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# Which negative number x makes

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Intern
Joined: 11 Jan 2015
Posts: 34
Which negative number x makes  [#permalink]

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11 Apr 2018, 05:30
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:52) correct 23% (02:17) wrong based on 57 sessions

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Which negative number x makes $$(7-x)/3$$ equal to $$x^2+x$$

A.) -2/3
B.) -4/3
C.) -7/3
D.) -7/5
E.) -9/5
Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: Which negative number x makes  [#permalink]

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11 Apr 2018, 09:18
Which negative number x makes $$(7-x)/3$$ equal to $$x^2+x$$

A.) -2/3
B.) -4/3
C.) -7/3
D.) -7/5
E.) -9/5

$$\frac{7-x}{3}=x^2+x..............7-x=3x^2+3x...............3x^2+4x-7+0.........(x-1)(3x+7)=0$$

so x = 1 or $$\frac{-7}{3}$$

C..

Ofcourse SUBSTITUTION from choices is a good method
_________________

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

GMAT online Tutor

Intern
Joined: 11 Jan 2015
Posts: 34
Re: Which negative number x makes  [#permalink]

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13 Apr 2018, 08:33
chetan2u wrote:
Which negative number x makes $$(7-x)/3$$ equal to $$x^2+x$$

A.) -2/3
B.) -4/3
C.) -7/3
D.) -7/5
E.) -9/5

$$\frac{7-x}{3}=x^2+x..............7-x=3x^2+3x...............3x^2+4x-7+0.........(x-1)(3x+7)=0$$

so x = 1 or $$\frac{-7}{3}$$

C..

Ofcourse SUBSTITUTION from choices is a good method

Dear chetan2u,

I somehow get stuck on the bold part. Could you briefly elaborate on this step?
Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: Which negative number x makes  [#permalink]

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13 Apr 2018, 09:26
1
1
chetan2u wrote:
Which negative number x makes $$(7-x)/3$$ equal to $$x^2+x$$

A.) -2/3
B.) -4/3
C.) -7/3
D.) -7/5
E.) -9/5

$$\frac{7-x}{3}=x^2+x..............7-x=3x^2+3x...............3x^2+4x-7+0.........(x-1)(3x+7)=0$$

so x = 1 or $$\frac{-7}{3}$$

C..

Ofcourse SUBSTITUTION from choices is a good method

Dear chetan2u,

I somehow get stuck on the bold part. Could you briefly elaborate on this step?

Hi...
$$7-x=3x^2+3x.........3x^2+4x-7=0.....3x^2+7x-3x-7=0.....x(3x+7)-1(3x+7)=0.....(x-1)(3x+7)=0$$..
So either x-1=0, that is x=1 OR 3x+7=0...x=-7/3 OR both x=1 and X=-7/3
But x is NEGATIVE , so x=-7/3

Hope it helps
_________________

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

GMAT online Tutor

Re: Which negative number x makes &nbs [#permalink] 13 Apr 2018, 09:26
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