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Manager  Joined: 21 Jan 2010
Posts: 130
Is 4 + n/6 an integer?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 87% (00:39) correct 13% (00:50) wrong based on 147 sessions

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Is 4 + n/6 an integer?

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

OA is B.

I thought it was E.

My reasoning: when n = 6, the answer is yes, but when n = -24, the answer would be no as 0 is not an integer.

Originally posted by calvinhobbes on 26 Jan 2010, 05:54.
Last edited by Bunuel on 27 Jul 2015, 14:53, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern  Joined: 21 Jan 2010
Posts: 46
Re: Is 4 + n/6 an integer?  [#permalink]

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calvinhobbes wrote:
Is 4 + (n/6) an integer?

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

OA is
B.

I thought it was .

My reasoning:
when n = 6, the answer is yes, but when n = -24, the answer would be no as 0 is not an integer.

(1) - if n is 3, n/6 is not an integer, but if n is 6, n/6 is an integer, so insufficient.
(2) - n divided by 6 has a remainder of 0,meaning n has to be a multiple of 6 (0, 6, 12, etc).

I would think the answer is B - (2) alone is sufficient.

It seems that there is confusion on the internet concerning 0 as an integer - my opinion for the GMAT is that 0 should be treated as an integer... does GMAC state otherwise?
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Re: Is 4 + n/6 an integer?  [#permalink]

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calvinhobbes wrote:
Is 4 + (n/6) an integer?

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

OA is
B.

I thought it was .

My reasoning:
when n = 6, the answer is yes, but when n = -24, the answer would be no as 0 is not an integer.

0 is an integer, moreover 0 is an even integer. Maybe you have mistaken this property for another: zero is neither positive nor negative?
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Re: Is 4 + n/6 an integer?  [#permalink]

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Thank you both of you.

Yes I've mistaken it is neither +ve nor -ve.
Manager  Joined: 21 Mar 2014
Posts: 55
Location: India
Concentration: Strategy, Technology
Is 4+n/6 an integer?  [#permalink]

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1
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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Joined: 02 Sep 2009
Posts: 58452
Re: Is 4+n/6 an integer?  [#permalink]

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raj44 wrote:
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

The point is that in a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Hope it's clear.
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Re: Is 4+n/6 an integer?  [#permalink]

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Thanks Bunuel ! It is clear now.
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Re: Is 4 + n/6 an integer?  [#permalink]

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St1: n = 3k --> Not sufficient
St2: n = 6k --> Sufficient

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Re: Is 4 + n/6 an integer?  [#permalink]

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Bunuel wrote:
Is 4 + n/6 an integer?

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

Solution:

Is 4 + n/6 an integer?--> is n/6 is an integer?---> is n multiple of 6?

Statement 1) n is a multiple of 3.

n = 3 , 6 or 9--> 3 is not a multiple of 6 , but 6 is.

Hence Insufficient.

Statement 2) n divided by 6 has a remainder of 0.

Clearly n is a multiple of 6.

Hence Sufficient.

Ans B.
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Re: Is 4 + n/6 an integer?  [#permalink]

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andrewcs wrote:
calvinhobbes wrote:
Is 4 + (n/6) an integer?

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

OA is
B.

I thought it was .

My reasoning:
when n = 6, the answer is yes, but when n = -24, the answer would be no as 0 is not an integer.

(1) - if n is 3, n/6 is not an integer, but if n is 6, n/6 is an integer, so insufficient.
(2) - n divided by 6 has a remainder of 0,meaning n has to be a multiple of 6 (0, 6, 12, etc).

I would think the answer is B - (2) alone is sufficient.

It seems that there is confusion on the internet concerning 0 as an integer - my opinion for the GMAT is that 0 should be treated as an integer... does GMAC state otherwise?

Can someone clarify whether this question is asking 4 + n/ 6 as a whole or 4 + (n/6)?
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Re: Is 4 + n/6 an integer?  [#permalink]

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Nunuboy1994 wrote:
andrewcs wrote:
calvinhobbes wrote:
Is 4 + (n/6) an integer?

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

OA is
B.

I thought it was .

My reasoning:
when n = 6, the answer is yes, but when n = -24, the answer would be no as 0 is not an integer.

(1) - if n is 3, n/6 is not an integer, but if n is 6, n/6 is an integer, so insufficient.
(2) - n divided by 6 has a remainder of 0,meaning n has to be a multiple of 6 (0, 6, 12, etc).

I would think the answer is B - (2) alone is sufficient.

It seems that there is confusion on the internet concerning 0 as an integer - my opinion for the GMAT is that 0 should be treated as an integer... does GMAC state otherwise?

Can someone clarify whether this question is asking 4 + n/ 6 as a whole or 4 + (n/6)?

4 + n/6 can only mean 4 + (n/6), nothing else. If it were (4 + n)/6 it would have been written this way.
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Re: Is 4 + n/6 an integer?  [#permalink]

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calvinhobbes wrote:
Is 4 + n/6 an integer?

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

Since 4 is already an integer, we really need to determine whether n/6 is an integer.

Statement One Alone:

n is a multiple of 3.

Statement one is not sufficient to answer the question. If n = 3, then n/6 is not an integer; however, if n = 6, then n/6 is an integer.

Statement Two Alone:

n divided by 6 has a remainder of 0.

Using the information in statement two, we see that n is a multiple of 6, and thus n/6 is an integer.

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Re: Is 4 + n/6 an integer?  [#permalink]

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Bunuel 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?

This is a good candidate for rephrasing the target question (see video below).

If 4 is an integer, then 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?

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

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_________________ Re: Is 4 + n/6 an integer?   [#permalink] 20 Apr 2018, 07:33
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