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.
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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.
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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.
- Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.
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