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# When positive integer n is divided by 7, the remainder is 2.

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Current Student
Joined: 11 May 2008
Posts: 552
When positive integer n is divided by 7, the remainder is 2. [#permalink]

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31 Jul 2008, 10:59
When positive integer n is divided by 7, the remainder is 2. n=?
(1) n is less than 20.
(2) when n is divided by 8, the remainder is 0.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Joined: 30 Apr 2008
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31 Jul 2008, 11:04
C

First could be either 9 or 16

Second could be a whole bunch of numbers. (i.e., 16, 72, 128, 184, etc.)

Only when we take the two of them together can we rule out every number in the list for #2 that is above 20 and come up with 1 single value for $$n$$.

arjtryarjtry wrote:
When positive integer n is divided by 7, the remainder is 2. n=?
(1) n is less than 20.
(2) when n is divided by 8, the remainder is 0.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Current Student
Joined: 11 May 2008
Posts: 552

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31 Jul 2008, 11:07
allen.. correct
Senior Manager
Joined: 23 May 2006
Posts: 309

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31 Jul 2008, 11:08
arjtryarjtry wrote:
When positive integer n is divided by 7, the remainder is 2. n=?
(1) n is less than 20.
(2) when n is divided by 8, the remainder is 0.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

S1. n < 20 hence n coud be 2,9,16; all divided by 7 leave a remainder of 2. MAYBE CASE AD out
S2. you can rearrange to say that n is a multiple of 8. Hence 16 and 72 both divided by 7 leave a remainder of two and both are divisible by 8 and leave a remainder of 0. Again Maybe case B out

Combine: you still get only 16 as the common value.
Hence C
Intern
Joined: 12 Jun 2008
Posts: 12

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31 Jul 2008, 11:20
arjtryarjtry wrote:
When positive integer n is divided by 7, the remainder is 2. n=?
(1) n is less than 20.
(2) when n is divided by 8, the remainder is 0.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

C is correct.
reason:
we should n=7x+2
1)==we also know n<20,so 7x+2<20 and n is positive , so 0<7x+2<20.==>n only can be 2,9, 16
2)==>n=8y..so n=7x+2,we can know their common divider is 56(7x8,they are prime number)
so n=56b+16..many numbers are suited for this equlation.
So 1and 2 ,we can get 16 is the only number.
SVP
Joined: 07 Nov 2007
Posts: 1757
Location: New York

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31 Jul 2008, 11:49
arjtryarjtry wrote:
When positive integer n is divided by 7, the remainder is 2. n=?
(1) n is less than 20.
(2) when n is divided by 8, the remainder is 0.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

state 1) n is less than 20 --insufficient
2, 9, 16 -- divided by 7 leads to remainder 2
state 2) when n is divided by 8 remainder 0--> 8, 16,24....
--insufficient

combine both.. n=16 (suff)

C

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Re: what is N?   [#permalink] 31 Jul 2008, 11:49
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# When positive integer n is divided by 7, the remainder is 2.

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