Practice GMAT Data Sufficiency Question
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If N, C, and D are positive integers, what is the remainder when D is divided by C?
 If D+1 is divided by C+1, the remainder is 5.
 If ND+NC is divided by CN, the remainder is 5.
Correct Answer: B
 For some students, the theoretical nature of this question makes it intimidating. For these individuals, we recommend picking numbers as a means of determining sufficiency.

Evaluate Statement (1) alone.
 Draw a table to quickly pick numbers in order to determine whether Statement (1) is sufficient. It is quickest to choose numbers for D+1 and C+1 that work (i.e., produce a remainder of 5) and then infer the values of D and C.
Let R(X/Y) = the remainder of X/Y
D C D+1 C+1 R[(D+1)/(C+1)] R(D/C) 14 9 15 10 5 5 22 5 23 6 5 2 44 19 45 20 5 6  Different legitimate values of D+1 and C+1 yield different remainders for D/C. Consequently, the information in Statement (1) is not sufficient to determine the remainder when D is divided by C.
 Algebraically, we know that D+1 divided by C+1 will not have the same remainder as D divided by C since fractions do not stay equivalent when you add to them (i.e., x divided by y does not equal x+1 divided by y+1).
 Statement (1) alone is NOT SUFFICIENT.
 Draw a table to quickly pick numbers in order to determine whether Statement (1) is sufficient. It is quickest to choose numbers for D+1 and C+1 that work (i.e., produce a remainder of 5) and then infer the values of D and C.

Evaluate Statement (2) alone.
 Before evaluating Statement (2), it is essential to simplify by factoring the numerator:
ND + NC = N(D+C)
Cancel out the N in both the numerator and denominator. Statement (2) can be simplified to: If D+C is divided by C, the remainder is 5.  We can further simplify by noticing that D+C divided by C is equal to D divided by C plus C divided by C.
 There are two parts to this equation: (1) D divided by C (2) the number 1
The sum of parts (1) and (2) will always have a remainder of 5 (this is what Statement 2 says). This remainder cannot come from the second part (i.e., C divided by C equals +1 and there is no remainder).
Consequently, the remainder of 5 must come from D divided by C. So, we know that D divided by C will always produce a remainder of 5, which provides sufficient information to answer the original question.  Statement (2) alone is SUFFICIENT.
 Before evaluating Statement (2), it is essential to simplify by factoring the numerator:
 Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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