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

It is currently 15 Dec 2018, 17:15

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,  [#permalink]

Show Tags

New post 16 Apr 2018, 04:13
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:25) correct 24% (01:52) wrong based on 56 sessions

HideShow timer Statistics

Manager
Manager
User avatar
B
Joined: 26 Sep 2017
Posts: 97
Re: If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,  [#permalink]

Show Tags

New post 16 Apr 2018, 10:33
2
If roots are real and equal then it must be
Discrimanate i.e
b^2 - 4ac = 0
By solving we get b = 80
Hence d...

Sent from my BND-AL10 using GMAT Club Forum mobile app
Senior Manager
Senior Manager
User avatar
G
Joined: 29 Dec 2017
Posts: 384
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Re: If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,  [#permalink]

Show Tags

New post 16 Apr 2018, 13:16
Bunuel wrote:
If there is exactly one solution to the equation 25x^2 − bx + 64 = 0, where b > 0, what is the value of b?

A. 26
B. 40
C. 52
D. 80
E. 100


Quadratic equation takes only one X when it looks like (x-n)^2 or (x+n)^2. In our case we have (ax-n)^2 => (ax)^2-2anx+n^2 => bx = 2*5*8*x = 80x. Answer (D)
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2211
Premium Member CAT Tests
If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,  [#permalink]

Show Tags

New post 20 Apr 2018, 10:25
2
Bunuel wrote:
If there is exactly one solution to the equation 25x^2 − bx + 64 = 0, where b > 0, what is the value of b?

A. 26
B. 40
C. 52
D. 80
E. 100

The expression \(b^2 - 4ac\) is the "discriminant" of the quadratic equation.

If \(b^2 - 4ac > 0\), there are two solutions

If \(b^2 - 4ac = 0\), there is one solution

If \(b^2 - 4ac < 0\), there are no solutions

There is one solution here, so
\(b^2 - 4ac = 0\)
\(a = 25\)
\(c = 64\)

\(b^2 - (4)(25)(64) = 0\)
\(b^2 - 6400 = 0\)
\(b^2 = 6400\)
\(b = 80\)


Answer D

Alternatively, try factoring the quadratic equation. True, we don't know \(b\), but the first and third terms are big hints.

Notice the coefficient of \(ax^2\) and the constant, \(c\): 25 and 64 are perfect squares

There is one solution. Some root times itself = this quadratic equation

The algebraic identity \((x-y)^2\) has such a factor pattern (as does \((x+y)^2\)).

That is
\((x-y)^2=(x-y)(x-y)=x^2-2xy+ y^2\)

Knowing the identity is not a must here, but it helps. Either way:

Use the square roots of the first and third terms to factor

\((5x-8)(5x-8)=25x^2-80x+64\)
That works. One solution.

\(b = 80\)

Answer D
GMAT Club Bot
If there is exactly one solution to the equation 25x^2 − bx + 64 = 0, &nbs [#permalink] 20 Apr 2018, 10:25
Display posts from previous: Sort by

If there is exactly one solution to the equation 25x^2 − bx + 64 = 0,

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.