If x and y are integers greater than 1, is x a multiple of y?
(1) 3y^2 + 7y = x
(2) x^2 - x is a multiple of y
ANSWER --> (1) alone is sufficient
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Multiples Problem
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ramannjit
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You can find explaination to the above in this postvongdn wrote:If x and y are integers greater than 1, is x a multiple of y?
(1) 3y^2 + 7y = x
(2) x^2 - x is a multiple of y
ANSWER --> (1) alone is sufficient
https://www.beatthegmat.com/is-x-a-multi ... 16147.html
Ramannjit
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Rahul@gurome
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(1) implies y(3y+7) = x.
Since y is an integer, 3y+7 is an integer.
Or x is a multiple of y.
So (1) alone is sufficient.
Next consider (2) alone.
Let x = 3 and y = 2.
So x^2 - x = 6 is a multiple of y = 2, but x = 3 is not a multiple of y =2.
Next let x = 4 and y = 2.
So x^2 - x = 12 is a multiple of y = 2 and x = 4 is a multiple of y = 2
We do not get a definite answer.
So (2) alone is not sufficient.
Since y is an integer, 3y+7 is an integer.
Or x is a multiple of y.
So (1) alone is sufficient.
Next consider (2) alone.
Let x = 3 and y = 2.
So x^2 - x = 6 is a multiple of y = 2, but x = 3 is not a multiple of y =2.
Next let x = 4 and y = 2.
So x^2 - x = 12 is a multiple of y = 2 and x = 4 is a multiple of y = 2
We do not get a definite answer.
So (2) alone is not sufficient.
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Gurome, Inc.
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Dear RahulRahul@gurome wrote:(1) implies y(3y+7) = x.
Since y is an integer, 3y+7 is an integer.
Or x is a multiple of y.
So (1) alone is sufficient.
Next consider (2) alone.
Let x = 3 and y = 2.
So x^2 - x = 6 is a multiple of y = 2, but x = 3 is not a multiple of y =2.
Next let x = 4 and y = 2.
So x^2 - x = 12 is a multiple of y = 2 and x = 4 is a multiple of y = 2
We do not get a definite answer.
So (2) alone is not sufficient.
is there any algebraic method for statement (2) other than the number pick?
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Rahul@gurome
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If x^2 - x is a multiple of y, we can write that y divides x(x-1).Dear Rahul
is there any algebraic method for statement (2) other than the number pick?
This means that there is a possibility that y divides (x-1) and y does not divide x.
In such a case x will not be a multiple of y.
However if y divides x(x-1), there is another possibility that y is dividing x.
In such a case x is a multiple of y.
Since nothing definite can be said (2) alone is not sufficient.
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)
