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Difficulty:
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91% (00:58) correct
9%
(01:36)
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based on 22
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If x and y are integers, is k the square of an integer?
(1) \(k = (x^2)(y^2)\)
(2) \(\sqrt{k} = 4\)
(1) \(k = (x^2)(y^2)\)
(2) \(\sqrt{k} = 4\)
27 Apr 2022, 12:00
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Step 1: Analyse Question Stem
x and y are integers. We have to find out if k is the square of an integer.
The square of an integer is a ‘Perfect Square’; therefore, we have to find out if k is a perfect square.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: k=(x^2)(\(y^2\))
From the question data, we know that x and y are integers.
Applying rules of exponents to the expression on the RHS, the equation can be rewritten as
k = \((xy)^2\).
Since x and y are integers, the product xy is also an integer. Therefore, k = \((integer)^2\); in other words, k is a perfect square.
The data in statement 1 is sufficient to answer the question with a definite Yes.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: \(\sqrt{k}\) = 4
Squaring both sides, k = \((4)^2\).
Clearly, k is the square of an integer.
The data in statement 2 is sufficient to answer the question with a definite Yes.
Statement 2 alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
x and y are integers. We have to find out if k is the square of an integer.
The square of an integer is a ‘Perfect Square’; therefore, we have to find out if k is a perfect square.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: k=(x^2)(\(y^2\))
From the question data, we know that x and y are integers.
Applying rules of exponents to the expression on the RHS, the equation can be rewritten as
k = \((xy)^2\).
Since x and y are integers, the product xy is also an integer. Therefore, k = \((integer)^2\); in other words, k is a perfect square.
The data in statement 1 is sufficient to answer the question with a definite Yes.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: \(\sqrt{k}\) = 4
Squaring both sides, k = \((4)^2\).
Clearly, k is the square of an integer.
The data in statement 2 is sufficient to answer the question with a definite Yes.
Statement 2 alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
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