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# What is the value of integer q?

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Math Expert
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What is the value of integer q? [#permalink]

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07 Mar 2016, 08:13
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What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s
[Reveal] Spoiler: OA

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Re: What is the value of integer q? [#permalink]

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07 Mar 2016, 22:58
qr+qs = r+s
q(r+s) = (r+s)
(q-1)(r+s) = 0
q = 1

St 2: insufficient

Ans; A

Ans :

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What is the value of integer q? [#permalink]

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09 Mar 2016, 01:46
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Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C

Last edited by TeamGMATIFY on 09 Mar 2016, 03:04, edited 1 time in total.

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What is the value of integer q? [#permalink]

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09 Mar 2016, 02:10
TeamGMATIFY wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = -1
SUFFICIENT

Option C

Hi
$$q=1$$ and not -1 as shown in Red coloured portion, although the same will not effect the answer
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Re: What is the value of integer q? [#permalink]

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09 Mar 2016, 03:02
chetan2u wrote:
Hi
$$q=1$$ and not -1 as shown in Red coloured portion, although the same will not effect the answer

Thanks a lot for pointing it out.

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What is the value of integer q? [#permalink]

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30 Oct 2016, 10:47
I'm confused why the answer is not (E).

From Statement (1):
q(r+s) = r +s
Therefore q = 1 or 0

From Statement (2):
We know (r+s) ≠ 0

Statements (1) + (2) - couldn't variable q still be 1 or 0?

Edit: Annnnnd, I just realized that q cannot be 0 because it were, statement (1) would not hold true. Too quick to post.

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Re: What is the value of integer q? [#permalink]

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21 Sep 2017, 18:22
stephyw wrote:
I'm confused why the answer is not (E).

From Statement (1):
q(r+s) = r +s
Therefore q = 1 or 0

From Statement (2):
We know (r+s) ≠ 0

Statements (1) + (2) - couldn't variable q still be 1 or 0?

Edit: Annnnnd, I just realized that q cannot be 0 because it were, statement (1) would not hold true. Too quick to post.

q=1 or r=-s; How are you calculating q=0? Had the equation been q(r+s)=0 then q=0, r=-s would have been the solution.

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Re: What is the value of integer q? [#permalink]

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21 Dec 2017, 08:00
TeamGMATIFY wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C

How did you get the colored step?
How did it become (q-1)
And can someone explain why can't we do this

qr + qs = r + s

q(r+s)= r +s
q=$$\frac{(r+s)}{(r+s)}$$

divide (r+s) on both sides of the equation. The answer will be q =1 Why is this step wrong here?

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What is the value of integer q? [#permalink]

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21 Dec 2017, 09:20
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mtk10 wrote:
TeamGMATIFY wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Required: q = ?

Statement 1: qr + qs = r + s
Or q (r + s) = (r+s)
(q-1)(r+s) = 0 (i)
Either q = 1 or r = -s
INSUFFICIENT

Statement 2: r ≠ -s (ii)
INSUFFICIENT

Combining Statement 1 and Statement 2:
From (i), we have (q-1)(r+s) = 0 (i)
And from (ii) r ≠ -s

Hence q = 1
SUFFICIENT

Option C

How did you get the colored step?
How did it become (q-1)
And can someone explain why can't we do this

qr + qs = r + s

q(r+s)= r +s
q=$$\frac{(r+s)}{(r+s)}$$

divide (r+s) on both sides of the equation
. The answer will be q =1 Why is this step wrong here?

Hi mtk10

The highlighted portion is not correct. r & s are variables whose value you don't know.

Suppose r=2 & s=-2, then

qr + qs = r + s =>2q-2q=2-2=0. Now q can be any integer, not necessarily 1

NEVER CANCEL OUT VARIABLES

so the equation will be q(r+s)=(r+s) => q(r+s)-(r+s)=0

(r+s)(q-1)=0 so Either r+s=0 or q=-1. Hence the statement is not sufficient

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What is the value of integer q?   [#permalink] 21 Dec 2017, 09:20
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