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 » Tue Feb 09, 2010 1:00 pm

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?

Infinite
1
3
4
6

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:00 pm

sparky_paris: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Feb 11, 2010 4:43 pm

by sparky_paris » Thu Feb 11, 2010 6:43 pm

Infinite assuming x does not have to be an integer

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swapna: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sat Jan 23, 2010 1:14 pm

by swapna » Thu Feb 11, 2010 7:57 pm

can u please elaborate how this sum works?

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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 » Thu Feb 11, 2010 11:38 pm

swapna wrote:can u please elaborate how this sum works?

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

Average age =( (x - 2) +(3x + 3) + (x - 5) +(11 - x) )/4
= (4x+7)/4
= x+7/4
now y =x+7/4 has to be an integer

Since nowhere it is mentioned that x is an integer so, technically we can have infinite number of x's which satisfies this.

Had it been mentioned in the question that x is an integer the answer becomes zero because if x is an integer y = x+7/4 cannot be an integer

Always borrow money from a pessimist, he doesn't expect to be paid back.

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kaustubh_b: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon Oct 26, 2009 10:55 pm; Thanked: 1 times; GMAT Score:670

by kaustubh_b » Mon Feb 15, 2010 12:21 pm

Since we are talking about ages here, should we not be assuming integer values for the ages?

OA plz...[/spoiler]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 15, 2010 4:14 pm

ajith wrote:
swapna wrote:can u please elaborate how this sum works?
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

Average age =( (x - 2) +(3x + 3) + (x - 5) +(11 - x) )/4
= (4x+7)/4
= x+7/4
now y =x+7/4 has to be an integer

Since nowhere it is mentioned that x is an integer so, technically we can have infinite number of x's which satisfies this.

Had it been mentioned in the question that x is an integer the answer becomes zero because if x is an integer y = x+7/4 cannot be an integer

This is an interesting question.
The solution above is almost there: y = x + 7/4 (or y = x + 1 3/4)
So, for example, x could equal 5 1/4, since 5 1/4 + 1 3/4 = 7, and 7 is an integer.
So, it seems that, since x can have any value, we can have an infinite number of y values such that y is an integer.
The only problem here is that this is a Real World question, and in the real world people have positive ages.

Consider that Deepak's age is x-5. This means that x must be greater than 5, otherwise Deepak will have either a negative age or an age of zero.
Similarly, since Dilshan's age is 11-x, x cannot be greater than 11, otherwise Dilshan will have a negative age (or an age = 0).
From this we can see that 5 < x < 11

For y to have an integral value, x can equal 5 1/4, 6 1/4, 7 1/4, 8 1/4, 9 1/4 and 10 1/4.
So, the answer is 6 (E)

Brent Hanneson - Creator of GMATPrepNow.com

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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 15, 2010 9:13 pm

Brent Hanneson wrote: Consider that Deepak's age is x-5. This means that x must be greater than 5, otherwise Deepak will have either a negative age or an age of zero.
Similarly, since Dilshan's age is 11-x, x cannot be greater than 11, otherwise Dilshan will have a negative age (or an age = 0).
From this we can see that 5 < x < 11

For y to have an integral value, x can equal 5 1/4, 6 1/4, 7 1/4, 8 1/4, 9 1/4 and 10 1/4.
So, the answer is 6 (E)

Thanks Brent for opening my eyes
This reminds me that I need to be more careful and should give more attention to details

Always borrow money from a pessimist, he doesn't expect to be paid back.

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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 15, 2010 9:57 pm

Thanks brent you really proposed a good solution. People were getting confused taking the fractional part 7/4 and integral value of X though integral value of Y was required.

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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 15, 2010 10:42 pm

Brent Hanneson wrote:
ajith wrote:
swapna wrote:can u please elaborate how this sum works?
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

Average age =( (x - 2) +(3x + 3) + (x - 5) +(11 - x) )/4
= (4x+7)/4
= x+7/4
now y =x+7/4 has to be an integer

Since nowhere it is mentioned that x is an integer so, technically we can have infinite number of x's which satisfies this.

Had it been mentioned in the question that x is an integer the answer becomes zero because if x is an integer y = x+7/4 cannot be an integer
This is an interesting question.
The solution above is almost there: y = x + 7/4 (or y = x + 1 3/4)
So, for example, x could equal 5 1/4, since 5 1/4 + 1 3/4 = 7, and 7 is an integer.
So, it seems that, since x can have any value, we can have an infinite number of y values such that y is an integer.
The only problem here is that this is a Real World question, and in the real world people have positive ages.

Consider that Deepak's age is x-5. This means that x must be greater than 5, otherwise Deepak will have either a negative age or an age of zero.
Similarly, since Dilshan's age is 11-x, x cannot be greater than 11, otherwise Dilshan will have a negative age (or an age = 0).
From this we can see that 5 < x < 11

For y to have an integral value, x can equal 5 1/4, 6 1/4, 7 1/4, 8 1/4, 9 1/4 and 10 1/4.
So, the answer is 6 (E)

Thanks Brent.Really interesting take on the question.Most of the people just saw that x can be a fraction and proceeded to say that it is a wrong question.It is better for us to consider all the alternatives rather than having a negative attitude and declaring the question incorrect.

Well,I see that just using the fact that "All the ages must be positive",you have formed 4 inequalities and solved the question.Can you also give some more tips as to what different kinds of inequalities can be spotted in a question??

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Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

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