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The product of two numbers is 5760 and their highest common factor is 12. How many such pairs are possible?

a. 1

b. 3

c. 2

d. 4

***My answer is (b) 3. My reasoning is as follows. Let x and y equal the two numbers.

12x * 12y = 5760

12xy = 5760

xy = 480

Possible pairs that total the product 480 are:

1*480; 2*240; 3*160, 4*120; 5*96; 6*80; 10*48; 12*40

Eliminate pairs that are not prime to one another leaves pairs:

1*480; 3*160 and 5*96

Official answer is answer choice (c) 2

Anyone?

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Pls include reasoning along with all answer posts.

****GMAT Loco****

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