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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Sat Mar 28, 2009 3:12 am

If the average (arithmetic mean) of positive integers x, y, and z is 10, what is the greatest
possible value of z ?
A. 8
B. 10
C. 20
D. 28
E. 30

OA: D
Please tell me if in question they have mentioned that there are 3 integers x, y, z like in the ques above, then how 2 of the integers could be same.
Please lemme know if the 2 integers could be same every time we come across the similar situation.

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Source: Beat The GMAT — Problem Solving | Sat Mar 28, 2009 3:12 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sat Mar 28, 2009 3:22 am

The arithmetic mean of x, y and z is 10. This is why (x + y + z)/3 = 30 or x + y + z = 30.
To maximize z, you need to minimize x and y. The smallest positive integer is 1, so we make x = y = 1. This will in turn maximize z to 30 - 1 - 1 = 28.

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Sat Mar 28, 2009 3:37 am

Danaz
The question here is that whether we can take 2 integers same in this problem. i.e. x=y=1.....
Also please lemme know if in question it is mentioned that 'there are 3 different integers' then in this case you cannot take x=y=1. right??

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sat Mar 28, 2009 3:40 am

As it is written, it's perfectly fine to pick x = y. If you don't see "distinct" in the question, then there's no reason to think that x cannot equal y.

If, however, the question goes smth like "the arithmetic mean of three distinct positive integers is 30", then indeed you'd have to consider that x and y cannot be equal.

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Sat Mar 28, 2009 3:46 am

thanks danaz for the expalanation.....
Is it possible for u to chat with me online so that i can clear some general doubts. please lemme know when is it possible? or u can give me ur yahoo id so that i can chat with u.
My Yahoo id is [email protected]
Thanks again.

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