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23 May 2020, 07:16
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B
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Difficulty:
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84% (01:04) correct
16%
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If n is a positive integer, is n odd?
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
DS21282
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
DS21282
Updated on: 17 May 2021, 07:42
Originally posted by BrentGMATPrepNow on 23 May 2020, 07:22.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:42, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:42, edited 1 time in total.
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Bunuel
If n is a positive integer, is n odd?
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
PS21282
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
PS21282
Target question: Is n odd?
---------------ASIDE------------------
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
---------------------------------------
Statement 1: When n is divided by 3, the remainder is 1.
So, some possible values of n are: 1, 4, 7, 10, 13, . . .
If n = 1, the answer to the target question is YES, n is odd
If n = 4, the answer to the target question is NO, n is not odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When n is divided by 8, the remainder is 1.
Some possible values of n are: 1, 9, 17, 25, 33, 41, 49, ...
So it certainly LOOKS LIKE n must be odd
Alternatively, statement 2 is telling us that n is 1 greater than some multiple of 8
Since all multiples of 8 are EVEN, we know that n is 1 greater than some EVEN integer. This means n must be odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
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23 May 2020, 07:38
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Bunuel
If n is a positive integer, is n odd?
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
PS21282
(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.
PS21282
the first thing that must come in thoughts are tables or multiples of 3 and 8, when you look at statements 1 and 2
table or multiple of 3= 3x = 3, 6, 9, 12, 15.... (odd, even, odd, even) ------ (i)
table or multiple of 8= 8x = 8,16,24,32,........ (even, even,,,,, always even) ------ (ii)
statement 1: When n is divided by 3, the remainder is 1.
from statement 1 we can say, n = 3x+1 (we know that 3x is odd, even , odd,,,,, from (i))
so, n=3x+1 = even, odd, even, odd, even........
so, n can be both even or odd
NOT SUFFICIENT
statement 2: When n is divided by 8, the remainder is 1.
from statement 2, we can say, n = 8x+1 (we know that 8x is always even)
therefore, adding 1 to 8x or adding 1 to an even number will always give an ODD Number.
n= odd
SUFFICIENT
hence, B
