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When positive integer n is divisible by 3, the remainder is [#permalink]

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30 Jan 2008, 02:04

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When positive integer “n” is divisible 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?

When positive integer “n” is divisible 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.

Could you please explain in detail? Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2 t = 5m + 3

Also (n-2) is divisible by 5 => 3k is divisible by 5 => k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3) => nt = 15km + 9k + 10m + 6

when divided by 15, you get nt = 15(km + 3k/5 + 5m/3) + 6 since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.
_________________

When positive integer “n” is divisible 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?

nt = (3k + 2) * (5m + 3) => nt = 15km + 9k + 10m + 6

when divided by 15, you get nt = 15(km + 3k/5 + 5m/3) + 6 since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

When positive integer “n” is divisible 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.

Could you please explain in detail? Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2 t = 5m + 3

Also (n-2) is divisible by 5 => 3k is divisible by 5 => k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3) => nt = 15km + 9k + 10m + 6

when divided by 15, you get nt = 15(km + 3k/5 + 5m/3) + 6 since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

When positive integer “n” is divisible 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.

Could you please explain in detail? Thank you.

1) and 2) alone are insufficient

The answer should be (C). The remainder will come to 6

n = 3k + 2 t = 5m + 3

Also (n-2) is divisible by 5 => 3k is divisible by 5 => k is divisible by 5

Similarly, m is divisible by 3

nt = (3k + 2) * (5m + 3) => nt = 15km + 9k + 10m + 6

when divided by 15, you get nt = 15(km + 3k/5 + 5m/3) + 6 since k is divisible by 5 and m is divisible by 3, the first 3 terms are not relevant to the remainder, leaving 6 as the answer.

Jimmy you're right - it should be 2m/3 instead of 5m/3, but shouldn't affect the overall solution
_________________

When positive integer “n” is divisible 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?