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# When positive integer n is divided by 3, the remainder is 2;

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Senior Manager
Joined: 07 Mar 2006
Posts: 352
When positive integer n is divided by 3, the remainder is 2; [#permalink]

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29 Jul 2006, 23:01
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When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

(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
Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes

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29 Jul 2006, 23:19
zoom612 wrote:
When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

C must be it!

Given
n = 3k+2 and t=5l+3

S1. n-2 = 5m => n = 5m+2
Thus, n = 15q+2 insufficient.

S2. t = 3m
Thus, t= 15Q+3 insufficient.

Combine S1 and S2
nt = (15q+2)(15Q+3)
remainder is 2*3 = 6
sufficient
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Re: DS: Gmat prep   [#permalink] 29 Jul 2006, 23:19
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