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Re: For positive integers m and n, when n is divided by 7, the quotient is
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22 Nov 2016, 05:59

Top Contributor

Bunuel wrote:

For positive integers m and n, when n is divided by 7, the quotient is m and the remainder is 2. What is the remainder when m is divided by 11?

(1) When n is divided by 11, the remainder is 2. (2) When m is divided by 13, the remainder is 0.

Target question:What is the remainder when m is divided by 11?

Given: When n is divided by 7, the quotient is m and the remainder is 2 There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

So, with the given information, we can write: n = 7m + 2

Statement 1: When n is divided by 11, the remainder is 2. In other words, n divided by 11 equals some unstated integer (say k) with remainder 2. Applying the above rule, we can write: n = 11k + 2 (where k is some integer) Since we already know that n = 7m + 2, we write the following equation: 7m + 2 = 11k + 2 Subtract 2 from both sides to get: 7m = 11k Divide both sides by 7 to get: m = 11k/7 Or we can say m = (11)(k/7) What does this tell us? First, it tells us that, since m is an integer, it MUST be true that k is divisible by 7. It also tells us that m is divisible by 11 If m is divisible by 11, then when m is divided by 11, the remainder will be 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: When m is divided by 13, the remainder is 0 Applying the above rule, we can write: m = 13j (where j is some integer) We already know that n = 7m + 2, but that doesn't help us much this time. We COULD take n = 7m + 2 and replace m with 13j to get n = 7(13j) + 2. However, this doesn't get us very far, since the target question is all about what happens when we divide m by 11, and our new equation doesn't even include m. At this point, I suggest that we start TESTING VALUES. There are several values of m that satisfy statement 2. Here are two: Case a: m = 13, in which case m divided by 11 gives us a remainder of 2 Case b: m = 26, in which case m divided by 11 gives us a remainder of 4 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Re: For positive integers m and n, when n is divided by 7, the quotient is
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06 Oct 2018, 08:56

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