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If 4 is one solution of the equation x2 + 3x + k = 10, where

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If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 01:57
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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

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Question: 45
Page: 158
Difficulty: 600
[Reveal] Spoiler: OA

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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 01:57
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SOLUTION

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

Viete's formula for the roots x_1 and x_2 of equation ax^2+bx+c=0: x_1+x_2=-\frac{b}{a} AND x_1*x_2=\frac{c}{a}.

Rewrite the equation given: x^2 + 3x +(k-10) =0
Thus according to the first property 4+x_2=-\frac{3}{1} --> x_2=-7. As we can see we can find the value of x_2 even without finding the value of k.

Answer: A.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 02:13
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Slove equation by putting x=4 as it is one of the solution.
u gets value of k=-18

now put k=-18 in the equation,u get eqn in the form of ax^2+bx+c=0. Solving it we get x=4 and x=-7

so other solution is -7.
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 04:07
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Shortcut for the question-

The sum of roots of a equation is = -b/a = -3
One of the given roots is 4
Thus the other root has to be -7
Check = 4-7 = -3 (confirm)

Thus Answer A
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 05:25
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Bunuel 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 4 is one of the solution, so it must satisfy the equation.
Putting 4 as value of x: 4^2 + 3*4 + k = 10 => k =-18
so the equations is
x^2 + 3x - 28 = 0

Solving this by factorization gives => (x-4)(x+7) = 0
So x = -7 is other solution.

Hence A
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 18 Sep 2012, 09:28
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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

Practice Questions
Question: 45
Page: 158
Difficulty: 600


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One sol. of equation is 4. therefor putting this as X in the equation and finout the constant K.
therefore K = -28.
so, equation can be rewritten as (X-4)(X+7) = 0.

other solution is X = -7.
ANswer "A"
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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 21 Sep 2012, 02:34
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SOLUTION

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

Viete's formula for the roots x_1 and x_2 of equation ax^2+bx+c=0: x_1+x_2=-\frac{b}{a} AND x_1*x_2=\frac{c}{a}.

Rewrite the equation given: x^2 + 3x +(k-10) =0
Thus according to the first property 4+x_2=-\frac{3}{1} --> x_2=-7. As we can see we can find the value of x_2 even without finding the value of k.

Answer: A.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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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.


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Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink] New post 23 Oct 2013, 05:03
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