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
Data sufficiency
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(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.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
(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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Given: k > 0, integerJoy 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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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!
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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Another example of this question type from the Official Guide: https://gmatclub.com/forum/is-the-positi ... 67953.html
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