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# Is pq < 4 ?

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Manager
Joined: 13 Apr 2010
Posts: 89
Is pq < 4 ?  [#permalink]

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28 Aug 2017, 12:47
2
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:13) correct 45% (02:12) wrong based on 37 sessions

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Is pq < 4 ?

1) $$p^2 + q^2$$ < 8
2) p - q < 1
Math Expert
Joined: 02 Aug 2009
Posts: 7686
Is pq < 4 ?  [#permalink]

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Updated on: 29 Aug 2017, 02:24
sb0541 wrote:
Is pq < 4 ?

1) $$p^2 + q^2$$ < 8
2) p - q < 1

Hi...

Is PQ<4..
Let's see the statements..
1) $$p^2+q^2<8$$..
$$(p-q)^2+2pq<8.........(p-q)^2<8-2pq$$
Now 2pq has to be LESS than 8 otherwise LHS, (p-q)^2 will become negative, which is NOT possible.
So 2pq<8.....PQ<4..
Sufficient

2) p-q<1
Various combinations possible
Insufficient

A
_________________

Originally posted by chetan2u on 28 Aug 2017, 17:51.
Last edited by chetan2u on 29 Aug 2017, 02:24, edited 1 time in total.
edited
Intern
Joined: 08 Jun 2015
Posts: 20
Location: United States
Concentration: Finance, Economics
WE: Engineering (Other)
Re: Is pq < 4 ?  [#permalink]

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29 Aug 2017, 01:42
1
chetan2u wrote:
sb0541 wrote:
Is pq < 4 ?

1) $$p^2 + q^2$$ < 8
2) p - q < 1

Hi...

Is PQ<4..
Let's see the statements..
1) $$p^2+q^2<8$$..
$$(p+q)^2-2pq<8.........(p+q)^2<8-2pq$$
Now 2pq has to be LESS than 8 otherwise LHS, (p+Q)^2 will become negative, which is NOT possible.
So 2pq<8.....PQ<4..
Sufficient

2) p-q<1
Various combinations possible
Insufficient

A

Hi chetan2u

Wouldn't the "-2pq" will become "+2pq" when taken from LHS to RHS??
Math Expert
Joined: 02 Aug 2009
Posts: 7686
Re: Is pq < 4 ?  [#permalink]

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29 Aug 2017, 02:26
shivam2506 wrote:
chetan2u wrote:
sb0541 wrote:
Is pq < 4 ?

1) $$p^2 + q^2$$ < 8
2) p - q < 1

Hi...

Is PQ<4..
Let's see the statements..
1) $$p^2+q^2<8$$..
$$(p+q)^2-2pq<8.........(p+q)^2<8-2pq$$
Now 2pq has to be LESS than 8 otherwise LHS, (p+Q)^2 will become negative, which is NOT possible.
So 2pq<8.....PQ<4..
Sufficient

2) p-q<1
Various combinations possible
Insufficient

A

Hi chetan2u

Wouldn't the "-2pq" will become "+2pq" when taken from LHS to RHS??

Hi Shivam,
Thanks. Typo, edited now.
Kudos
_________________
Re: Is pq < 4 ?   [#permalink] 29 Aug 2017, 02:26
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