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0< x< y< 1
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Updated on: 08 Apr 2021, 01:57
Updated on: 08 Apr 2021, 01:57
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0< x< y< 1
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(y-x\) |
\( (x-y)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Originally posted by harishsridharan on 08 Apr 2021, 01:52.
Last edited by harishsridharan on 08 Apr 2021, 01:57, edited 1 time in total.
Last edited by harishsridharan on 08 Apr 2021, 01:57, edited 1 time in total.
0< x< y< 1
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08 Apr 2021, 02:30
08 Apr 2021, 02:30
1
0< x< y< 1
Qt B
\((x-y)^2\)
As it is square, we can write this as \((y-x)^2\)
Now divide both the quantities with \(y-x\)
Qt A = 1
Qt B = \(y-x\)
We are given that 0< x< y< 1
Qt A > Qt B
Answer A
Qt B
\((x-y)^2\)
As it is square, we can write this as \((y-x)^2\)
Now divide both the quantities with \(y-x\)
Qt A = 1
Qt B = \(y-x\)
We are given that 0< x< y< 1
Qt A > Qt B
Answer A
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0< x< y< 1
[#permalink]
09 Apr 2021, 05:09
09 Apr 2021, 05:09
1
harishsridharan wrote:
\(0< x< y< 1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(y-x\) |
\( (x-y)^2\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Useful property: \(a-b = -1(b-a)\)
So, \( (x-y)^2=[(-1)(y-x)]^2\)
\(=(-1)^2(y-x)^2\)
\(=(1)(y-x)^2\)
\(=(y-x)(y-x)\)
We're now ready to solve the question...
Given:
Quantity A: \(y-x\)
Quantity B: \( (x-y)^2\)
Replace Quantity B with its equivalent value:
Quantity A: \(y-x\)
Quantity B: \((y-x)(y-x)\)
Since \(0< x< y< 1\), we know that \(y - x\) is POSITIVE, which means we can safely divide both quantities by \(y - x\) to get:
Quantity A: \(1\)
Quantity B: \(y-x\)
From here, a nice way to determine which quantity is greater is to first add \(x\) to both quantities to get:
Quantity A: \(1+x\)
Quantity B: \(y\)
Since x is positive, we know that Quantity A is greater than 1.
Conversely, we are told that y < 1.
So Quantity A must be greater.
Answer: A
