Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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 \(k\).

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

18 Sep 2012, 06:25

5

This post received KUDOS

1

This post was BOOKMARKED

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.

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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.

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.
_________________

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

23 Oct 2013, 06:03

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

04 Dec 2014, 10:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

01 Mar 2015, 19:52

1

This post received KUDOS

You don't need to solve for K, we know that 4 is a solution so we already know one of the terms (x-4)(x+......) we also have x2 + 3x + k = 10, -4 + 7=3 so (x-4)(x+7):0 hence x: -7

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

17 Apr 2016, 22:04

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If 4 is one solution of the equation x2 + 3x + k = 10, where [#permalink]

Show Tags

18 Apr 2016, 12:48

solving for 4 to find k 16+12+k=10 k=-18 (x^2)+3x-18=10 testing values you find -7
_________________

Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.

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

The phrase “4 is one solution of the equation” means that one value of x is 4. Thus, we first must plug 4 for x into the given equation to determine the value of k. So we have

4^2 + (3)(4) + k = 10

16 + 12 + k = 10

28 + k = 10

k = -18

Next we plug -18 into the given equation for k and then solve for x.

x^2 + 3x – 18 = 10

x^2 + 3x – 28 = 0

(x+7)(x-4) = 0

x = -7 or x = 4

Thus, -7 is the other solution. Answer A.
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...