MGMAT, Inequalities!

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Ahmed MS: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Wed Apr 06, 2011 8:35 pm; Followed by:1 members

MGMAT, Inequalities!

by Ahmed MS » Fri Oct 21, 2011 11:32 pm

Q: If x>y, x<6, and y>-3, what is the largest prime number that could be equal to x+y? ( source: Manhattan equation, chapter 12 problem set).

The answer is 11 but I failed to understand the explanation, please help.

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Source: Beat The GMAT — Problem Solving | Fri Oct 21, 2011 11:32 pm

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Anurag@Gurome: 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 » Fri Oct 21, 2011 11:38 pm

Ahmed MS wrote:Q: If x>y, x<6, and y>-3, what is the largest prime number that could be equal to x+y? ( source: Manhattan equation, chapter 12 problem set).

-3 < y < x < 6

To find the largest prime number which is equal to (x + y), we have to maximize both x and y such that their sum is a prime number. Note that this does not mean that x and y have to be integer.

Maximum possible value for x and y is just less than 6.
Hence, maximum possible sum of x and y will be just less than (6 + 6) = 12

The largest prime number less than 12 is 11.
If we take x = 5.9 and y = 5.1, (x + y) = (5.9 + 5.1) = 11
Hence, it is possible that (x + y) can be equal to 11.

Therefore, 11 is the largest prime number that could be equal to (x + y).

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