GmatPrep I--x^4 + y^4 = 100

This topic has expert replies
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sun Jan 02, 2011 12:22 am
prachich1987 wrote:If x^4 + y^4 = 100, the greatest possible value of x is between

a. 0 and 3
b. 3 and 6
c. 6 and 9
d. 9 and 12
e. 12 and 15
(x^4 + y^4) = 100 => x^4 = (100 - y^4)

Note that when x is maximum, x^4 is also maximum. Now to maximize x we have to maximize (100 - y^4), which is equivalent to minimization of y^4. Now minimum value of y^4 is 0. Therefore maximum value of (100 - y^4) is 100.

Thus, maximum value of x^4 is 100.
Therefore, maximum value of x = 4-th root of 100 = √10 ≈ 3.(something)

The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

User avatar
Legendary Member
Posts: 752
Joined: Sun Sep 12, 2010 2:47 am
Thanked: 20 times
Followed by:10 members
GMAT Score:700

by prachich1987 » Sun Jan 02, 2011 12:27 am
Thanks Anurag.
Even I had marked B.
But the answer given in the document is A.It must be wrong.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Sun Jan 02, 2011 1:22 am
prachich1987 wrote:Thanks Anurag.
Even I had marked B.
But the answer given in the document is A.It must be wrong.
yep

i noticed that you titled this thread "gmatprep I" -- did you actually see this problem on gmatprep, with this solution, with your own two eyes? or did you get it from some kind of archive?
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

User avatar
Legendary Member
Posts: 752
Joined: Sun Sep 12, 2010 2:47 am
Thanked: 20 times
Followed by:10 members
GMAT Score:700

by prachich1987 » Sun Jan 02, 2011 1:24 am
lunarpower wrote:
prachich1987 wrote:Thanks Anurag.
Even I had marked B.
But the answer given in the document is A.It must be wrong.
yep

i noticed that you titled this thread "gmatprep I" -- did you actually see this problem on gmatprep, with this solution, with your own two eyes? or did you get it from some kind of archive?
This is from the document "198 Level 700+ questions from GMAT Prep I which I downloaded from BTG.

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3380
Joined: Mon Mar 03, 2008 1:20 am
Thanked: 2256 times
Followed by:1535 members
GMAT Score:800

by lunarpower » Sun Jan 02, 2011 1:41 am
prachich1987 wrote:
lunarpower wrote:
prachich1987 wrote:Thanks Anurag.
Even I had marked B.
But the answer given in the document is A.It must be wrong.
yep

i noticed that you titled this thread "gmatprep I" -- did you actually see this problem on gmatprep, with this solution, with your own two eyes? or did you get it from some kind of archive?
This is from the document "198 Level 700+ questions from GMAT Prep I which I downloaded from BTG.
ah. ok.

i downloaded it and wrote a post about it here:
https://www.beatthegmat.com/198-level-70 ... tml#327982

there are a couple of other sketchy problems in there -- for instance, #74 says that two INTEGERS x and y have a sum of 72, but statement (1) says that x = y + 1. this is impossible; if x = y + 1 and x+y = 72, then you get x = 36.5 and y = 35.5, contradicting the statement that they are integers.
so, overall, that's a decent source, but (a) be careful, and (b) they aren't all "top difficulty" problems (not that this matters anyway -- it doesn't).
in fact, any claim by anyone who purports to know the exact difficulty levels of official GMAC problems will always be a lie; GMAC has never published the adaptive performance curves of any of its problems, nor does it ever plan to do so.
Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi

--

Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron