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Data sufficiency

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by 800_or_bust » Thu Jul 07, 2016 6:08 am
Joy Shaha wrote:Q. If k is a positive integer, is k a multiple of 40?
K is a multiple of 4
K is a multiple of 10
(1) NOT SUFFICIENT. K could be 4, which is obviously not a multiple of 40, or K could be 40, which is a multiple of 40.

(2) NOT SUFFICIENT. K could be 10, which is not a multiple of 40. Or K could be 40, which is a multiple of 40.

(1) & (2) Combined. NOT SUFFICIENT. K could be 20 (i.e. 5x4 = 2x10), which is not a multiple of 40. Or K could be 40, which is a multiple of 40.

Answer choice: E
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by OptimusPrep » Thu Jul 07, 2016 8:47 am
Joy Shaha wrote:Q. If k is a positive integer, is k a multiple of 40?
K is a multiple of 4
K is a multiple of 10
Given: k > 0, integer
Required: Is k a multiple of 40?

Statement 1: k is a multiple of 4
Case 1: k = 8, here k is not a multiple of 40
Case 2: k = 40, here k is a multiple of 40
INSUFFICIENT

Statement 2: k is a multiple of 10
Case 1: k = 20, k is not a multiple of 40
Case 2: k = 40, k is a multiple of 40
INSUFFICIENT

Combining both statements:
k is a multiple of 4 and 10. Hence k will be a multiple of the LCM (20)
Case 1: k = 20, not a multiple of 40
Case 2: k = 40, multiple of 40
INSUFFICIENT

Correct Option: E
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by [email protected] » Thu Jul 07, 2016 6:23 pm
Hi Joy Shaha,

This question can be solved rather easily by TESTing VALUES. You might also find it useful to 'brute force' the solution by quickly writing down a bunch of examples so that you can physically 'see' the possibilities:

We're told that K is a positive integer. We're asked if K is a multiple of 40. This is a YES/NO question.

1) K is a multiple of 4

With this Fact, we know that K could be 4, 8, 12, 16, 20, 24, 28, 32, 36, 40....

IF....
K = 4, then the answer to the question is NO.
K = 40, then the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) K is a multiple of 10

With this Fact, we know that K could be 10, 20, 30, 40....

IF....
K = 10, then the answer to the question is NO.
K = 40, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that K has to be a multiple of 4 AND a multiple of 10. From our two lists of possibilities, we can see two possible values for K that fit BOTH pieces of information:

IF....
K = 20, then the answer to the question is NO.
K = 40, then the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer: E

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by Matt@VeritasPrep » Fri Jul 08, 2016 1:56 pm
The basic idea here: if x is a multiple of a and of b, then x is a multiple of the LCM of a and b.

In our case, the LCM of 4 and 10 is 20, so we know k is a multiple of 20. Some multiples of 20 are multiples of 40, some are not, so the answer is E.

This is also a classic example of the too-easy C. If you find yourself thinking, "Ha! Obviously C" ... THE ANSWER IS ALMOST CERTAINLY NOT C! Run screaming from it, and pick something else!
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by 800_or_bust » Fri Jul 08, 2016 2:48 pm
Another example of this question type from the Official Guide: https://gmatclub.com/forum/is-the-positi ... 67953.html
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