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26 Feb 2014, 02:26
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Question Stats:
86% (00:57) correct
14%
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wrong
based on 1432
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If d is a positive integer, is \(\sqrt{d}\) an integer?
(1) d is the square of an integer.
(2) \(\sqrt{d}\) is the square of an integer.
(1) d is the square of an integer.
(2) \(\sqrt{d}\) is the square of an integer.
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26 Feb 2014, 02:26
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SOLUTION
If d is a positive integer, is \(\sqrt{d}\) an integer?
Given: \(d=integer\).
Question: is \(\sqrt{d}=integer\)? or: is \(d\) a perfect square: is \(d=integer^2\)?
(1) \(d\) is the square of an integer --> \(d=integer^2\) --> directly gives an answer. Sufficient.
(2) \(\sqrt{d}\) is the square of an integer --> \(\sqrt{d}=integer^2=integer\) (as square of an integer is an integer). Sufficient.
Answer: D.
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If d is a positive integer, is \(\sqrt{d}\) an integer?
Given: \(d=integer\).
Question: is \(\sqrt{d}=integer\)? or: is \(d\) a perfect square: is \(d=integer^2\)?
(1) \(d\) is the square of an integer --> \(d=integer^2\) --> directly gives an answer. Sufficient.
(2) \(\sqrt{d}\) is the square of an integer --> \(\sqrt{d}=integer^2=integer\) (as square of an integer is an integer). Sufficient.
Answer: D.
Similar questions:
https://gmatclub.com/forum/if-n-p-q-p-a ... 01475.html
https://gmatclub.com/forum/if-d-is-a-po ... 09384.html
https://gmatclub.com/forum/if-x-is-a-po ... 65976.html
https://gmatclub.com/forum/if-d-is-a-po ... 67950.html
https://gmatclub.com/forum/if-z-is-a-po ... 01464.html
https://gmatclub.com/forum/if-y-is-a-po ... 08287.html
https://gmatclub.com/forum/if-sqrt-4a-i ... 06886.html
https://gmatclub.com/forum/what-is-the- ... 07195.html
https://gmatclub.com/forum/is-s-an-odd- ... 06562.html
General Discussion
26 Feb 2014, 04:15
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\(\)If d is a positive integer, is \(\sqrt{d}\) an integer?
(1) d is the square of an integer.
(2) \(\sqrt{d}\) is the square of an integer.
Sol: Given d is a postive integer we need to check whether \(\sqrt{d}\) = I where I is an integer
st1: Given d=a^2 where " a" is some postive integer then \(\sqrt{d}\) =a which is an integer So St 1 is sufficent
St2: given \(\sqrt{d}\) = b^2 where b is some integer so \(\sqrt{d}\) is an integer.
Ans is D.
Note: • When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \sqrt{[4]{x}}, then the only accepted answer is the positive root.
That is, \(\sqrt{25}\) , NOT +5 or -5. In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.
• Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
Courtesy GMAT CLUB Math Book
(1) d is the square of an integer.
(2) \(\sqrt{d}\) is the square of an integer.
Sol: Given d is a postive integer we need to check whether \(\sqrt{d}\) = I where I is an integer
st1: Given d=a^2 where " a" is some postive integer then \(\sqrt{d}\) =a which is an integer So St 1 is sufficent
St2: given \(\sqrt{d}\) = b^2 where b is some integer so \(\sqrt{d}\) is an integer.
Ans is D.
Note: • When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \sqrt{[4]{x}}, then the only accepted answer is the positive root.
That is, \(\sqrt{25}\) , NOT +5 or -5. In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.
• Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
Courtesy GMAT CLUB Math Book
