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What is the value of (x-y)^4

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by alex.gellatly » Wed Aug 08, 2012 8:25 pm
What is the value of (x-y)^4?
1. The product of x and y is 7
2. x and y are integers

Thanks
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Aug 08, 2012 8:31 pm
alex.gellatly wrote:What is the value of (x-y)^4?
1. The product of x and y is 7
2. x and y are integers

Thanks
(1) xy = 7
If x = 7, y = 1, then (x - y)^4 = (7 - 1)^4 = 6^4
If x = 14, y = 1/2, then (x - y)^4 = (14 - 1/2)^4 = (13.5)^4
No definite answer; NOT sufficient.

(2) x and y are integers.
x and y can take any values, so (x - y)^4 will have no definite answer; NOT sufficient.

Combining (1) and (2), x and y are integers such that xy = 7
So, the only possible value of x = 7 and y = 1 respectively; SUFFICIENT.

The correct answer is C.
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by mcdesty » Fri Aug 10, 2012 7:52 pm
Anurag@Gurome wrote:
alex.gellatly wrote:What is the value of (x-y)^4?
1. The product of x and y is 7
2. x and y are integers

Thanks
(1) xy = 7
If x = 7, y = 1, then (x - y)^4 = (7 - 1)^4 = 6^4
If x = 14, y = 1/2, then (x - y)^4 = (14 - 1/2)^4 = (13.5)^4
No definite answer; NOT sufficient.

(2) x and y are integers.
x and y can take any values, so (x - y)^4 will have no definite answer; NOT sufficient.

Combining (1) and (2), x and y are integers such that xy = 7
So, the only possible value of x = 7 and y = 1 respectively; SUFFICIENT.

The correct answer is C.

Well the answer is C but why can't X can be 1 and y 7?..
I know C still works because we are raising the difference to an even power which makes the sign of the base inconsequential.
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by Anurag@Gurome » Fri Aug 10, 2012 8:33 pm
mcdesty wrote: Well the answer is C but why can't X can be 1 and y 7?..
I know C still works because we are raising the difference to an even power which makes the sign of the base inconsequential.
You can take x = 1 and y = 7, that wouldn't change anything; x = 1, y = 7, then (x - y)^4 = (1 - 7)^4 = (-6)^4 = 6^4
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by mcdesty » Sat Aug 11, 2012 9:13 am
Anurag@Gurome wrote:
mcdesty wrote: Well the answer is C but why can't X can be 1 and y 7?..
I know C still works because we are raising the difference to an even power which makes the sign of the base inconsequential.
You can take x = 1 and y = 7, that wouldn't change anything; x = 1, y = 7, then (x - y)^4 = (1 - 7)^4 = (-6)^4 = 6^4
You are absolutely right sir..The only reason I brought it up was beacuse you said "The only possible value of x = 7 and y = 1"
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by vk_vinayak » Sat Aug 11, 2012 9:23 am
Anurag@Gurome wrote:
mcdesty wrote: Well the answer is C but why can't X can be 1 and y 7?..
I know C still works because we are raising the difference to an even power which makes the sign of the base inconsequential.
You can take x = 1 and y = 7, that wouldn't change anything; x = 1, y = 7, then (x - y)^4 = (1 - 7)^4 = (-6)^4 = 6^4
Correct. X and Y can be even -1 and -7, still the answer would be same, because the absolute difference between -1 an -7 is equivalent to absolute difference between 1 and 7.
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by mcdesty » Sat Aug 11, 2012 10:10 am
vk_vinayak wrote:
Anurag@Gurome wrote:
mcdesty wrote: Well the answer is C but why can't X can be 1 and y 7?..
I know C still works because we are raising the difference to an even power which makes the sign of the base inconsequential.
You can take x = 1 and y = 7, that wouldn't change anything; x = 1, y = 7, then (x - y)^4 = (1 - 7)^4 = (-6)^4 = 6^4
Correct. X and Y can be even -1 and -7, still the answer would be same, because the absolute difference between -1 an -7 is equivalent to absolute difference between 1 and 7.
(-1-7) is -8 and that is 8 away from zero not 6...X and Y can't be -1 and -7...
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by eagleeye » Sat Aug 11, 2012 10:32 am
mcdesty wrote:
(-1-7) is -8 and that is 8 away from zero not 6...X and Y can't be -1 and -7...
-1, -7
(-1) - (-7) = -1 + 7 = -6.
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by mcdesty » Sat Aug 11, 2012 10:44 am
eagleeye wrote:
mcdesty wrote:
(-1-7) is -8 and that is 8 away from zero not 6...X and Y can't be -1 and -7...
-1, -7
(-1) - (-7) = -1 + 7 = -6.
"The absolute difference"...Must have read what he wrote poorly...Thkx
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by alex.gellatly » Wed Aug 29, 2012 6:05 pm
Anurag@Gurome wrote:
alex.gellatly wrote:What is the value of (x-y)^4?
1. The product of x and y is 7
2. x and y are integers

Thanks
(1) xy = 7
If x = 7, y = 1, then (x - y)^4 = (7 - 1)^4 = 6^4
If x = 14, y = 1/2, then (x - y)^4 = (14 - 1/2)^4 = (13.5)^4
No definite answer; NOT sufficient.

(2) x and y are integers.
x and y can take any values, so (x - y)^4 will have no definite answer; NOT sufficient.

Combining (1) and (2), x and y are integers such that xy = 7
So, the only possible value of x = 7 and y = 1 respectively; SUFFICIENT.

The correct answer is C.
So on questions like these it is advisable NOT to factor it all out. I was tying a whole bunch of different algebraic things... all to no avail.
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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