Problem Solving

Hmna wrote:If M and N are negative integers and 5M - 4N = 20, which of the following CAN NOT be a value of M?
A) -4
B) -8
C) -10
D) -12

Given: 5M - 4N = 20
Add 4N to get: 5M = 20 + 4N
Divide by 5 to get: M = 4 + 4N/5
Factor out a 4 to get: M = 4(1 + N/5)
This tells us that M must be a multiple of 4 (it also tells us that N must be a multiple of 5, in order for N/5 to be an integer)

Since M must be a multiple of 4, we can see that the correct answer is C

Cheers,
Brent

Hi hoppycat,

TESTing THE ANSWERS can be a fast and easy way to tackle certain Quant questions (and you'll see at least a few opportunities on the Official GMAT to do so). And to answer your question: YES, that's a great way to approach this question.

GMAT assassins aren't born, they're made,
Rich

hoppycat wrote:

Hmna wrote:If M and N are negative integers and 5M - 4N = 20, which of the following CAN NOT be a value of M?
A) - 4
B) - 8
C) - 10
D) - 12

I tested each answer
For A I got M = -4 and N = -10
For B I got M = -8 and N = -15
For C I got M = -10 and N = -17.5 which isn't an integer
Is this a valid way to go?

If anything, your approach might actually be faster

Hmna wrote:If M and N are negative integers and 5M - 4N = 20, which of the following CAN NOT be a value of M?
A) - 4
B) - 8
C) - 10
D) - 12

I think plug-in the values approach is the most efficient for this particular problem.

Here is the Algebraic route to this problem.

We have 5M - 4N = 20

=> -5|M| + 4|N| = 20; since M and N are negative integers

=> |M| = [4|N| - 20]/5

=> |M| = (4/5)*|N| - 4

Since M is an integer, (4/5)*|N| must be an integer. thus, |N| must be a multiple of 5.

Thus, N can be -5, -10, -15, -20, etc.

N ≠ -5 since this leads to |M| = 0, which is not possible as M a negative integer

For N = -10, |M| = (4/5)*|-10| - 4 = 8 - 4 = 4 => M = -4 --- Oprion A is possible
For N = -15, |M| = (4/5)*|-15| - 4 = 12 - 4 = 8 => M = -8 --- Oprion B is possible
For N = -20, |M| = (4/5)*|-20| - 4 = 16 - 4 = 12 => M = -12 --- Oprion D is possible

The correct answer: C

Hope this helps!

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Hmna wrote:If M and N are negative integers and 5M - 4N = 20, which of the following CAN NOT be a value of M?
A) - 4
B) - 8
C) - 10
D) - 12

We are given that M and N are negative integers. Let's isolate N in the equation 5M - 4N = 20:

5M - 20 = 4N

N = (5M - 20)/4

N = 5M/4 - 5

We see that the only way N can be an integer is if M is divisible by 4 (since 5 is not divisible by 4). Looking at the choices, only -10 is not divisible by 4; thus, it cannot be a value of M.

Answer: C