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The greatest possible value of

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The greatest possible value of [#permalink] New post 07 Dec 2017, 03:06
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Question Stats:

77% (01:09) correct 22% (00:37) wrong based on 45 sessions
Quantity A
Quantity B
The greatest possible value of \(\frac{2}{x-y}\) where x and y are integers and \(9 \leq x \leq 12\) and \(-2 \leq y \leq 8\)
2


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Last edited by chetan2u on 03 Nov 2018, 22:14, edited 1 time in total.
Corrected the question
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Re: The greatest possible value of [#permalink] New post 08 Dec 2017, 00:06
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the answer is C?
that x could be 9, y could be 8
2/1=2 ?
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Re: The greatest possible value of [#permalink] New post 08 Dec 2017, 02:17
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OA added

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Re: The greatest possible value of [#permalink] New post 17 Feb 2018, 01:32
Maximum value of Quantity A will be obtained if we put least possible value of x-y in denominator. That will be minimum value of x and maximum of y.
Hence, Choice C is correct.
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Re: The greatest possible value of [#permalink] New post 17 Feb 2018, 04:04
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Yes, I have C as well. Because of the negative in x-y, plug in the least value of x (=9) with the greatest value of y (=8).
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Re: The greatest possible value of [#permalink] New post 03 Nov 2018, 17:30
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I'm sorry to revive an old topic but I disagree with the answer.
What if X = 8.5 and Y = 8?
The difference would be 1/2 = 0.5, which would duplicate the value of A, making it bigger than B.
Is there something Im missing?
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Re: The greatest possible value of [#permalink] New post 03 Nov 2018, 22:12
Expert's post
RCDMC wrote:
I'm sorry to revive an old topic but I disagree with the answer.
What if X = 8.5 and Y = 8?
The difference would be 1/2 = 0.5, which would duplicate the value of A, making it bigger than B.
Is there something Im missing?


Yes you are correct.
A could be actually infinity in the present state as it is NOT given that x and y are integers..
Carcass wrote:
Quantity A
Quantity B
The greatest possible value of \(\frac{2}{x-y}\) where \(9 \leq x \leq 12\) and \(-2 \leq y \leq 8\)
2



say x is 9 and y is 8.999999, \(\frac{2}{x-y}=\frac{2}{9-8.999999}=\frac{2}{0.000001}=2*10^6\), way bigger than B

So editing to make it correct..
Now when we take them as integers we take minimum value of x as 9 and maximum value of y as 8
\(A=\frac{2}{x-y}=\frac{2}{9-8}=\frac{2}{1}=2=B\)
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: The greatest possible value of [#permalink] New post 20 Dec 2018, 15:25
chetan2u wrote:
RCDMC wrote:
I'm sorry to revive an old topic but I disagree with the answer.
What if X = 8.5 and Y = 8?
The difference would be 1/2 = 0.5, which would duplicate the value of A, making it bigger than B.
Is there something Im missing?


Yes you are correct.
A could be actually infinity in the present state as it is NOT given that x and y are integers..
Carcass wrote:
Quantity A
Quantity B
The greatest possible value of \(\frac{2}{x-y}\) where \(9 \leq x \leq 12\) and \(-2 \leq y \leq 8\)
2



say x is 9 and y is 8.999999, \(\frac{2}{x-y}=\frac{2}{9-8.999999}=\frac{2}{0.000001}=2*10^6\), way bigger than B

So editing to make it correct..
Now when we take them as integers we take minimum value of x as 9 and maximum value of y as 8
\(A=\frac{2}{x-y}=\frac{2}{9-8}=\frac{2}{1}=2=B\)


Please check that −2≤y≤8 means max value for y is 8 not even 8.000.......001, let alone 8.9999999, and
again for x, min vale is 9 because 9≤x≤12.

As a result, 2/(9-8)=2/1=2.
Answer is C.
_______________________________________________________________
Please let me know if I am wrong.
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Re: The greatest possible value of [#permalink] New post 20 Dec 2018, 18:04
Expert's post
AE wrote:
chetan2u wrote:
RCDMC wrote:
I'm sorry to revive an old topic but I disagree with the answer.
What if X = 8.5 and Y = 8?
The difference would be 1/2 = 0.5, which would duplicate the value of A, making it bigger than B.
Is there something Im missing?


Yes you are correct.
A could be actually infinity in the present state as it is NOT given that x and y are integers..
Carcass wrote:
Quantity A
Quantity B
The greatest possible value of \(\frac{2}{x-y}\) where \(9 \leq x \leq 12\) and \(-2 \leq y \leq 8\)
2



say x is 9 and y is 8.999999, \(\frac{2}{x-y}=\frac{2}{9-8.999999}=\frac{2}{0.000001}=2*10^6\), way bigger than B

So editing to make it correct..
Now when we take them as integers we take minimum value of x as 9 and maximum value of y as 8
\(A=\frac{2}{x-y}=\frac{2}{9-8}=\frac{2}{1}=2=B\)


Please check that −2≤y≤8 means max value for y is 8 not even 8.000.......001, let alone 8.9999999, and
again for x, min vale is 9 because 9≤x≤12.

As a result, 2/(9-8)=2/1=2.
Answer is C.
_______________________________________________________________
Please let me know if I am wrong.


Yes , that is correct,
For some reason I took −2≤y≤8 as −2≤y≤9..
If it is −2≤y≤8, we have to take minimum value of x-y to get maximum of 2/(x-y)... Ans least value of x-y is 1 when x is 9 and y is 8
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: The greatest possible value of [#permalink] New post 21 Dec 2018, 10:25
C
if we try all the border cases we can't seem to get x-y less than 1 in order to get A to its highest value with the lowest denominator
Re: The greatest possible value of   [#permalink] 21 Dec 2018, 10:25
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