BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Quadratic match

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1578
Joined: Sun Dec 28, 2008 1:49 am
Thanked: 82 times
Followed by:9 members
GMAT Score:720

Quadratic match

by maihuna » Fri Nov 13, 2009 12:32 pm
If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6

[spoiler]E/D[/spoiler]
Charged up again to beat the beast :)
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 am
Location: Montreal
Thanked: 1090 times
Followed by:355 members
GMAT Score:780

Re: Quadratic match

by Ian Stewart » Fri Nov 13, 2009 1:11 pm
maihuna wrote:If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value
of c?
If x^2 + bx + c = (x + d)^2 for *all* values of x, then the equation is certainly true when x=0. Plugging in, we find that c = d^2. So Statement 1 is sufficient.

Now, expanding the right side, and replacing c with d^2:

x^2 + bx + d^2 = x^2 + 2dx + d^2
bx = 2dx
b = 2d

So if we know b, we can find d, and therefore find c, and Statement 2 is also sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Fri Nov 13, 2009 7:50 am

by Lance123 » Fri Nov 13, 2009 9:35 pm
If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6


Is it possible to look at it from this point of view.

Taking statement 1 Alone:
d=3

x^2 + bx + c = (x + d)^2 , d=3
x^2 + bx + c = (x + 3)^2
expanding the RHS and comparing coefficients, it is possible to determine c

So 1 is sufficient.

Taking statement 2
b = 6
x^2 + bx + c = (x + d)^2

x^2 + 6x + c = (x + d)^2
x^2 + 6x + c = x^2 + 2dx + d^2

comparing coefficients,

2d=6
d=3

c= d^2
c= (3)^2
c=9

Statement 2 is Sufficient.
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sat Nov 14, 2009 8:04 am

by notts5 » Sun Nov 15, 2009 1:08 am
But we know by comparing the two sides that c=d^2 and Statement one provides us with the value of d=3.

Therefore, c=d^2=(3)^2=9

Hence, Statement 1 is sufficient.
Top
Post new topic Post Reply
• Page 1 of 1