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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).

(1) m > p > 0. Since given that \(m>0\), then we can reduce by positive \(m\) and the question becomes: is \(p>1\)? We know that \(p>0\), but that's not enough. Not sufficient.

(2) p is less than 1. No info about \(m\). Not sufficient.

(1)+(2) From (1) the question became: "is \(p>1\)?" and (2) says that \(p<1\), so we have definite NO answer to the question. Sufficient.

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).

The question can be rephrased as "Is \(mp-m>0\) or \(m(p-1)>0,\) which is the same as asking whether \(m\) and \(p-1\) have the same sign?"

(1) Not sufficient. In order to know the sign of \(p-1\) we have to know whether \(p\) is greater or less than \(1.\) (2) Not sufficient. We know nothing about \(m.\)

(1) and (2): Now we know for sure that both \(m\) and \(p-1\) are positive. Sufficient.

Answer C.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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).

The question can be rephrased as "Is \(mp-m>0\) or \(m(p-1)>0,\) which is the same as asking whether \(m\) and \(p-1\) have the same sign?"

(1) Not sufficient. In order to know the sign of \(p-1\) we have to know whether \(p\) is greater or less than \(1.\) (2) Not sufficient. We know nothing about \(m.\)

(1) and (2): Now we know for sure that both \(m\) and \(p-1\) are positive. Sufficient.

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).

The question can be rephrased as "Is \(mp-m>0\) or \(m(p-1)>0,\) which is the same as asking whether \(m\) and \(p-1\) have the same sign?"

(1) Not sufficient. In order to know the sign of \(p-1\) we have to know whether \(p\) is greater or less than \(1.\) (2) Not sufficient. We know nothing about \(m.\)

(1) and (2): Now we know for sure that both \(m\) and \(p-1\) are positive. Sufficient.

Answer C.

Since p<1 then p-1 is negative.

Oooops! You are right. So, m is positive, p - 1 is negative, the answer to the stem question is a definite NO. Luckily, the answer is the same C.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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.

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).

m(p-1)>0. So m>0 and P>1. NO. It simply means that both \(m\) and \(p-1\) have the same sign, meaning either both are positive or both are negative.
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

So, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked to solve this question.. Answer will be (C) _________________

Thanks and Regards

Abhishek....

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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).

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