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17 Apr 2022, 23:07
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:37) correct
29%
(01:30)
wrong
based on 195
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If \(x^2 + y^2 = 100\), what is the value of \((x - y)^2\) ?
(1) \(x=\frac{48}{y}\)
(2) \(x^2-y^2=-28\)
(1) \(x=\frac{48}{y}\)
(2) \(x^2-y^2=-28\)
18 Apr 2022, 09:14
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Step 1: Analyse Question Stem
We know that \( x^2 + y^2\) = 100.
The value of \((x – y)^2\) is to be calculated.
\((x-y)^2\) = \(x^2\) +\( y^2\) – 2xy, we need the value of xy to be able to calculate the answer since \(x^2 + y^2\) is given as question data.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x = \(\frac{48 }{ y}\)
Therefore, xy = 48. This is sufficient to calculate the value of \((x-y)^2\).
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: \(x^2−y^2\) = −28
From the question, \(x^2 + y^2\) = 100.
These two equations can be solved as simultaneous equations. Doing so, we get,
\(x^2\) = 36 and \(y^2\) = 64
Therefore, x = +6 or -6 and y = +8 or -8.
This means that we can different values for (x-y) and hence different values for \((x-y)^2\).
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
We know that \( x^2 + y^2\) = 100.
The value of \((x – y)^2\) is to be calculated.
\((x-y)^2\) = \(x^2\) +\( y^2\) – 2xy, we need the value of xy to be able to calculate the answer since \(x^2 + y^2\) is given as question data.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x = \(\frac{48 }{ y}\)
Therefore, xy = 48. This is sufficient to calculate the value of \((x-y)^2\).
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: \(x^2−y^2\) = −28
From the question, \(x^2 + y^2\) = 100.
These two equations can be solved as simultaneous equations. Doing so, we get,
\(x^2\) = 36 and \(y^2\) = 64
Therefore, x = +6 or -6 and y = +8 or -8.
This means that we can different values for (x-y) and hence different values for \((x-y)^2\).
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
18 Apr 2022, 10:55
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I am a little confused about when we are supposed to consider negative values of square root and when not. I selected option D, thinking we can discard the value of -6 for x. Can someone please clarify?
