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If pq = -8, what is the value of pq(p - q) ?

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If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 12:53
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If pq = -8, what is the value of pq(p - q) ?

(1) p + q = 7
(2) pq^2 = -64
[Reveal] Spoiler: OA

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 13:15
nifoui wrote:
DS question from Knewton's free CAT test

If pq = -8, what is the value of pq(p-q) ?
1. p + q = 7
2. pq² = -64

I do not agree with OA provided and would like to know your reasoning and OA.

Will share OA and OE later.


IMO B,

Statement 1:

Given pq=-1, so what can be the values of (p,q) >>> (1,-8),(2,-4),(-1,8),(-2,4),(4,-2),(-4,2),(-8,1),(8,-1)
Given p+q =7, it means >>> possible values are >>> (1,-8),(-1,8),(-8,1),(8,-1)

let say p=-1 and q=8
So pq(p-q) = -8(-1-8)= 72

Let say p= 1 and q= -8
So pq(p-q) = -8(1 + 8)= -72. Insufficient

Statement 2:

pq² = -64, also pq = -8...so
(pq)q =- 64
(-8)q =- 64
q= 8.....>>> So p can only be -1.
so pq(p-q) = -8(-1-8)= 72

OA plz.

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 13:22
You are right OA is B, but I answered C and still hold my position.

Here is my reasoning:
From statement 2, there are multiple solutions:
p=-1 and q=8
or
p=-4 and q=4

Therefore statement 2 is not sufficient alone, but we can answer the question with both statements together.

Why is that wrong?
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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 13:25
As I re-read your explanation, I just understood my error!!

I had forgotten in the process that we were given pq = -8...

I'm loosing points with such mistakes!!

Thanks anyway :)
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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 14:01
nifoui wrote:
You are right OA is B, but I answered C and still hold my position.

Here is my reasoning:
From statement 2, there are multiple solutions:
p=-1 and q=8
or
p=-4 and q=4

Therefore statement 2 is not sufficient alone, but we can answer the question with both statements together.

Why is that wrong?


Given in the question : p*q=-8
But if p=-4 and q=4 ..>>> Then p*q=-16

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 17 May 2010, 15:03
If pq = -8, what is the value of pq(p-q) ?
1. p + q = 7
2. pq² = -64

1) Insufficient because it provides two values of pq(p-q) i.e. +72 and -72. If p+q and pq are known then we can derive square of p-q using the formula (p-q)^2 = (p+q)^2 -4pq. This formula gives p-q = +9 and -9.
So statement 1 doesn't provide unique value of pq(p-q).
2) Sufficient beacuse it provides p=8. and then plug p into pq will give q.

So Answer is B

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 08 Aug 2017, 15:22
nverma wrote:
nifoui wrote:
DS question from Knewton's free CAT test

If pq = -8, what is the value of pq(p-q) ?
1. p + q = 7
2. pq² = -64

I do not agree with OA provided and would like to know your reasoning and OA.

Will share OA and OE later.


IMO B,

Statement 1:

Given pq=-1, so what can be the values of (p,q) >>> (1,-8),(2,-4),(-1,8),(-2,4),(4,-2),(-4,2),(-8,1),(8,-1)
Given p+q =7, it means >>> possible values are >>> (1,-8),(-1,8),(-8,1),(8,-1)

let say p=-1 and q=8
So pq(p-q) = -8(-1-8)= 72

Let say p= 1 and q= -8
So pq(p-q) = -8(1 + 8)= -72. Insufficient

Statement 2:

pq² = -64, also pq = -8...so
(pq)q =- 64
(-8)q =- 64
q= 8.....>>> So p can only be -1.
so pq(p-q) = -8(-1-8)= 72

OA plz.


exactly my approach.

in statement 1, i ended up with q^2 + p^2 = 65. we can have different options here... so no way to find it...

statement2 - q=8, and p=-1. we can find the answer.

B

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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 08 Aug 2017, 17:46
nverma wrote:
nifoui wrote:
DS question from Knewton's free CAT test

If pq = -8, what is the value of pq(p-q) ?
1. p + q = 7
2. pq² = -64

I do not agree with OA provided and would like to know your reasoning and OA.

Will share OA and OE later.


IMO B,

Statement 1:

Given pq=-1, so what can be the values of (p,q) >>> (1,-8),(2,-4),(-1,8),(-2,4),(4,-2),(-4,2),(-8,1),(8,-1)
Given p+q =7, it means >>> possible values are >>> (1,-8),(-1,8),(-8,1),(8,-1)

let say p=-1 and q=8
So pq(p-q) = -8(-1-8)= 72

Let say p= 1 and q= -8
So pq(p-q) = -8(1 + 8)= -72. Insufficient

Statement 2:

pq² = -64, also pq = -8...so
(pq)q =- 64
(-8)q =- 64
q= 8.....>>> So p can only be -1.
so pq(p-q) = -8(-1-8)= 72

OA plz.
in statement 1, why did you assume that p,q are integers?


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Re: If pq = -8, what is the value of pq(p - q) ? [#permalink]

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New post 08 Aug 2017, 20:07
pq^2 is confusing to me.
I thought it would be (pq)^2
but actually it is p*q*q,
now I know something

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Re: If pq = -8, what is the value of pq(p - q) ?   [#permalink] 08 Aug 2017, 20:07
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