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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, 09:13
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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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Joined: 07 May 2015
Posts: 175
Location: India
GMAT 1: 660 Q48 V31
GPA: 3
Re: What is the value of integer q? [#permalink]

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07 Mar 2016, 23:58
qr+qs = r+s
q(r+s) = (r+s)
(q-1)(r+s) = 0
q = 1

St 2: insufficient

Ans; A

Ans :
Senior Manager
Joined: 20 Aug 2015
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What is the value of integer q? [#permalink]

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Updated on: 09 Mar 2016, 04:04
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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

Originally posted by TeamGMATIFY on 09 Mar 2016, 02:46.
Last edited by TeamGMATIFY on 09 Mar 2016, 04:04, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 5771
What is the value of integer q? [#permalink]

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09 Mar 2016, 03:10
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, 04:02
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.
Intern
Joined: 11 Jun 2015
Posts: 9
What is the value of integer q? [#permalink]

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30 Oct 2016, 11:47
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, 19:22
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, 09:00
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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Location: India
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What is the value of integer q? [#permalink]

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21 Dec 2017, 10:20
1
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BOOKMARKED
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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Joined: 14 Dec 2016
Posts: 11
What is the value of integer q? [#permalink]

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17 Mar 2018, 10:41
chetan2u 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

Hi
$$q=1$$ and not -1 as shown in Red coloured portion, although the same will not effect the answer

there is nothing said about r and s, then cant we say that r and s are both zero and thus q can take any value. Both statements wont be able to deduce the result.
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Joined: 22 Aug 2013
Posts: 1021
Location: India
Re: What is the value of integer q? [#permalink]

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17 Mar 2018, 10:51
qazi11 wrote:
chetan2u wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

there is nothing said about r and s, then cant we say that r and s are both zero and thus q can take any value. Both statements wont be able to deduce the result.

Hello

We CANNOT take the case where r=s=0, because its mentioned that r is not equal to -s. If we take r=s=0, then -s=-0=0, and r will become equal to -s. That is not possible.
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Joined: 16 Aug 2015
Posts: 5255
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: What is the value of integer q? [#permalink]

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20 Mar 2018, 23:18
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Posts: 45
Re: What is the value of integer q? [#permalink]

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05 Apr 2018, 12:11
MathRevolution wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Quant Newbie here and I dont understand how to get to the highlighted step, can someone explain?
Math Expert
Joined: 02 Sep 2009
Posts: 44586
What is the value of integer q? [#permalink]

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05 Apr 2018, 13:35
lostnumber wrote:
MathRevolution wrote:
Bunuel wrote:
What is the value of integer q?

(1) qr + qs = r + s
(2) r ≠ -s

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (q, r and s) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
qr+qs = r+s
⇔ q(r+s) = r+s
⇔ q(r+s) - (r+s) = 0
⇔ (q-1)(r+s) = 0
⇔ q-1=0 or r+s = 0
⇔ q-1=0 since r≠-s
⇔ q = 1.

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
q = 1, r = 1, s = 1
q = 2, r = 1, s = -1

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
Since we don't have information about q, condition 2) is not sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Quant Newbie here and I dont understand how to get to the highlighted step, can someone explain?

It's done by factoring out r + s from q(r + s) - (r + s) = 0:

(r + s)(q - 1) = 0.

Does this makes sense?
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Re: What is the value of integer q? [#permalink]

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06 Apr 2018, 06:29
That is helpful Bunuel, thank you! Clearly I need to brush up on my factoring
Re: What is the value of integer q?   [#permalink] 06 Apr 2018, 06:29
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# What is the value of integer q?

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