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If 4 is one solution of the equation x^2 + 3x + k = 10

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If 4 is one solution of the equation x^2 + 3x + k = 10 [#permalink]

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New post 06 May 2012, 09:38
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sravanth wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

A. –7
B. –4
C. –3
D. 1
E. 6


Since x=4 is one of the solutions then substitute 4 for x: 4^2+3*4+k=10 --> k=-18.

So, we have x^2+3x-18=10 --> x^2+3x-28=0 --> (x+7)(x-4)=0 --> x=-7 or x=4.

Answer: A.
[Reveal] Spoiler: OA

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Re: If 4 is one solution of the equation x^2 + 3x + k = 10 [#permalink]

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New post 19 Jan 2015, 06:25
Bunuel wrote:
sravanth wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

A. –7
B. –4
C. –3
D. 1
E. 6


Since x=4 is one of the solutions then substitute 4 for x: 4^4+3*4+k=10 --> k=-18.

So, we have x^2+3x-18=10 --> x^2+3x-28=0 --> (x+7)(x-4)=0 --> x=-7 or x=4.

Answer: A.


Hi Bunuel,

Shouldn't the equation be "4^2+3*4+k=10" and not "4^4+3*4+k=10".
Expert Post
Math Expert
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Joined: 02 Sep 2009
Posts: 32616
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Kudos [?]: 68615 [0], given: 9816

Re: If 4 is one solution of the equation x^2 + 3x + k = 10 [#permalink]

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New post 19 Jan 2015, 06:29
Expert's post
tarikk wrote:
Bunuel wrote:
sravanth wrote:
If 4 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?

A. –7
B. –4
C. –3
D. 1
E. 6


Since x=4 is one of the solutions then substitute 4 for x: 4^4+3*4+k=10 --> k=-18.

So, we have x^2+3x-18=10 --> x^2+3x-28=0 --> (x+7)(x-4)=0 --> x=-7 or x=4.

Answer: A.


Hi Bunuel,

Shouldn't the equation be "4^2+3*4+k=10" and not "4^4+3*4+k=10".


Clearly it was a typo. Edited. Thank you.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32616
Followers: 5653

Kudos [?]: 68615 [0], given: 9816

Re: If 4 is one solution of the equation x^2 + 3x + k = 10 [#permalink]

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New post 19 Jan 2015, 06:30
Expert's post
Re: If 4 is one solution of the equation x^2 + 3x + k = 10   [#permalink] 19 Jan 2015, 06:30
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If 4 is one solution of the equation x^2 + 3x + k = 10

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