I got this one correct but looking for an easier approach, Thanks in advance
If n is a positive integer greater than 6, what is the remainder when n is divided by 6?
(1) n^2 - 1 is not divisible by 3.
(2) n^2 - 1 is even.
Manahattan Q :Nice one !
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Approach 1:himu wrote: If n is a positive integer greater than 6, what is the remainder when n is divided by 6?
(1) n^2 - 1 is not divisible by 3.
(2) n^2 - 1 is even.
Since n is greater than 6, and the statements refer to n², make a list of perfect squares greater than 6²:
n² = 49, 64, 81, 100, 121, 144, 169, 196, 225.
Subtracting 1 from these values, we get the following options for n² - 1:
n² - 1 = 48, 63, 80, 99, 120, 143, 168, 195, 224.
Statement 1: n² - 1 is not divisible by 3
From the list in red, the following options are viable:
80, 143, 224.
If n² - 1 = 80, then n=9, which yields a remainder of 3 when divided by 6.
If n² - 1 = 143, then n=12, which yields a remainder of 0 when divided by 6.
Since the remainder can be different values, INSUFFICIENT.
Statement 2: n² - 1 is even
From the list in red, the following options are viable:
48, 80, 120, 168, 224.
If n² - 1 = 48, then n=7, which yields a remainder of 1 when divided by 6.
If n² - 1 = 80, then n=9, which yields a remainder of 3 when divided by 6.
Since the remainder can be different values, INSUFFICIENT.
Statements combined:
From the list in red, the following options satisfy both statements:
80, 224.
If n² - 1 = 80, then n=9, which yields a remainder of 3 when divided by 6.
If n² - 1 = 224, then n=15, which yields a remainder of 3 when divided by 6.
Since the remainder is the same in each case, SUFFICIENT.
The correct answer is C.
Approach 2:
n-1, n, and n+1 are 3 consecutive integers.
Of every 3 consecutive integers, EXACTLY ONE must be a multiple of 3.
Statement 1: n² - 1 is not divisible by 3
(n-1)(n+1) = non-multiple of 3.
Implication:
Since neither n-1 nor n+1 is a multiple of 3 -- and one of every 3 consecutive integers must be a multiple of 3 -- n MUST BE A MULTIPLE OF 3.
If n=9, then dividing by 6 will yield a remainder of 3.
If n=12, then divided by 6 will yield a remainder of 0.
Since the remainder can be different values, INSUFFICIENT.
Statement 2: n² - 1 is even
(n-1)(n+1) = even.
Implication:
n-1 and n+1 must both be even, implying that n is ODD.
If n=7, then dividing by 6 will yield a remainder of 1.
If n=9, then dividing by 6 will yield a remainder of 3.
Since the remainder can be different values, INSUFFICIENT.
Statements combined:
Statement 1: n is a multiple of 3
Statement 2: n is odd
Options for n:
9, 15, 21, 27...
In every case, dividing by 6 will yield a remainder of 3.
SUFFICIENT.
The correct answer is C.
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Hi GMATGuruNY,
I was wondering, there seem to be (recently) a lot of data sufficiency questions posted that have the answer:
Statement 1 = INSUFFICIENT
Statement 2 = INSUFFICIENT
Combined = SUFFICIENT
Does this mean that this is the most common correct answer? I mean, if we knew the statistical history of such questions, and we found that, say, 88% of them had this answer, might we save ourselves some time in the test by blindly choosing it, to give us more time on another question? Do you know such historical information? Would this be an unwise move?
I was wondering, there seem to be (recently) a lot of data sufficiency questions posted that have the answer:
Statement 1 = INSUFFICIENT
Statement 2 = INSUFFICIENT
Combined = SUFFICIENT
Does this mean that this is the most common correct answer? I mean, if we knew the statistical history of such questions, and we found that, say, 88% of them had this answer, might we save ourselves some time in the test by blindly choosing it, to give us more time on another question? Do you know such historical information? Would this be an unwise move?
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- ceilidh.erickson
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Ignoring pooja181's completely useless comments...
(edited to include image below):
As you can see, C was below 1/5 of correct answers from OG13, but more than 1/5 of correct answers in Q2.
Also interesting - A and B were perfectly matched in OG13, but there were more than twice as many A's as B's in Q2. There should be no reason statement 1 should be more often sufficient than statement 2, so it's probably random.
Our conclusions? That - just as with every other question type - each answer has roughly a 20% chance of being right on DS.
To your question... no, C is definitely NOT the most common right answer! Be wary of making these kinds of assumptions based on a few problems. In fact, the breakdown on DS answer distribution from OG13 and Q2 (which we have to assume is probably a representative sample) is as follows:Does this mean that this is the most common correct answer? I mean, if we knew the statistical history of such questions, and we found that, say, 88% of them had this answer, might we save ourselves some time in the test by blindly choosing it, to give us more time on another question? Do you know such historical information? Would this be an unwise move?
(edited to include image below):
As you can see, C was below 1/5 of correct answers from OG13, but more than 1/5 of correct answers in Q2.
Also interesting - A and B were perfectly matched in OG13, but there were more than twice as many A's as B's in Q2. There should be no reason statement 1 should be more often sufficient than statement 2, so it's probably random.
Our conclusions? That - just as with every other question type - each answer has roughly a 20% chance of being right on DS.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education