Age

Question

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

sparky_paris · Answer

Infinite assuming x does not have to be an integer

swapna · Answer

can u please elaborate how this sum works?

ajith · Answer

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

kaustubh_b · Answer

Since we are talking about ages here, should we not be assuming integer values for the ages? OA plz...[/spoiler]

Brent@GMATPrepNow · Answer

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)

ajith · Answer

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

shashank.ism · Answer

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.

harsh.champ · Answer

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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