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705-805 (Hard)|   Algebra|      
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nifoui
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 12:53
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

50% (02:10) correct 50% (02:07) wrong based on 193 sessions

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

(1) p + q = 7
(2) pq^2 = -64
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B
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nverma
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 13:15
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nifoui
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.
Show more

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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nifoui
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 13:22
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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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nifoui
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 13:25
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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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nverma
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 14:01
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nifoui
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?
Show more

Given in the question : p*q=-8
But if p=-4 and q=4 ..>>> Then p*q=-16
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If pq = -8, what is the value of pq(p - q) ? 17 May 2010, 15:03
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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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If pq = -8, what is the value of pq(p - q) ? 08 Aug 2017, 15:22
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nifoui
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.
Show more

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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If pq = -8, what is the value of pq(p - q) ? 08 Aug 2017, 17:46
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nifoui
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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in statement 1, why did you assume that p,q are integers?


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If pq = -8, what is the value of pq(p - q) ? 08 Aug 2017, 20:07
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pq^2 is confusing to me.
I thought it would be (pq)^2
but actually it is p*q*q,
now I know something

Posted from my mobile device
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If pq = -8, what is the value of pq(p - q) ? 19 Feb 2019, 03:12
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nifoui
If pq = -8, what is the value of pq(p - q) ?

(1) p + q = 7
(2) pq^2 = -64
Show more

From 1, we can get 2 values for p and q, such as p = -1 & q = 8 or p = 8 q =-1
Both will give different values

from 2, we will only get an unique value
p = -1 q = 8

B
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If pq = -8, what is the value of pq(p - q) ? 21 Apr 2023, 23:18
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