GetThisDone wrote:

Is mp greater than m?

(1) m > p > 0

(2) p is less than 1

Hello experts,

Could anyone please explain how to approach this problem algebraically. As detailed an explanation as possible will be greatly appreciated. I was trying to understand the following.

a. I am clear on getting the first set of roots based on the information given in the stem. i.e mp-m>o --> m(p-1)>0. So m>0 and P>1. But didn't understand the reasoning behind obtaining the second set of roots by flipping the signs.

b. Also need help on understanding how to use the obtained roots in conjunction with options (1) and (2).

There are some great takeaways on number properties in this question. Let's look at them:

Question: Is mp greater than m?

Forget greater, think less because it is less intuitive so there will be fewer cases to worry about. When will the product of 2 numbers be less than one of them? Two simple cases we can think of are 6*(1/2) = 3 or 6*(-3) = -18 (One number is greater than 1 and the other is less than 1, one number is positive and the other is negative).

Numbers between 0 to 1 when multiplied to positive numbers, make the product smaller.

Numbers between 0 to 1 when multiplied to negative numbers, make the product greater because the product becomes 'less negative'.

Negative numbers when multiplied to positive numbers make the product smaller (negative).

Now go on to the statements:

(1) m > p > 0

This only tells us that both the numbers are positive. We don't know whether p is less than 1 or greater than 1. Not sufficient.

(2) p is less than 1

If p is less than 1, it will make the product mp less than m if m is positive. But if m is negative, the product will become greater. Not sufficient.

Using both, given that m is positive and p is less than 1, we can say that the product mp will be less than m. Hence, together both the statements are sufficient.

Answer (C)

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Karishma

Veritas Prep GMAT Instructor

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