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When n is divided by 5, what is the remainder? [#permalink]

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01 Mar 2018, 09:12

MathRevolution wrote:

[GMAT math practice question]

When n is divided by \(5\), what is the remainder?

1) When \(n\) is divided by \(3\), the remainder is \(2\) 2) When \(n+1\) is divided by \(5\), the remainder is \(3\)

Statement 1: implies \(n=3k+2\). if \(k=1\), then \(n\) is divisible by \(5\), hence remainder will be \(0\) but if \(k=2\), then \(n=8\) and remainder will be \(3\). Insufficient

Statement 2: implies \(n+1=5q+3=>n=5q+2\). Hence when divided by \(5\), remainder will be \(2\). Sufficient

When n is divided by \(5\), what is the remainder?

1) When \(n\) is divided by \(3\), the remainder is \(2\) 2) When \(n+1\) is divided by \(5\), the remainder is \(3\)

Target question:When n is divided by 5, what is the remainder?

Statement 1: When n is divided by 3, the remainder is 2 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, if n divided by 3 yields a remainder of 2, some possible values of n are: 2, 5, 8, 11, 14, 17, etc Let's test two possible values of n Case a: n = 2. In this case, n divided by 5 yields are remainder of 2 Case b: n = 5. In this case, n divided by 5 yields are remainder of 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n+1 is divided by 5, the remainder is 3 There's a nice rule that says, 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

Given: When n+1 is divided by 5, the remainder is 3 We're not told the quotient (Q), so let's say the quotient is some integer k We can say "When n+1 is divided by 5, the quotient is k and the remainder is 3" So, we can say that n+1 = 5k + 3 Subtract 1 from both sides to get: n = 5k + 2 5k is a multiple of 5, so 5k+2 is 2 greater than some multiple of 5 So, if we divide 5k+2 by 5, the remainder will be 2. In other words, n divided by 5 yields are remainder of 2 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

=> Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. It is suggested we plug in numbers for the remainder questions.

Condition 1): \(n=3p+2=2,5,8\)…….. \(n = 2\) : The remainder of n is \(2\) when it is divided by \(5\). \(n = 5\) : The remainder of n is \(0\) when it is divided by \(5\).

Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2): We have \(n + 1 = 5q + 3\) for some integer, since \(n + 1\) has the remainder \(3\) when it is divided by \(5\). It is equivalent to \(n = 5q + 2=2,7,12,17,….\) The remainder is \(2\) when n is divided by \(5\). Thus condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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