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03 Feb 2021, 01:15
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C
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45%
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wrong
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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.
Are You Up For the Challenge: 700 Level Questions
(1) n is a positive number having 8 as a factor.
(2) n is a positive number having 6 as a factor.
Are You Up For the Challenge: 700 Level Questions
03 Feb 2021, 05:54
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Bunuel
n=6x+p.
If x is even, say x=2y, then the answer is No, as n=6(2y)+p=12y+p. Thus, p=q.
If x is odd, say x=2y-1, then n=6(2y-1)+p=12y-6+p=12(y-1)+6+p. Thus q=6+p, and ans is Yes as p<q.
(1) n is a positive number having 8 as a factor.
n=8a=6x+p
Say a=x=1, then x is odd and answer is YES. If n=8, then p=2, but q=8.
But say a=2 and x=2, then x is even and answer is NO. If n=16, then p=q=4
Insufficient
(2) n is a positive number having 6 as a factor.
n=6b=6x+p
This means that p=0.
x=1, then n=6. p=0, but q=6.
x=2, then n=12. p=q=0.
Insufficient
Combined
The number n is multiple of both 8 and 6 or multiple of LCM(6,8), that is 24.
So n=24z=6*(4z). Thus x is even.
Also divisible by 24 means divisible by all its factors : 1,2,3,4,6,8,12,24
remainder is 0 in each case, that is p=q
Sufficient
C
03 Feb 2021, 12:28
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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?
Stat1: n is a positive number having 8 as a factor.
n/6, remainder p = 2,4,0,2.. and n/12, remainder q = 8,4,0,8...., so, for p<q, not sufficient
Stat2: n is a positive number having 6 as a factor.
n/6, remainder p = 0. and n/12, remainder q = 6,0,6...., so, for p<q, not sufficient
Combining both, LCM (8,6)= 24
n/6, remainder p = 0. and n/12, remainder q = 0 so, p=q Sufficient
So, I think C.
Stat1: n is a positive number having 8 as a factor.
n/6, remainder p = 2,4,0,2.. and n/12, remainder q = 8,4,0,8...., so, for p<q, not sufficient
Stat2: n is a positive number having 6 as a factor.
n/6, remainder p = 0. and n/12, remainder q = 6,0,6...., so, for p<q, not sufficient
Combining both, LCM (8,6)= 24
n/6, remainder p = 0. and n/12, remainder q = 0 so, p=q Sufficient
So, I think C.
