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a70
If m and n are positive integers and m*n = 40 what is m+n?


(1) The number of positive factors of m is twice the number of positive factors of n.

(2) m has 4 different positive factors

Given that m×n=40 where m and n are positive integers.

1. The number of positive factors of m is twice the number of positive factors of n

The positive factors of 40 are: 1, 2, 4, 5, 8, 10, 20 and 40

And the number of positive factors of these factors of 40 is as under:

1 has only 1 positive factor

2 has two positive factors

4 has three positive factors

5 has two positive factors

8 has four positive factors

10 has four positive factors

20 has six positive factors

40 has eight positive factors

Since, the number of positive factors of m is twice the number of positive factors of n and

as, m×n=40
Thus, the only possible values m and n could hold will be when;

n = 5 and m = 8 because 5 has two positive factors and 8 has four positive factors and their

product is 40

Therefore, m+n=5+8=13 hence giving us a definite value.

Hence, statement (1) alone is sufficient.

2. m has four positive factors.

Since, m has four positive factors, so m could be 8 or 10

Accordingly n will be 5 or 4

Thus, m + n could be equal to (8 + 5) = 13 or (10 + 4) = 14, hence, not getting a definite value

of m + n.

Hence, statement (2) alone is insufficient.
answer is A.
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Hello from the GMAT Club BumpBot!

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