If j and k are different positive odd integers, are j and k both divis

Question

If j and k are different positive odd integers, are j and k both divisible by 7?

(1) j + k is divisible by 7.
(2) j − k is divisible by 14.

JerryAtDreamScore · Answer

Breaking Down the Info:

Both statements individually talk about the sum or difference of j and k. We cannot know anything about j or k alone, so both statements alone are insufficient.

Both Statements Combined:

From (2), we can infer that j - k is also divisible by 7 if it is divisible by 14. Therefore  j + k  and  j - k  are both multiples of 7.

If we add two multiples of 7, we still get a multiple of 7, so  j + k + j - k = 2j  is a multiple of 7. Since j is an integer, our factor of 7 must belong to the j (and not 2). Therefore j itself is a multiple of 7.

Similarly, subtract the two numbers to get  j + k - (j - k) = 2k  is also a multiple of 7. Therefore k is a multiple of 7. Then combined it is sufficient.

Answer: C

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If j and k are different positive odd integers, are j and k both divis

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