# Practice GMAT Data Sufficiency Question

If N, C, and D are positive integers, what is the remainder when D is divided by C?
1. If D+1 is divided by C+1, the remainder is 5.
2. If ND+NC is divided by CN, the remainder is 5.
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. 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.
2. Evaluate Statement (1) alone.
1. 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
2. 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.
3. 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).
4. Statement (1) alone is NOT SUFFICIENT.
3. Evaluate Statement (2) alone.
1. 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.
2. We can further simplify by noticing that D+C divided by C is equal to D divided by C plus C divided by C. 3. 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.
4. Statement (2) alone is SUFFICIENT.
4. Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.