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Age

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
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6
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by sparky_paris » Thu Feb 11, 2010 6:43 pm
Infinite assuming x does not have to be an integer
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by swapna » Thu Feb 11, 2010 7:57 pm
can u please elaborate how this sum works?
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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
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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?

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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)
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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 :|
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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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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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