If m and n are nonzero integers and 390m = 150n, then mn must be divis

Question

If m and n are nonzero integers and 390m = 150n, then mn must be divisible by

A. 10
B. 45
C. 50
D. 65
E. 70

Bunuel · Answer

390m = 150n;

m/n = 5/13.

m is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13 = 65.

Answer: D.

Abhishek009 · Answer

Is this a GMAT Question ( Wondering just because of 4 options ) ?

Anyways -

390m = 150n

Or, 390m = 150n = 1950  { 1950 is the LCM of 390 & 150 }

So, m = 5 & n = 13

So, m*n = 13*5 => 65

Hence only (D) is our answer...

Hope this helps !!

voccubd · Answer

I'm not sure. This was collected from an MBA admission test question of IBA, Dhaka University. They usually follow Gmat a lot. Thanks for your help.

Abhishek009 · Answer

390m = 150n = 1950

Or, m = 5 & n = 13

So, mn = 65

Thus mn must be divisible by 65
 
Answer must be (D) 65

ScottTargetTestPrep · Answer

We can start by simplifying the equation 390m = 150n.

390m = 150n

39m = 15n

13m = 5n

Since 13m = 5n, n = 13m/5 and m = 5n/13. We see that m is a multiple of 5 and n is a multiple of 13. Since 13 is the smallest positive multiple of 13, and 5 is the smallest multiple of 5, the product of m and n MUST be divisible by 5 x 13 = 65.

Answer: D

Advait01 · Answer

We can start by simplifying the equation 390m = 150n.

390m = 150n

39m = 15n

13m = 5n

Since m/n = 5/13. We see that m is a multiple of 5 and n is a multiple of 13. Since 13 is the smallest positive multiple of 13, and 5 is the smallest multiple of 5, the product of m and n MUST be divisible by 5 x 13 = 65.

Answer: D

If m and n are nonzero integers and 390m = 150n, then mn must be divis

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GMAT Problem Solving (PS) Questions

If m and n are nonzero integers and 390m = 150n, then mn must be divis

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