Is mp greater than m?

Since p<1 then p-1 is negative.

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.

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.

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)

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

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

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)

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?

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.

Posted from my mobile device

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.

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)

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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