Age

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 11:15 am

The age of the four friends namely Abhishek, Aman, Deepak and Dilshan is (x - 2), (3x + 3), (x - 5) and (11 - x) respectively. The average age (in years) of the 4 mentioned friends is 'y'. How many integral values of 'y' are possible?

a) 1
b) 3
c) 4
d) 6
e) infinite

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 11:15 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 11:17 am

shashank.ism wrote:The age of the four friends namely Abhishek, Aman, Deepak and Dilshan is (x - 2), (3x + 3), (x - 5) and (11 - x) respectively. The average age (in years) of the 4 mentioned friends is 'y'. How many integral values of 'y' are possible?

a) 1
b) 3
c) 4
d) 6
e) infinite

It can be calculated that y =
(4x + 7)/4= x +7/4
= x + 1.75
Also, the age of each of the mentioned friends has to be non-negative.
Therefore, the range of values of 'x' is 5 < x < 11.
Possible values of 'x' for which the value of 'y' is an integer is
5.25, 6.25, 7.25, 8.25, 9.25 and 10.25 respectively.[spoiler]
Hence, there are 6 possible integral values of 'y'.
Hence,D.[/spoiler]

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 11:40 am

shashank.ism wrote:The age of the four friends namely Abhishek, Aman, Deepak and Dilshan is (x - 2), (3x + 3), (x - 5) and (11 - x) respectively. The average age (in years) of the 4 mentioned friends is 'y'. How many integral values of 'y' are possible?

a) 1
b) 3
c) 4
d) 6
e) infinite

y= x-2+ x-5+ 3x+3 + 11-x = 4x+7/4 = x +7/4

Now x <11 x>5
possible values for x for y to be integral is 5.25, 6.25, 7.25, 8.25, 9.25 and 10.25

6 of them

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