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# Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1

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Math Expert
Joined: 02 Sep 2009
Posts: 51307
Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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10 Jul 2018, 19:50
1
1
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Difficulty:

95% (hard)

Question Stats:

32% (02:00) correct 68% (01:46) wrong based on 65 sessions

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Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7113
Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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10 Jul 2018, 19:56
1
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

the equation will hold true for every value except when left side is 0.

And the left side will be 0, only when q is 0..
So is $$|qp+q^2|>qp$$ actually MEANS is $$q\neq{0}$$

Let's see the statements..
1) q>0..
Ans is YES, q is not equal to 0..
Suff

2)$$\frac{q}{p}>1$$..
Again ans is YES..
If q was 0, q/p would be 0..
Suff

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 14 Dec 2017
Posts: 518
Location: India
Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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10 Jul 2018, 20:39
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

Given
is |qp + q^2| > qp ?

can be written as, |q(p + q)| > qp

Statement 1: q > 0

Plug in numbers,
q = 1, p = -1, we get LHS = 0 & RHS = -1....we get YES
q = 1, p = 0, we get LHS = 1, RHS = 0...we get YES
q = 1, p = 1, we get LHS = 2, RHS = 1...we get YES

Statement 1 is Sufficient.

Statement 2: q/p > 1, hence q & p have the same sign.

Plug in numbers
q = 2, p = 1, we get LHS = 6, RHS = 2...we get YES
q = -2, p = -1, we get LHS = 6, RHS = 2, we get YES

Statement 2 is Sufficient.

Thanks,
GyM
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Posts: 33
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Concentration: General Management, Finance
GMAT 1: 660 Q49 V29
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Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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10 Jul 2018, 22:12
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

Left side is always positive. q^2 is making left side greater than RHS when p,q>0. when p<0, RHS is negative and LHS positive.

So, D
Intern
Joined: 01 Jul 2018
Posts: 5
Location: India
Concentration: Finance, General Management
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Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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12 Jul 2018, 10:16
chetan2u wrote:
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

the equation will hold true for every value except when left side is 0.

And the left side will be 0, only when q is 0..
So is $$|qp+q^2|>qp$$ actually MEANS is $$q\neq{0}$$

Let's see the statements..
1) q>0..
Ans is YES, q is not equal to 0..
Suff

2)$$\frac{q}{p}>1$$..
Again ans is YES..
If q was 0, q/p would be 0..
Suff

D

Hi Chetan,

Could you please explain why we are not considering value of q=0;

It is not given anywhere in the original question
Math Expert
Joined: 02 Aug 2009
Posts: 7113
Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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14 Jul 2018, 00:08
PKGMAT wrote:
chetan2u wrote:
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

the equation will hold true for every value except when left side is 0.

And the left side will be 0, only when q is 0..
So is $$|qp+q^2|>qp$$ actually MEANS is $$q\neq{0}$$

Let's see the statements..
1) q>0..
Ans is YES, q is not equal to 0..
Suff

2)$$\frac{q}{p}>1$$..
Again ans is YES..
If q was 0, q/p would be 0..
Suff

D

Hi Chetan,

Could you please explain why we are not considering value of q=0;

It is not given anywhere in the original question

I think you are referring to statement II
(2) q/p > 1
Now if we consider q=0..$$\frac{q}{p}=\frac{0}{p}=0$$
But it is given that $$\frac{q}{p}>1$$, so how can 0>1
this means $$q\neq{0}$$

the equation q/p>1 itself means that q is not 0

hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Manager
Joined: 08 Oct 2015
Posts: 241
Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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14 Jul 2018, 00:46
chetan2u wrote:
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

the equation will hold true for every value except when left side is 0.

And the left side will be 0, only when q is 0..
So is $$|qp+q^2|>qp$$ actually MEANS is $$q\neq{0}$$

Let's see the statements..
1) q>0..
Ans is YES, q is not equal to 0..
Suff

2)$$\frac{q}{p}>1$$..
Again ans is YES..
If q was 0, q/p would be 0..
Suff

D

can you explain how this can be done by opening the absolute sign?

one way is -- qp+q^2-qp>o , i.e. is q not equal to 0

second way is -qp-q^2> qp
simplified to 2qp + q^2<0

with this second way, how can we say with statement 1 we can prove sufficient

Bunuel chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 7113
Re: Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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14 Jul 2018, 01:34
rahulkashyap wrote:
chetan2u wrote:
Bunuel wrote:
Is |qp + q^2| > qp?

(1) q > 0

(2) q/p > 1

the equation will hold true for every value except when left side is 0.

And the left side will be 0, only when q is 0..
So is $$|qp+q^2|>qp$$ actually MEANS is $$q\neq{0}$$

Let's see the statements..
1) q>0..
Ans is YES, q is not equal to 0..
Suff

2)$$\frac{q}{p}>1$$..
Again ans is YES..
If q was 0, q/p would be 0..
Suff

D

can you explain how this can be done by opening the absolute sign?

one way is -- qp+q^2-qp>o , i.e. is q not equal to 0

second way is -qp-p^2> qp
simplified to 2qp + p^2<0

with this second way, how can we say with statement 1 we can prove sufficient

Bunuel chetan2u

Let's take the second statement..
2pq+p^2<0
p^2 is surely positive so 2pq<0
This means - are p AND q of different sign
Statement II tells us both are of same sign..
Sufficient
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 08 Oct 2015
Posts: 241
Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1  [#permalink]

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14 Jul 2018, 01:37
Hi chetan2u

The question can be simplified into either (1) or (2)

In 2, on simplification, we get 2pq+p² <0
Using statement 1 of the question, we can not prove this as sufficient

That is my question

Also, as stated by you "2pq+p^2<0
p^2 is surely positive so 2pq<0
This means - are p AND q of different sign"

this is simplified into 2pq<-p^2 and not otherwise as stated by you.

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Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1 &nbs [#permalink] 14 Jul 2018, 01:37
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# Is |qp + q^2| > qp? (1) q > 0 (2) q/p > 1

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