It is currently 20 Nov 2017, 01:08

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 141

Kudos [?]: 959 [1], given: 15

Reviews Badge
If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 23 Aug 2010, 08:51
1
This post received
KUDOS
18
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (01:02) correct 54% (02:06) wrong based on 276 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 959 [1], given: 15

Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42259

Kudos [?]: 132744 [6], given: 12371

Re: Equation DS [#permalink]

Show Tags

New post 23 Aug 2010, 09:14
6
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
udaymathapati 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?
(1) d = 3
(2) b = 6


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?

\(x^2 + bx + c = (x + d)^2\) --> \(x^2+bx+c=x^2+2dx+d^2\) --> \(bx+c=2dx+d^2\).

Now, as above expression is true "for ALL values of \(x\)" then it must hold true for \(x=0\) too --> \(c=d^2\).

Next, substitute \(c=d^2\) --> \(bx+d^2=2dx+d^2\) --> \(bx=2dx\) --> again it must be true for \(x=1\) too --> \(b=2d\).

So we have: \(c=d^2\) and \(b=2d\). Question: \(c=?\)

(1) \(d=3\) --> as \(c=d^2\), then \(c=9\). Sufficient
(2) \(b=6\) --> as \(b=2d\) then \(d=3\) --> as \(c=d^2\), then \(c=9\). Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 132744 [6], given: 12371

Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17809 [6], given: 235

Location: Pune, India
Re: Equation DS [#permalink]

Show Tags

New post 18 Oct 2010, 12:59
6
This post received
KUDOS
Expert's post
This question is based on special algebraic equations, particularly on (x + y)^2 = x^2 + 2xy + y^2.

So (x + d)^2 = x^2 + 2xd + d^2 = x^2 + bx + c

Equating the co-efficients of x, 2d = b
and equating the constant terms, d^2 = c

If I have d = 3, I get b = 6 and c = 9. (Statement I alone is sufficient.)
If I have b = 6, I get d = 3 and then c = 9 (Statement II alone is sufficient.)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17809 [6], given: 235

BSchool Thread Master
avatar
Joined: 19 Feb 2010
Posts: 390

Kudos [?]: 201 [0], given: 76

Re: Equation DS [#permalink]

Show Tags

New post 18 Oct 2010, 21:31
Ha, I had this question yesterday in a practice set. I chose A but when reviewed all the answers, understood why it was D. I usually only remember the answer if I reviewed the question. I hope to get a similar one in the real exam now that I know how to solve it!

Kudos [?]: 201 [0], given: 76

Manager
Manager
avatar
Joined: 30 Sep 2010
Posts: 56

Kudos [?]: 60 [0], given: 0

Re: If b, c, and d are constants [#permalink]

Show Tags

New post 07 Nov 2010, 10:05
Hi,

This question should be put under the DS section.

Also the question should read as:

If b, c, and d are constants and x2 + bx + c = (x + d)^2 for all values of x, what is the value of c?

(1) d = 3
(2) b = 6

The answer will be D.

As the equation is true for all the values of X.
Hence corresponding constants attached to the powers of X should be equal
x2 + bx + c = x2 + 2dx + d^2
so b=2d and c=d^2
That means if we know the value of b or d, we can find out c

Hence answer should be D.

Kudos [?]: 60 [0], given: 0

Intern
Intern
avatar
Joined: 25 Jul 2009
Posts: 11

Kudos [?]: 3 [0], given: 2

DS: GMAT paper test: If b, c, and d are constants a [#permalink]

Show Tags

New post 25 Nov 2010, 15:36
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

since expanding (x + d)^2 = x^2 + 2xd + D^2

hence we have
bx + c = 2xd + D^2

we need to know value of b and value of d to get the correct answer.

Can you please explain if it is other wise.
_________________

Failure it not and option -- Gene Kranz

Kudos [?]: 3 [0], given: 2

1 KUDOS received
Current Student
User avatar
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1914

Kudos [?]: 2227 [1], given: 210

Concentration: General Management, Nonprofit
GMAT ToolKit User
Re: DS: GMAT paper test: If b, c, and d are constants a [#permalink]

Show Tags

New post 25 Nov 2010, 15:52
1
This post received
KUDOS
vrajesh wrote:
If b, c, and d are constants and x^2 + bx + c = (x + d)^2 f[highlight]or all values of x[/highlight], what is the value of c?
(1) d = 3
(2) b = 6

since expanding (x + d)^2 = x^2 + 2xd + D^2

hence we have
bx + c = 2xd + D^2

we need to know value of b and value of d to get the correct answer.

Can you please explain if it is other wise.


Given \(x^2 + bx + c = (x+d)^2\)
Expanding on both sides, we get: \(x^2 + 2dx + d^2 = x^2 + bx + c.\) We can cancel the x^2 on both sides and that leaves us with: \(2dx + d^2 = bx + c\)

And this is valid for all values of x, we are given. Let's just substitute two values of x:

\(x = 1\)

Then \(2d + d^2 = b + c\)

\(x = 2\)

\(4d + d^2 = 2b + c\)
Now taking these two equations together:
\(2d + d^2 = b + c
4d + d^2 = 2b + c\)

Multiplying the first equation by 2 and solving, we get:

\(4d + 2d^2 = 2b + 2c
4d + d^2 = 2b + c\)

So we get: \(d^2 = c\)

Thus, from our two statements, we know that statement one is sufficient by itself. Now look at statement 2. And look at the first equation we had: \(2d + d^2 = b + c.\) But then \(c = d^2\), which means that \(2d = b\). So, if b is given, you can find d and hence c. Thus statement 2 is also sufficient.

