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Is the square root of "a" an integer? (1) the last

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Is the square root of "a" an integer? (1) the last [#permalink] New post   02 Aug 2010, 04:26
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1.Is the square root of "a" an integer?
(1) the last digit of a is 8.
(2) a is divisible by 6.

2.If x^3 = y, is y a fraction?
(1) x^2 is a fraction.
(2) x > y.

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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   02 Aug 2010, 06:48
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1. A
Statement 1:
0²=0, 1²=1, 2²=4, 3²=9, 4²=...6, 5²=...5, 6²=...6, 7²=...7, 8²=...4, 9²=...1
so \(\sqrt{a}\) is not an integer --> Sufficient
Statement 2:
a=36, \(\sqrt{a} = 6\) integer
a=72, \(\sqrt{a}=6\sqrt{2}\) not integer

2. E
Both statement 1 and 2:
\(x=\frac{3}{4}\), \(y=\frac{27}{64}\)
\(x=\frac{\sqrt{3}}{4}\), \(y=\frac{3\sqrt{3}}{64}\)
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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   02 Aug 2010, 07:27
bogos wrote:
1. A
Statement 1:
0²=0, 1²=1, 2²=4, 3²=9, 4²=...6, 5²=...5, 6²=...6, 7²=...7, 8²=...4, 9²=...1
so \(\sqrt{a}\) is not an integer --> Sufficient
Statement 2:
a=36, \(\sqrt{a} = 6\) integer
a=72, \(\sqrt{a}=6\sqrt{2}\) not integer

2. E
Both statement 1 and 2:
\(x=\frac{3}{4}\), \(y=\frac{27}{64}\)
\(x=\frac{\sqrt{3}}{4}\), \(y=\frac{3\sqrt{3}}{64}\)


think 7 square = ...9
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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   02 Aug 2010, 20:39
Bogos can you explain question 2 in more details?

Thanks
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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   03 Aug 2010, 02:01
Hi Swdatta, for question 2, I took 2 examples which satisfy both statements but give different results.
More precisely,
example 1: \(x=\frac{3}{4}\), \(x^2=\frac{9}{16}\) is a fraction (stt1) and \(x=\frac{3}{4}>y=x^3=\frac{27}{64}\) (stt2), then \(y=\frac{27}{64}\) is a fraction
example 2: \(x=\frac{\sqrt{3}}{4}\), \(x^2=\frac{3}{16}\) is a fraction (stt1) and \(x=\frac{\sqrt{3}}{4}>y=x^3=\frac{3\sqrt{3}}{64}\) (stt2), then \(y=\frac{3\sqrt{3}}{64}\) is a NOT fraction

Both statements together are not sufficient, then E.
Hope it is clear.
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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   18 Oct 2010, 09:19
2.If x^3 = y, is y a fraction?
(1) x^2 is a fraction.
(2) x > y

my solution:
(2) x=-2 y=-8 y is no a fraction
x=1/2 y=1/8 y is a fraction
not sufficient

(1) \(x^2\)is a fraction, so x and \(x^3\)are fractions
So, should be sufficient
Where did I go wrong? :?
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Re: Is the square root of "a" an integer? (1) the last [#permalink] New post   19 Oct 2010, 09:51
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Eden wrote:
2.If x^3 = y, is y a fraction?
(1) x^2 is a fraction.
(2) x > y

my solution:
(2) x=-2 y=-8 y is no a fraction
x=1/2 y=1/8 y is a fraction
not sufficient

(1) \(x^2\)is a fraction, so x and \(x^3\)are fractions
So, should be sufficient
Where did I go wrong? :?


This is not a GMAT type of question, so don't worry about it. Generally ANY number can be written as a fraction (or in another way) so there is no sense in asking whether y is a fraction or saying in (1) that x^2 is a fraction. It might be that the question means "proper fraction" (fraction between 0 and 1) or "rational number" (number which can be written as the ratio of two integers a/b). Anyway not a good question so I'd advice not to study it.

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Re: Is the square root of "a" an integer? (1) the last [#permalink]
19 Oct 2010, 09:51
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