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Is mp greater than m?

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10 Oct 2012, 10:09

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Is mp greater than m?

(1) m > p > 0
(2) p is less than 1

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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).

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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.

For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum

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Bunuel

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10 Oct 2012, 10:19

Is mp greater than m?

Question: is \(mp>m\)?

(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.

Answer: C.

Hope it's clear.

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10 Oct 2012, 10:22

GetThisDone

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).

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.

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Bunuel

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10 Oct 2012, 10:24

EvaJager

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Since p<1 then p-1 is negative.

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10 Oct 2012, 10:45

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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.

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10 Oct 2012, 10:51

Bunuel

EvaJager

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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.

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KarishmaB

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10 Oct 2012, 23:25

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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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23 May 2013, 00:44

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Is mp greater than m?

(1) m > p > 0

(2) p is less than 1

please explain

How can I practice a gazillion questions like this? I keep getting them wrong.

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31 Jul 2014, 13:22

serendipiteez

u2lover

Is mp greater than m?

(1) m > p > 0

(2) p is less than 1

please explain

How can I practice a gazillion questions like this? I keep getting them wrong.

practice more I think. Here are some other examples

is-the-value-of-expression-k-m-1-greater-than-the-141322.html?fl=similar
if-m-is-a-positive-integer-greater-than-1-can-m-be-expressed-129063.html?fl=similar

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14 Oct 2016, 23:19

GetThisDone

Is mp greater than m?

(1) m > p > 0
(2) p is less than 1

Question :Is mp greater than m?

Question :Is mp - m > 0?
Question :Is m(p - 1) > 0?

Statement 1: m > p > 0
Now we know that m and p are positive but whether p-1 is greater than 0 or not is still unknown hence
NOT SUFFICIENT

Statement 2: p < 1
Now we know that p-1 is Negative but whether m is greater than 0 or not is still unknown hence
NOT SUFFICIENT

Combining the two statements
Now we know that p-1 is Negative and m is positive hence
m(p-1) will be less than zero for sure
SUFFICIENT

Answer: Option C

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15 Oct 2016, 05:01

GetThisDone

Is mp greater than m?

(1) m > p > 0
(2) p is less than 1

Solved by plugging in some values -

If m > p > 0

Let, 2 > 1 > 0

So, mp = 2 and m = 2

Now, mp is not greater than m

Again -

If m > p > 0

Let, 3 > 2 > 0

So, mp = 6 and m = 3

Now, mp is greater than m

Thus option (1) alone can not be used...

From (2) we get nothing -

Using (1) and (2)

If If m > p > 0 and p < 1

Let, 1/3 > 1/2 > 0

So, mp = 1/6 and m = 1/3

Thus , mp will always be greater than m

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)

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23 Aug 2020, 04:13

Question- whether mp> m?

Statement 1- Not sufficient because mp could be greater than m when p is greater than 1 or it could be equal to m when p=1.
Statement 2 - This is where I am facing the problem when it says p<1. Can someone please explain this statement in detail?

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23 Oct 2020, 03:08

dontmesswithme

Let me try:
The inequality presented here asks whether m*(p-1)>0? Which if you think about says that both m and p-1 need to possess the same signs.

Statement 1:
m is positive, alright great, but you should also have p>1 for this to hold true. But this only says that p>0. Not sufficient.

Statement 2:
Just talks about p. Not sufficient

Together:
Think about it, if both need to have the same signs, and m is positive (from statement 1) we need to establish the fact whether p-1 is positive or not. Now since p is less than 1, p-1 has to be negative, right. So m is positive, p-1 is definitely negative, so their product is negative, which is not greater than 0, so you can answer with certainty that mp is not greater than m. Hence C

Thanks,
PV66.

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29 Oct 2020, 09:47

Is \(mp > m\)?
Is \(mp - m > 0\)?
Is \(m (p - 1) > 0?\)

(1) \(m > p > 0\)

This statement tells us that m is positive however we don't know if p is greater than 1. Insufficent.

(2) p is less than 1

This statement tells us that p is less than 1 however we don't know anything about m. Insufficient.

(1&2) m > p > 0; 1 > p

From the statements combined we can conclude that m (p - 1) < 0. Sufficient.

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12 May 2022, 12:47

IMO C
Is mp greater than m?

We basically need to know if p is positive , negative or fraction

(1) m > p > 0 --> so p is positive but it could be fraction ==> not sufficient

(2) p is less than 1 --> could be negative or fraction ==> not sufficient

Combining we know p is positive and fraction thus mp<m (Sufficient)

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14 May 2022, 04:55

Is mp greater than m?

(1) m > p > 0
(2) p is less than 1

mp>m?
when i rephrase the question it is saying is p>1?
from statement 1
m>P>0
two possibilities
1>0.5>0 where p is less than 1
3>2>0 where p is greater than 1
statement 1 is NS

statement 2 directly says p<1 which answers our rephrase question that P is not greater than 1
so according to me ans is B

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07 Oct 2024, 20:16

Can someone explain where am i going wrong please?

Q. Is mp - m > 0?

rephrased

Is mp > m?

cancelling m out on both sides

Is p > 1?

Statement 1 - m >p > 0

Not sufficient as p can or cannot be greater than 1

Statement II - p is less than 1

Sufficient as p is not greater than 1

Ans: Statement II is sufficient

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07 Oct 2024, 22:42

Venu01298

Bunuel

We cannot divide mp > m by m because we don't know its sign. If m is positive, then yes, we would get p > 1. However, if p is negative, dividing by a negative value would flip the inequality sign, resulting in p < 1. Remember, never reduce an inequality by a variable if its sign is unknown.

P.S. Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems
Work Problems
Distance Problems
Mixture Problems
Percent and Interest Problems
Overlapping Sets Problems
Statistics Problems
Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check GMAT Syllabus for Focus Edition

You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

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