in which the answer is YES.

Since data sufficiency basically tests how the sufficiency of data is interpreted, my question is this...

Statement clearly gives us the answer as either YES or NO..and therefore we can answer the question stem as:

4+n/6 is an integer if n=6,12..and it is not an integer if n=3,5 etc

Moving on statement 2, which is sufficient to answer the question stem.

But, the answer is B and I feel it should be D since we can answer the question stem using each statement- either statement is sufficient by itself to determine YES/NO for an "IS" question.

Can someone please clarify my reasoning and advise where I am wrong?

Thanks
Rajeev

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GMATGuruNY GMAT Instructor
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Tue Aug 12, 2014 5:26 am
raj44 wrote:
Is 4+n/6 an integer?

1. n is a multiple of 3
2. n divided by 6 has a remainder of 0
Statement 1: n is multiple of 3
If n=3, then 4 + n/6 = 4 + 3/6 = 4.5.
Is 4.5 an integer?
NO.

If n=6, then 4 + n/6 = 4 + 6/6 = 5.
Is 5 an integer?
YES.

Since the answer is NO in the first case but YES in the second case, INSUFFICIENT.

Statement 2: n divided by 6 has a remainder of 0
In the words, n is a multiple of 6:
6, 12, 18, 24, 30, 36...

If n=6, then 4 + n/6 = 4 + 6/6 = 5.
Is 5 an integer?
YES.

If n=12, then 4 + n/6 = 4 + 12/6 = 6.
Is 6 an integer?
YES.

If n=30, then 4 + n/6 = 4 + 30/6 = 9.
Is 9 an integer?
YES.

Since the answer is YES in every case, SUFFICIENT.

Quote:
Though the problem looks pretty straight forward, it underlines a very imp fact regarding Data Sufficiency YES/NO questions and this fact I want to be cleared!

Now, if we look at the individual statements, obviously we choose values and evaluate the Question Stem.

1. n is a multiple of 3

we can select n to be 3, in which the answer is NO and we can select n as 6 in which the answer is YES.

Since data sufficiency basically tests how the sufficiency of data is interpreted, my question is this...

Statement clearly gives us the answer as either YES or NO..and therefore we can answer the question stem as:

4+n/6 is an integer if n=6,12..and it is not an integer if n=3,5 etc

Moving on statement 2, which is sufficient to answer the question stem.

But, the answer is B and I feel it should be D since we can answer the question stem using each statement- either statement is sufficient by itself to determine YES/NO for an "IS" question.

Can someone please clarify my reasoning and advise where I am wrong?

Thanks
Rajeev
A statement is sufficient only if the answer to the question stem is THE SAME IN EVERY CASE.
Statement 2 yields the same answer in every case (YES).
Thus, statement 2 is SUFFICIENT.
Statement 1 yields YES in some cases but NO in others.
Since statement 1 does NOT yield the same answer in every case, statement 1 is INSUFFICIENT.

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raj44 Senior | Next Rank: 100 Posts
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Tue Aug 12, 2014 7:56 am
Thank you Mitch! I feel much better now wrt IS data sufficiency questions !

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Tue Aug 12, 2014 12:44 pm
Hi raj44,

Data Sufficiency questions are about whether the answers that you get to the given question are consistent or inconsistent.

Every DS question that you face on Test Day has AT LEAST one answer, but your task is to determine if the possible answers stay the same or vary.

If a series of results is consistent, then the given Fact is Sufficient.
If a series of results is inconsistent, then the given Fact is insufficient.

This applies to ALL DS questions (Yes/No and Value).

GMAT assassins aren't born, they're made,
Rich

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Brent@GMATPrepNow GMAT Instructor
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Tue Aug 12, 2014 4:10 pm
raj44 wrote:
Is 4 + n/6 an integer?

1) n is a multiple of 3
2) n divided by 6 has a remainder of 0

Target question: Is 4 + n/6 an integer?

Since 4 is an integer, 4 + n/6 will be an integer if and only if n/6 is an integer. Moreover, n/6 will be an integer if and only if n is divisible by 6. So, we can REPHRASE the target question as....

REPHRASED target question: Is n divisible by 6?

Aside: We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: n is a multiple of 3
There are several values of n that satisfy this condition. Here are two values that yield conflicting answers to the REPHRASED target question :
Case a: n = 3, in which case n is NOT divisible by 6
Case b: n = 6, in which case n IS divisible by 6
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n divided by 6 has a remainder of 0
If n is divided 6 leaves remainder 0, then n is definitely divisible by 6.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

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