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# What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2

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Math Expert
Joined: 02 Sep 2009
Posts: 53768
What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2  [#permalink]

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26 Jul 2018, 00:09
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Difficulty:

25% (medium)

Question Stats:

69% (01:03) correct 31% (01:07) wrong based on 103 sessions

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What is the value of x?

(1) x^2 + 4x = –8x – 35
(2) x^2 + 3x = –7x – 25

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Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2  [#permalink]

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26 Jul 2018, 00:22
Bunuel wrote:
What is the value of x?

(1) x^2 + 4x = –8x – 35
(2) x^2 + 3x = –7x – 25

OA: B
Statement 1 :$$x^2 + 4x = –8x – 35$$
$$x^2 + 12x+35=0$$
$$x^2 + 7x+5x+7*5=0$$
$$(x+7)(x+5)=0$$
$$x=-5,-7$$
Two different value of $$x$$ , hence Statement 1 alone is not sufficient.

Statement 2:$$x^2 + 3x = –7x – 25$$
$$x^2 + 10x+25 =0$$
$$x^2 + 5x+5x+5*5 =0$$
$$(x+5)(x+5)=0$$
$$x=-5$$
1 unique value of $$x$$ , hence Statement 2 alone is sufficient.
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Math Expert
Joined: 02 Aug 2009
Posts: 7424
What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2  [#permalink]

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26 Jul 2018, 00:23
What is the value of x?

A quadratic equation has almost always two roots. if the equation is in the form of $$a^2-2ab+b^2$$ or $$a^2+2ab+b^2$$, when both the roots are same, the value will be one...

(1) x^2 + 4x = –8x – 35
$$x^2+12x+35=0$$...Had this been $$x^2+12x+36=0$$, we would have had only one value as $$x^2+12x+36=0........x^2+2*1*6x+6^2=0$$
but now there will be two values
insuff

(2) x^2 + 3x = –7x – 25
$$x^2+10x+25=0............x^2+2*1*5x+5^2=0..........(x+5)^2=0$$
hence x is -5
sufficient

B
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2  [#permalink]

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03 Jan 2019, 20:27
I think the key to getting this problem right is:

What is the value of x? Dont think that previous comments stressed it enough

The here indicates that there is only 1 possible solution that we are looking for. Algebra in the previous comments is good and you can look at it to see how to arrive to just 1 value.

I think
Re: What is the value of x? (1) x^2 + 4x = –8x – 35 (2) x^2 + 3x = –7x – 2   [#permalink] 03 Jan 2019, 20:27
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