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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
For positive integers m and n, when n is divided by 7, the quotient is
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22 Apr 2020, 23:47
As per question data, m and n are positive integers. Also, when n is divided by 7, the quotient is m and the remainder is 2.
Dividend = Divisor * Quotient + Remainder.
Therefore, n = 7 * m + 2. Since m is a positive integer, m = 1 or 2 or 3 and so on.
From statement I alone, when n is divided by 11, the remainder is 2. From the question data, when n is divided by 7, the remainder is 2.
Therefore, n = LCM (7, 11) k + 2, i.e. n = 77k + 2.
The possible values of n are 79, 156 and so on. Since n = 7m +2, the possible values of m are 11, 22 and so on.
For any of these values of m, the remainder will be ZERO when m is divided by 11. Statement I alone is sufficient to answer the question. Answer options B, C and E can be eliminated. Possible answer options are A or D.
From statement II alone, when m is divided by 13, the remainder is 0. This means that m is a multiple of 13. Therefore, m = 13 or 26 or 39…. and so on. The possible remainders, when m is divided by 11 are 2, 4, 6 and so on.
Statement II alone is insufficient to find a unique value for the remainder. Answer option D can be eliminated.