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achandwa
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I am not quite convinced with the explaination of the answer. If someone has insights please let me know. Search for [ASHISH] for my question.
Thanks, Ashish
Question
Given that n is an integer, is n — 1 divisible by 3?
(1) is not divisible by 3
(2) , where k is a positive multiple of 3
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer
Statement (1) gives us information about , which can be rewritten as the product of two consecutive integers as follows:
Since the question asks us about n — 1, we can see that we are dealing with three consecutive integers: n — 1, n, and n + 1 .
By definition, the product of consecutive nonzero integers is divisible by the number of terms. Thus the product of three consecutive nonzero integers must be divisible by 3.
Since we are told in Statement (1) that the product is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
[ASHISH]
Why so? I thought that 0 was divisible by any real number? If out of n-1, n and n+1, n and n+1 are not divisible by 3, then n-1 has to be divisible by 3. I marked A as my answer (you can see below that the second condition is not sufficient). I still can't see how it is wrong.
Statement (2) can be rewritten as follows:
Given that k is a positive multiple of 3, we know that n must be greater than or equal to 2. This tells us that the members of the consecutive set n — 1, n, n + 1 are nonzero integers.
By itself, this information does not give us any information about whether n — 1 is divisible by 3. Thus Statement (2) alone is not sufficient.
When both statements are taken together, we know that the members of the consecutive set n — 1, n, n + 1 are nonzero integers and that neither n nor n + 1 is divisible by 3. Therefore, n — 1 must be divisible by 3.
The correct answer is C: both statements together are sufficient but neither statement alone is sufficient to answer the question.
Thanks, Ashish
Question
Given that n is an integer, is n — 1 divisible by 3?
(1) is not divisible by 3
(2) , where k is a positive multiple of 3
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Answer
Statement (1) gives us information about , which can be rewritten as the product of two consecutive integers as follows:
Since the question asks us about n — 1, we can see that we are dealing with three consecutive integers: n — 1, n, and n + 1 .
By definition, the product of consecutive nonzero integers is divisible by the number of terms. Thus the product of three consecutive nonzero integers must be divisible by 3.
Since we are told in Statement (1) that the product is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
[ASHISH]
Why so? I thought that 0 was divisible by any real number? If out of n-1, n and n+1, n and n+1 are not divisible by 3, then n-1 has to be divisible by 3. I marked A as my answer (you can see below that the second condition is not sufficient). I still can't see how it is wrong.
Statement (2) can be rewritten as follows:
Given that k is a positive multiple of 3, we know that n must be greater than or equal to 2. This tells us that the members of the consecutive set n — 1, n, n + 1 are nonzero integers.
By itself, this information does not give us any information about whether n — 1 is divisible by 3. Thus Statement (2) alone is not sufficient.
When both statements are taken together, we know that the members of the consecutive set n — 1, n, n + 1 are nonzero integers and that neither n nor n + 1 is divisible by 3. Therefore, n — 1 must be divisible by 3.
The correct answer is C: both statements together are sufficient but neither statement alone is sufficient to answer the question.
