Is rt(7x) an integer?
(1) rt(x/7) is an integer.
(2) rt(28x) is an integer.
A
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Solution:
Let us first consider statement (1) alone.
It says sqrt(x/7) is an integer.
Now sqrt(7x) = sqrt(49*(x/7)) = 7*sqrt(x/7).
Since sqrt(x/7) is an integer, 7*sqrt(x/7) is also an integer.
Or (1) alone is sufficient.
Next consider (2) alone.
It says sqrt(28x) is an integer.
Sqrt(28x) = sqrt(4*7x) = 2*sqrt(7x).
If 2*sqrt(7x) is an integer, it is not necessary that sqrt(7x) is an integer.
For example let 2*sqrt(7x) be 5.
Then, sqrt(7x) = 5/2 which is not an integer.
If 2*sqrt(7x) is 4, sqrt(7x) is 4/2 = 2 which is an integer.
So (2) alone is not sufficient.
The correct answer is (A).
Let us first consider statement (1) alone.
It says sqrt(x/7) is an integer.
Now sqrt(7x) = sqrt(49*(x/7)) = 7*sqrt(x/7).
Since sqrt(x/7) is an integer, 7*sqrt(x/7) is also an integer.
Or (1) alone is sufficient.
Next consider (2) alone.
It says sqrt(28x) is an integer.
Sqrt(28x) = sqrt(4*7x) = 2*sqrt(7x).
If 2*sqrt(7x) is an integer, it is not necessary that sqrt(7x) is an integer.
For example let 2*sqrt(7x) be 5.
Then, sqrt(7x) = 5/2 which is not an integer.
If 2*sqrt(7x) is 4, sqrt(7x) is 4/2 = 2 which is an integer.
So (2) alone is not sufficient.
The correct answer is (A).
Rahul Lakhani
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
