GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Aug 2018, 23:43

### GMAT Club Daily Prep

#### 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

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

# If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for

Author Message
Manager
Joined: 10 Oct 2008
Posts: 56
If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for  [#permalink]

### Show Tags

10 Oct 2008, 10:04
If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

x^2 +b^x+c=x^2+2xd+d^2 bx-2xd=d^2-c x( b-2d)=d^2-c

Stm1 d=3 x(b-6)=9-c insufficient
Stm2 b=6 x(6-2d)=d^2-c insufficient
Combine stm1 and stm2
c=3 the answer is C. Is that correct?

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager
Joined: 27 Sep 2008
Posts: 76
Re: discuss a math problem  [#permalink]

### Show Tags

10 Oct 2008, 11:12
I think the answer is (E)

you have 4 unknowns

b,c,d,x

even if you know what d,b are then you are left with

$$x^2+6^x+c = (x+3)^2$$

$$x^2+6^x+c = x^2+6x+9$$

$$6^x+c=6x+9$$

cannot be solved

x can be 1 and c can be 9 or x can be 2 and c can be -15

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345
Re: discuss a math problem  [#permalink]

### Show Tags

10 Oct 2008, 13:13
Jcpenny wrote:
If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for all values of x, what is the value of c?
(1) d = 3
(2) b = 6

First, I'm absolutely certain that the question should read:

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

because otherwise it's mathematically impossible that what is stated in the stem is true, unless b = 1, d = 0 and c = -1. Proceeding on that assumption:

We know that

$$x^2 + bx + c = (x+d)^2$$

for all values of x. In particular, it's true for x=0:

$$0^2 + b*0 + c = (0+d)^2 \\ c = d^2$$

So you can find c if you know d, and Statement 1 is sufficient.

Further, knowing that $$c = d^2$$, we have

$$x^2 + bx + d^2 = (x+d)^2 \\ x^2 + bx + d^2 = x^2 + 2dx + d^2 \\ bx = 2xd \\ b = 2d \\$$

so if you can find b, you can find d, and therefore you can find c. Statement 2 is sufficient.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: discuss a math problem &nbs [#permalink] 10 Oct 2008, 13:13
Display posts from previous: Sort by

# If b, c, and d are constants and x^2 + b^x + c = (x+d)^2 for

Moderator: chetan2u

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.