Is 4 + n/6 an integer?

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.

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

Answer = B

RELATED VIDEO

Thank you both of you.

Yes I've mistaken it is neither +ve nor -ve.

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

Thanks Bunuel ! It is clear now.

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

Answer: B

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.

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.

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.

Answer: B

Reading quickly and not paying attention, I thought the expression was:

Numerator: (4 + n)
Denominator: 6

In which case the answer would be D (definite NO for each statement alone)

But the question is much simpler

(Integer 4) + (n / 6)

If n is a multiple of 6, then the expression is an integer result

B - only statement 2 is sufficient alone

Statement 1: n = 3 or n = 6

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