The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?
(1) n is a positive number having 8 as a factor.
(2) n is a positive number having 6 as a factor.
OA C
Pl. help me with algebraic way as well as plug-in value way.
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The remainder, when a number n
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Say n = 6k + p; where k is any integer and p is any value among 1, 2, 3, 4, and 5.aaron1981 wrote:The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?
(1) n is a positive number having 8 as a factor.
(2) n is a positive number having 6 as a factor.
OA C
Pl. help me with algebraic way as well as plug-in value way.
Also, say n = 12m + q; where m is any integer and q is any value among 1, 2, 3, 4, ..., and 11.
We have to deduce whether p < q.
Statement 1: n is a positive number having 8 as a factor.
Since n is a positive number having 8 as a factor, n is one among 8, 18, 24, 32, 40, ...
Case 1: If n = 8, the remainder when n = 8 divided by 6 is p = 2, and the remainder when n = 8 divided by 12 is q = 8.
p = 2 < q = 8. The answer is YES.
Case 2: If n = 24, the remainder when n = 24 divided by 6 is p = 0, and the remainder when n = 24 divided by 12 is q = 0.
p = q = 0. The answer is No. No unique answer.
Statement 2: n is a positive number having 6 as a factor.
Since n is a positive number having 6 as a factor, n is one among 6, 12, 18, 24, ...
Case 1: If n = 6, the remainder when n = 6 divided by 6 is p = 0, and the remainder when n = 6 divided by 12 is q = 6.
p = 0 < q = 6. The answer is YES.
Case 2: If n = 24, the remainder when n = 24 divided by 6 is p = 0, and the remainder when n = 24 divided by 12 is q = 0.
p = q = 0. The answer is No. No unique answer.
Statement 1 & 2: n is a positive number having 6 as well as 8 as a factor.
=> n is a positive number having LCM of 6 and 8 as a factor.
LCM of 6 & 8 = 24.
=> n = 24k; k is any integer
Since 24 is divisible by 6 and 8, the reminders would be 0, thus p = q = 0. The answer is NO. A unique answer.
The correct answer: C
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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Statement 1:aaron1981 wrote:The remainder, when a number n is divided by 6, is p. The remainder, when the same number n is divided by 12, is q. Is p < q?
(1) n is a positive number having 8 as a factor.
(2) n is a positive number having 6 as a factor.
Case 1: n=8
Since n/6 = 8/6 = 1 R2, p=2.
Since n/12 = 8/12 = 0 R8, q=8.
In this case, p<q, with the result that the answer to the question stem is YES.
Case 2: n=16
Since n/6 = 16/6 = 2 R4, p=4.
Since n/12 = 16/12 = 1 R4, q=4.
In this case, p=q, with the result that the answer to the question stem is NO.
INSUFFICIENT.
Statement 2:
Case 3: n=6
Since n/6 = 6/6 = 1 R0, p=0.
Since n/12 = 6/12 = 0 R6, q=6.
In this case, p<q, with the result that the answer to the question stem is YES.
Case 3: n=12
Since n/6 = 12/6 = 2 R0, p=0.
Since n/12 = 12/12 = 1 R0, q=0.
In this case, p=q, with the result that the answer to the question stem is NO.
INSUFFICIENT.
Statements combined:
Since n must be divisible by 8 and 6, n must be a multiple of 24:
24, 48, 72...
Dividing a multiple of 12 by 6 will yield a remainder of 0.
Thus, p=0.
Dividing a multiple of 24 by 12 will also yield a remainder of 0.
Thus, q=0.
Since p=q, the answer to the question stem is NO.
SUFFICIENT.
The correct answer is C.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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