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30 Jan 2017, 02:46
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B
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Difficulty:
15%
(low)
Question Stats:
82% (00:52) correct
18%
(00:53)
wrong
based on 78
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When a positive integer n is divided by 2, what is the remainder?
1) The remainder is 1 when n is divided by 5
2) The remainder is 1 when n is divided by 10
1) The remainder is 1 when n is divided by 5
2) The remainder is 1 when n is divided by 10
30 Jan 2017, 08:05
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MathRevolution
1) when n is even multiple of 5 then n+1 =odd thus remainder =1 (eg:- n=5*2=10)
when n is odd multiple of 5 then n+1 = even thus remainder =0 (eg:- n=5*3=15)
hence not suff
2) As 10 is even number thus any multiple of 10 will give even number
thus n = odd always
remainder=1
suff
Ans B
01 Feb 2017, 02:29
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==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you can solve it by using direct substitution.
For con 1), from n=5p+1(p=any positive integer), you get n=1,6,… However, from n=1=2(0)+1, you get r=1, but n=6=2(3)+0, you get r=0, hence it is not unique and not sufficient.
For con 2), from n=10q+1(q=any positive integer), you get n=1,11,21,… However, for all cases, the remainder=1, hence it is unique and sufficient.
Therefore, the answer is B
For con 1), from n=5p+1(p=any positive integer), you get n=1,6,… However, from n=1=2(0)+1, you get r=1, but n=6=2(3)+0, you get r=0, hence it is not unique and not sufficient.
For con 2), from n=10q+1(q=any positive integer), you get n=1,11,21,… However, for all cases, the remainder=1, hence it is unique and sufficient.
Therefore, the answer is B
