Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Aug 2015, 13:42

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two

Author Message
TAGS:
Intern
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 92 [0], given: 117

If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  12 May 2012, 06:23
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (03:31) correct 43% (01:16) wrong based on 30 sessions
If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two greatest possible values of y ?

A. 4
B. 9/2
C. 7
D. 41/4
E. 25

I get stuck when trying to solve this one. I can see that it will end up something along the lines of (x^2)^2=x^2 to factor it but still struggling.
[Reveal] Spoiler: OA
Intern
Joined: 23 Mar 2012
Posts: 4
Followers: 0

Kudos [?]: 12 [0], given: 0

Re: If 4y4 − 41y2 + 100 = 0, then what is the sum of the two gre [#permalink]  12 May 2012, 07:04
alexpavlos wrote:
I get stuck when trying to solve this one. I can see that it will end up something along the lines of (x^2)^2=x^2 to factor it but still struggling.

If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two greatest possible values of y ?

A) 4
B) 9/2
C) 7
D) 41/4
E) 25

Hi this can be solved as below:-
we have
4y^4 − 41y^2 + 100 = 0
that can be factorised as (a-b)^2=a^2+b^2-2ab------------------------(a)
so we have (2y^2)^2-(2*(2y^2)(10))+10^2-y^2=0

or using (a)
(2y^2-10)^2-2y^2=0
or (2y^2-10)^2=2y^2
i.e we have two solns
on taking square root on both sides
(2y^2-10)=2y-----------------------(b)
or (2y^2-10)=-2y-----------------(c)
on solving (b) as normal eqn we have
(2y-5)(y+2) =0
so max value is y =5/2
on solving (c) we have
(2y+5)(y-2) =0
or max value as y=2
so adding these two values we have
2+5/2==9/2

I hope this helps
Math Expert
Joined: 02 Sep 2009
Posts: 29108
Followers: 4725

Kudos [?]: 49736 [2] , given: 7403

Re: If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  12 May 2012, 10:32
2
KUDOS
Expert's post
alexpavlos wrote:
If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two greatest possible values of y ?

A. 4
B. 9/2
C. 7
D. 41/4
E. 25

I get stuck when trying to solve this one. I can see that it will end up something along the lines of (x^2)^2=x^2 to factor it but still struggling.

Factor $$4y^4-41y^2+100=0$$ (or just solve for $$y^2$$) --> $$(y^2-4)(4y^2-25)=0$$:

$$y^2-4=0$$ --> $$y=-2$$ or $$y=2$$;
$$4y^2-25=0$$ --> $$y=-\frac{5}{2}$$ or $$y=\frac{5}{2}$$;

So, the sum of the two greatest possible values of $$y$$ is $$2+\frac{5}{2}=\frac{9}{2}$$.

Hope it helps.
_________________
Current Student
Joined: 05 Jun 2010
Posts: 123
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 680 Q50 V31
GMAT 2: 690 Q47 V38
GMAT 3: 710 Q49 V39
WE: Design (Manufacturing)
Followers: 1

Kudos [?]: 12 [0], given: 12

Re: If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  12 May 2012, 13:14
4y^4 − 41y^2 + 100 = 0

Let y^2=x

4x^2-41x+100=0

by finding the roots of the equation we get using [(-b(+/_)[square_root]b^2-4ac[/square_root)/2a}]

x=4 or 25/4

so y=2 or -2 or y=5/2 or -5/2

=2+5/2=9/2

Hence B

Hope that helps!!
_________________

Work with hope in Heart and dreams in the eyes .... And leave the mind for GMAT problems

Senior Manager
Joined: 19 Apr 2009
Posts: 435
Location: San Francisco, California
Followers: 77

Kudos [?]: 284 [1] , given: 5

Re: If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  12 May 2012, 20:08
1
KUDOS
See attached image.

Dabral
Attachments

image22.png [ 78.65 KiB | Viewed 1988 times ]

_________________

New!2016 OFFICIAL GUIDE FOR GMAT REVIEW: Free Video Explanations.
http://www.gmatquantum.com

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 293 [0], given: 11

If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  21 Dec 2012, 05:33
rphardu wrote:
If 4y4 − 41y2 + 100 = 0, then what is the sum of the two greatest possible values of y ?

A)4
B)9/2
C)7
D)41/4
E)25

Let y^2 = x

4x^2 - 41x + 100 = 0
(4x - 25)(x - 4) = 0
x = 25/4 or x = 4

y = 5/2 or y = 2

= 5/2 + 2 = 9/2

_________________

Impossible is nothing to God.

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 293 [0], given: 11

If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two great [#permalink]  26 Dec 2012, 21:58
rphardu wrote:
If 4y4 − 41y2 + 100 = 0, then what is the sum of the two greatest possible values of y ?

A)4
B)9/2
C)7
D)41/4
E)25

Let $$x = y^2$$

$$4(y^2)^2 - 41 (y^2) + 100 = 0$$
$$4x^2 - 41x^2 + 100 = 0$$

$$(4x - 25)(x - 4) = 0$$
$$x = \frac{25}{4} = y^2$$
$$y = \frac{5}{2}$$

$$x = 4$$
$$x = y^2 = 4$$
$$y = 2$$

Answer: $$\frac{5}{2} + 2 = \frac{9}{2}$$

_________________

Impossible is nothing to God.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 6106
Followers: 340

Kudos [?]: 69 [0], given: 0

Re: If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two [#permalink]  05 Jul 2015, 02:21
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 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two   [#permalink] 05 Jul 2015, 02:21
Similar topics Replies Last post
Similar
Topics:
9 If x^4 + y^4 = 100, then the greatest possible value of x is 3 26 Feb 2012, 08:58
1 What is the probability that the sum of two dice will yield 2 08 Feb 2012, 13:50
7 If 4y^4 − 41y^2 + 100 = 0, then what is the sum of the two 2 06 Aug 2011, 15:43
6 If x^4 + y^4 = 100, then the greatest possible value of x 8 07 Aug 2010, 08:25
2 If x^4+y^4=100, then the greatest possible value of x is 5 23 Aug 2008, 03:22
Display posts from previous: Sort by