shiblee wrote:

If m is a positive integer, is m/24 also an integer ?

(1) greatest common factor of m and 40 is 4

(2) greatest common factor of m and 84 is 12.

When will m/24 be an integer? When m is divisible by 24. Say, if m is 240, m/24 = 10 (an integer) but if m = 36, m/24 = 3/2 (not an integer)

So we need to find whether m is a multiple of 24 or not.

24 = 3*8.

So for m to be a multiple of 24, it should have both 3 and 8 as factors.

(1) greatest common factor of m and 40 is 4

40 = 5*8

Greatest common factor between 40 and m is 4. This means m has 4 as a factor but does not have 8 as a factor. If m had 8 as a factor too, the greatest common factor between 40 and m would have been 8 because 40 has an 8. Since m does not have 8 as a factor, it is not a multiple of 24 so m/24 is not an integer. Sufficient

(2) greatest common factor of m and 84 is 12.

84 = 3*4*7

m has 12 i.e. 3 and 4 as factors but we do not know whether it has 8 as a factor or not. Note why this statement is different from statement 1. In statement 1, 40 has 8 as a factor but since the GCF is 4 only, we know m does not have 8.

Here, 84 itself does not have 8 as a factor so we can't say whether m has 8 as a factor or not. It is possible that m had 8 as a factor but since 84 doesn't have it, GCF is 12 only. It is also possible that m does not have 8 as a factor. Hence, this statement alone is not sufficient.

Answer (A)

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Karishma

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