Algebra Question

One question from GMAT prep is haunting me? I could not simplify the way to reach the answer. Please suggest some simple way to answer following types of question.

a^4+b^4=100. What can be the maximum value of "a" in the following range?
1. (1,2)
2. (2,3)
3. (3,4)
4. (4,5)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Mon Apr 09, 2012 6:41 am

smishrajec wrote:One question from GMAT prep is haunting me? I could not simplify the way to reach the answer. Please suggest some simple way to answer following types of question.

a^4+b^4=100. What can be the maximum value of "a" in the following range?
1. (1,2)
2. (2,3)
3. (3,4)
4. (4,5)

To MAXIMIZE one value, try to MINIMIZE the other values.
The smallest possible value of bâ�´ is 0.
Thus, the MAXIMUM possible value of aâ�´ is 100.
Since 3â�´=81 and 4â�´=256, the maximum possible value of a is between 3 and 4.

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smishrajec: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Wed May 18, 2011 9:07 pm; Location: Pune, India; GMAT Score:410

by smishrajec » Mon Apr 09, 2012 6:58 am

Thanks Mitch!!!!!!
It works with other questions of same types too...

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