Practice GMAT Data Sufficiency Question
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If x is a positive integer, is x divided by 5 an odd integer?
- x contains only odd factors
- x is a multiple of 5
Correct Answer: C
- A number divided by 5 will be an odd integer if and only if that number contains only odd factors, one of which is 5. In other words, there are two conditions under which x divided by 5 will be an odd integer:
(1) x is a multiple of 5
(2) x contains only odd factors
-
Evaluate Statement (1) alone.
- If x contains only odd factors, there is no guarantee that one of those factors is 5. Consequently, there is no guarantee that x will be divisible by 5.
- For example:
9 = 3*3 --> not an odd integer when divided by 5 since 5 is not a factor
21 = 3*7 --> not an odd integer when divided by 5 since 5 is not a factor
15 = 3*5 --> an odd integer when divided by 5 since 5 is a factor
105 = 3*7*5 --> an odd integer when divided by 5 since 5 is a factor
- Statement (1) alone is NOT SUFFICIENT.
-
Evaluate Statement (2) alone.
- Simply because x is a multiple of 5 does not guarantee that x only contains odd factors. Consequently, there is no guarantee that x is divisible by 5.
5 = 5*1 --> an odd integer when divided by 5 because 5 is a factor and there are only odd factors
15 = 5*3 --> an odd integer when divided by 5 because 5 is a factor and there are only odd factors
25 = 5*5 --> an odd integer when divided by 5 because 5 is a factor and there are only odd factors
20 = 5*4 --> not an odd integer when divided by 5 because there is at least one even factor
30 = 6*5 --> not an odd integer when divided by 5 because there is at least one even factor
- Statement (2) alone is NOT SUFFICIENT.
-
Evaluate Statements (1) and (2) together.
- With only odd factors and x as a multiple of 5 (i.e., with 5 as a factor), you know that x divided by 5 must be an odd number since the two conditions laid out earlier are fulfilled.
- Consider the following examples:
5 = 5*1 --> an odd integer when divided by 5
15 = 5*3 --> an odd integer when divided by 5
25 = 5*5 --> an odd integer when divided by 5
35 = 5*7 --> an odd integer when divided by 5
- Statements (1) and (2), when taken together, are SUFFICIENT.
- Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is NOT SUFFICIENT, but Statements (1) and (2), when taken together, are SUFFICIENT, answer C is correct.
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