Thus the trick here is to read the question carefully. If it's valid for all values of x, it's valid for any two values of x. You can arbitrarily pick x. In fact, picking x = 0 might be even better and help you solve the problem much faster, in hindsight.

Kudos [?]: 2227 [1], given: 210

Intern
Intern
avatar
Joined: 07 Jun 2014
Posts: 17

Kudos [?]: 11 [0], given: 42

Location: India
GMAT 1: 720 Q49 V38
GPA: 2.91
WE: Consulting (Energy and Utilities)
If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 14 Aug 2014, 23:32
What if I solve it the way described below? will it be wrong?

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

When these two equations will equate to zero

- From (x+d)^2=0 we can determine that x will only have one unique value i.e. x=-d

- if x will have only one unique value, then from x^2 + bx + c = 0 we can say b^2 - 4ac = 0, where a=1

which means b^2 = 4c
-> c= (b^2)/4 ....(a)

also when b^2 - 4ac = 0 then
x= -b/2a (using x = (-b ±√(b^2 - 4ac))/2a )
where x=d
hence
d=-b/2
b=-2d ...(b)

using (b) on (a)

c=d ...(c)


Now,
evaluating statement (1), value of d is sufficient to determine value of c using (c)
evaluating statement (2), value of b is sufficient to determine value of c using (a)

Hence the answer is D

Is this approach correct?
_________________

I would rather "crash and burn" than "sulk and cry"!!

Kudos [?]: 11 [0], given: 42

Intern
Intern
User avatar
B
Joined: 24 Jun 2013
Posts: 9

Kudos [?]: 8 [0], given: 47

Location: India
Concentration: General Management, Economics
Schools: Tuck '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 05 Jul 2016, 21:46
The discriminant of \(x^2+bx+c\) should be zero -> \(b^2-4c=0\)
Equating the roots of expression \(-b/2=-d\)
Hence if either b or d is known c can be calculated.

Kudos [?]: 8 [0], given: 47

Manager
Manager
User avatar
B
Joined: 27 Mar 2014
Posts: 110

Kudos [?]: 8 [0], given: 19

Schools: ISB '19, IIMA , IIMB
GMAT 1: 660 Q49 V30
Re: If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 17 Sep 2017, 01:59
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

---------------------------------------------------------------------------------------------------------------------------------------------------------

x^2 + bx + c = (x + d)^2 ...................... (1)

using equation 1 , we can say : x^2 + bx + c can be converted into whole square only when b^2 - 4ac = 0 OR -b/2a = -d

Statement 1 :

d = 3 ; also we know a=1

-b/2a = -d
-b/2(1) = -(3)
b=6

b^2-4ac=0
(6)^2 - 4(1)(c) = 0
c=9

sufficient.

Statement 2

b=6

b^2-4ac=0
(6)^2 - 4(1)(c) = 0
c=9

sufficient.

Answer D


Experts pls comment.

Kudos [?]: 8 [0], given: 19

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17809 [0], given: 235

Location: Pune, India
Re: If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 25 Sep 2017, 22:00
Responding to a pm:
Quote:
As we know, in the equation in the form "ax^2 + bx + c", b means summation of the roots when a = 1, and c means product of the roots when a = 1. Here in this DS, the roots are the same, so, as, d = 3, c= 9, and as, b = 6, root is 6/2 = 3, and c = 9, that's okay ...

In problems, however, where roots are different, is there any elegant way to work with ....?


Equate the co-efficients as shown in my post above:
https://gmatclub.com/forum/if-b-c-and-d ... ml#p802314

Depending on what is asked and what is given, you can answer the question.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17809 [0], given: 235

Manager
Manager
User avatar
B
Status: love the club...
Joined: 24 Mar 2015
Posts: 193

Kudos [?]: 17 [0], given: 442

Re: If b, c, and d are constants and x^2 + bx + c = (x + d)^2 [#permalink]

Show Tags

New post 26 Sep 2017, 08:00
VeritasPrepKarishma wrote:
Responding to a pm:
Quote:
As we know, in the equation in the form "ax^2 + bx + c", b means summation of the roots when a = 1, and c means product of the roots when a = 1. Here in this DS, the roots are the same, so, as, d = 3, c= 9, and as, b = 6, root is 6/2 = 3, and c = 9, that's okay ...

In problems, however, where roots are different, is there any elegant way to work with ....?


Equate the co-efficients as shown in my post above:
https://gmatclub.com/forum/if-b-c-and-d ... ml#p802314

Depending on what is asked and what is given, you can answer the question.



thanks mam :-)

Kudos [?]: 17 [0], given: 442

Re: If b, c, and d are constants and x^2 + bx + c = (x + d)^2   [#permalink] 26 Sep 2017, 08:00
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.