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When positive integer n is divided by 3, the remainder is 2 [#permalink]
 01 Nov 2009, 13:06
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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.
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Re: DS problem : remainders [#permalink]
28 Nov 2010, 18:36
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hogwarts wrote: Saw this question on a GMATPrep test, and I can't figure out how to get to the correct answer. Can anyone help?  Thanks! 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. The correct answer is (C) - both statements together are sufficient, but neither statement alone is sufficient. Can anybody out there help explain to me how to get to this answer though? Thanks! This is how I would approach this question. When positive integer n is divided by 3, the remainder is 2; I say n = 3a + 2 ( a is a non negative integer) and when positive integer t is divided by 5, the remainder is 3. So t = 5b + 3 (b is a non negative integer.) What is the remainder when the product nt is divided by 15?So nt = (3a + 2)(5b + 3) = 15ab + 9a + 10b + 6 15ab is divisible by 15. But I don't know anything about ( 9a + 10b + 6) yet. Stmnt 1: n-2 is divisible by 5. From above, n - 2 is just 3a. If n - 2 is divisible by 5, then 'a' must be divisible by 5. So I get that 9a is divisible by 15. I still don't know anything about b. If b = 1, remainder of nt is 1. If b = 2, remainder of nt is 11 and so on... Not sufficient. Stmnt 2: t is divisible by 3. If t is divisible by 3, then (5b + 3) is divisible by 3. Therefore, b must be divisible by 3. (If this is unclear, think: 15 + 3 will be divisible by 3 but 20 + 3 will not be. If the second term is 3, the first term must also be divisible by 3 to make the whole expression divisible by 3). So 10b is divisible by 15 but we do not know anything about a. If a = 1, remainder of nt is 0, if a = 2, remainder of nt is 9. Not sufficient. Using both statements together, we know 9a and 10b are divisible by 15. So remainder must be 6. Sufficient. Answer (C).
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Re: GMAT Prep 2 remainder [#permalink]
01 Nov 2009, 14:07
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. From the stem: n=3p+2 and t=5q+3. nt=15pq+9p+10q+6, we should find the remainder when this expression is divided by 15. (1) n-2=5m --> n=5m+2=3p+2 --> 5m=3p, 15m=9p --> nt=15pq+9p+10q+6=15pq+15m+10q+6. Clearly 15pq and 15m are divisible by 15, so remainder by dividing these components will be 0. But we still know nothing about 10q+6. Not sufficient. (2) t is divisible by 3 means that 5q+3 is divisible by 3 --> 5q is divisible by 3 or q is divisible by 3 --> 5q=5*3z=15z --> 10q=30z --> nt=15pq+9p+10q+6=15pq+9p+30z+6. 15pq and 30z are divisible by 15. Know nothing about 9p+6. Not sufficient. (1)+(2) 9p=15m and 10q=30z --> nt=15pq+9p+10q+6=15pq+15m+30z+6. Remainder when this expression is divided by 15 is 6. Sufficient. Answer: C. OR:From the stem: n=3p+2 and t=5q+3. (1) n-2 is divisible by 5 --> n-2=5m --> n=5m+2 and n=3p+2 --> general formula for n would be n=15k+2 (about deriving general formula for such problems at: good-problem-90442.html#p723049 and manhattan-remainder-problem-93752.html#p721341) --> nt=(15k+2)(5q+3)=15*5kq+15*3k+10q+6 --> first two terms are divisible by 15 ( 15*5kq+15*3k) but we don't know about the last two terms ( 10q+6). Not sufficient. (2) t is divisible by 3 --> t=3r and t=5q+3 --> general formula for t would be t=15x+3 --> nt=(3p+2)(15x+3)=15*3px+9p+15*2x+6. Not sufficient. (1)+(2) nt=(15k+2)(15x+3)=15*15kx+15*3k+15*2x+6 this expression divided by 15 yields remainder of 6. Sufficient. Answer: C.
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Use Remainders to Figure out Multiples [#permalink]
18 May 2010, 13:24
I educated guessed and got it right...no clue how I'd approach this. Thoughts?
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Re: GMAT Prep 2 remainder [#permalink]
24 May 2010, 17:52
If the explanation above is not helpful, you may find a step by step video solution of this question useful. On GMATFix site, this is GMATPrep question 1045
Best of luck,
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DS problem : remainders [#permalink]
28 Nov 2010, 15:24
Saw this question on a GMATPrep test, and I can't figure out how to get to the correct answer. Can anyone help? Thanks! 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. The correct answer is (C) - both statements together are sufficient, but neither statement alone is sufficient. Can anybody out there help explain to me how to get to this answer though? Thanks!
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Re: GMAT Prep 2 remainder [#permalink]
16 Mar 2011, 00:55
Bunuel 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.
Answer: C. I have another approach to this ds, plz correct me if i'm wrong. n=3x + 2 t = 5y + 3 Clearly we cannot solve the problem with either n or t. We need both information concerning n and t because we need to figure out the remaining of n*t. => left with C or E (1): n-2 is divisible by 5 & n=3x + 2 => x is multiple of 5. (2): t is divisible by 3. & t = 5y + 3 => y is multiple of 3 (1)& (2) => n*t = (3x+2) (5y+3) = (3x*5y) + (9x) + (10y) + 6 we know that: x is multiple of 5, y is multiple of 3 so: (3x*5y) + (9x) + (10y) + 6 will have remaining of 6 because: each (3x*5y); (9x); (10y) is all multiple of 15.
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Re: GMAT Prep 2 remainder [#permalink]
17 Mar 2011, 00:34
I tried plugging numbers: n = 3k + 2 = 2,5,8,11,14,17 t = 5m + 3 = 3,8,13,18,23,28 (1) n - 2 = 5l => n = 5l + 2 = 2,7,12,17 So n = 15k + 2 = 2,17,32,47 But n* t = 6 (2*3), 16(2*8) so n/15 can have rem 1 or 6 Hence (1) is not enough (2) t = 3p = 3,6,12,15,18,21 So t = 15q + 3 = 3,18,33,48 But n*t = 6, 15, so rem can be 6, 0 etc. Combining (1) and (2), it can be seen that nt = 15 * an integer + 6, so remainder is 6, answer is C.
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Re: GMAT Prep 2 remainder [#permalink]
02 Oct 2011, 17:42
I did a similar thing with plugging numbers.
First you have to see that (1) and (2) alone are not sufficient alone before it really works in a time effective manner though.
(1) n = 17,32,47,etc, t still has so many values and remainder can differ (17*3 and 17*8 for example)
(2) t = 18,33,48,etc, same as above but with n
(1)+(2)
(15p+2)(15p+3) will always have r6 when divided by 15
breaking it out in factored form like that is helpful for me to see it very clearly.
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Re: GMAT Prep 2 remainder
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02 Oct 2011, 17:42
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