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What is the value of x?

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Sachin9
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What is the value of x? [#permalink] New post   Updated on: 02 Nov 2012, 23:29
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What is the value of x?

(1) x^2 + 5x + 6 = 0
(2) x^2 - 10x -24=0
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C

Originally posted by Sachin9 on 02 Nov 2012, 21:14.
Last edited by Bunuel on 02 Nov 2012, 23:29, edited 1 time in total.
Renamed the topic and edited the question.
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Re: beat this: contradicting statements [#permalink] New post   02 Nov 2012, 22:01
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Sachin9 wrote:
What is the value of x?

1)x^2 + 5x + 6 = 0
2)x^2 - 10x -24=0


St 1: insufficient: x^2+5x+6 => x^2+3x+2x+6 => x(x+3) + 2(x+3) => (x+2) (x+3)
So x = -2 or -3
St 2: insufficient: x^2-10x-24 => x^2 -12x+2x-24 => x(x-12) + 2(x-12) => (x+2) (x-12)
So x= -2 or 12

1)+2) x=-2

Hence C.
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Re: beat this: contradicting statements [#permalink] New post   02 Nov 2012, 23:04
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Sachin9 wrote:
What is the value of x?

1)x^2 + 5x + 6 = 0
2)x^2 - 10x -24=0


1) x = -2 or x = -3. Insufficient.
2) x = -2 or x = 12. Insufficient.

1 & 2 together. x = -2. Sufficient.

The statements never contradict each other. For these statements to contradict each other, statement 2 should not have neither -2 nor -3 as a root. For the statements to be insufficient together, both statements should have more than one common root.

Kudos Please... If my post helped.
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Re: beat this: contradicting statements [#permalink] New post   02 Nov 2012, 23:10
yeh Macfauz.

If we incorrectly solve 2nd equation by factoring (x-4)(x-6) , then the 2 statements would contradict..

So I guess, if we find that the statements are contradicting , then we can be sure that we have made a mistake somewhere ..
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Re: beat this: contradicting statements [#permalink] New post   02 Nov 2012, 23:27
Sachin9 wrote:
yeh Macfauz.

If we incorrectly solve 2nd equation by factoring (x-4)(x-6) , then the 2 statements would contradict..


Why would we be solving the equation incorrectly? :lol:
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Re: beat this: contradicting statements [#permalink] New post   02 Nov 2012, 23:30
Marcab wrote:
Sachin9 wrote:
yeh Macfauz.

If we incorrectly solve 2nd equation by factoring (x-4)(x-6) , then the 2 statements would contradict..


Why would we be solving the equation incorrectly? :lol:

in case you ever do, in the heat of the pressure . then this knowledge will help you know you have gone wrong :D
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Re: beat this: contradicting statements [#permalink] New post   03 Nov 2012, 05:20
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Sachin9 wrote:
Marcab wrote:
Sachin9 wrote:
yeh Macfauz.

If we incorrectly solve 2nd equation by factoring (x-4)(x-6) , then the 2 statements would contradict..


Why would we be solving the equation incorrectly? :lol:

in case you ever do, in the heat of the pressure . then this knowledge will help you know you have gone wrong :D


You can not do the factorization incorrectly if you know the concept. The -ve sign before 24 indicates you to choose two factors of 24 and subtract it from each other to make 10. So only (12,2) this pair will satisfy.

As per your factorization (x-4)(x-6) the equation becomes x^2-10x+24(which is not in the question).

So the + or - sign before the last constant term will give u clue whether u need to add or subtract.
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Re: What is the value of x? [#permalink] New post   03 Nov 2012, 07:28
agreed mate.. i said if you do commit mistake in the heat of the pressure...
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Re: What is the value of x? [#permalink] New post   27 Jun 2021, 09:12
IMO C

Equating both individually we get
1. x = -2 or x = -3. not sufficient
2. x = -2 or x = 12. not sufficient.

thus 1 and 2 together are sufficient and we get X =2
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Re: What is the value of x? [#permalink]
27 Jun 2021, 09:12
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