Is x > y?
(1) x^(1/2)> y
(2) x^3 > y
MGMAT
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Stmt1:
x^(1/2) > y
Square both sides:
x > y^2 implies x > y. Sufficient.
Stmt2:
x^3 > y.
suppose x = 2, y = 4
x^3 = 8 is > y but x < y.
Suppose x = 2, y = 1
x^3 = 8 is > y and x > y. Insufficient.
Hence answer should be A.
x^(1/2) > y
Square both sides:
x > y^2 implies x > y. Sufficient.
Stmt2:
x^3 > y.
suppose x = 2, y = 4
x^3 = 8 is > y but x < y.
Suppose x = 2, y = 1
x^3 = 8 is > y and x > y. Insufficient.
Hence answer should be A.
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I think the ans should be C....
In GMAT the square root of a number always refers to the positive root...So in this case we have to assume x to be a positive number
statement 1:
sqrt(x)>y
Let x=4 and y=1
then sqrt(4)>1
Let x=1 and y=4
then sqrt(1)<4
statement 1 is not sufficient
statement 2:
x^3>y
let x=2 and y=1 ......x^3>y
let x=1 and y=2 ......x^3<y
statement 2 is not sufficient
Combining both statements 1 and 2
x=2 y=1 we get x>y
x=1 y=2 we get x<y
x=1/4 y=1 we get x<y
x=16 y=-2 we get >y
As a general rule if both square root and cube of a number is greater than the other number,the number is always greater than the other number.
In GMAT the square root of a number always refers to the positive root...So in this case we have to assume x to be a positive number
statement 1:
sqrt(x)>y
Let x=4 and y=1
then sqrt(4)>1
Let x=1 and y=4
then sqrt(1)<4
statement 1 is not sufficient
statement 2:
x^3>y
let x=2 and y=1 ......x^3>y
let x=1 and y=2 ......x^3<y
statement 2 is not sufficient
Combining both statements 1 and 2
x=2 y=1 we get x>y
x=1 y=2 we get x<y
x=1/4 y=1 we get x<y
x=16 y=-2 we get >y
As a general rule if both square root and cube of a number is greater than the other number,the number is always greater than the other number.
- Morgoth
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You cant take x=1 & y=4raju232007 wrote:I think the ans should be C....
In GMAT the square root of a number always refers to the positive root...So in this case we have to assume x to be a positive number
statement 1:
sqrt(x)>y
Let x=4 and y=1
then sqrt(4)>1
Let x=1 and y=4
then sqrt(1)<4
statement 1 is not sufficient
because these values do not hold true for statement I
You dont have to prove the statement I, it is given as a fact.
You cant take x=1 & y=2statement 2:
x^3>y
let x=2 and y=1 ......x^3>y
let x=1 and y=2 ......x^3<y
statement 2 is not sufficient
because these values do not hold true for statement 2
You dont have to prove the statement 2, it is given as a fact.
As a general rule if both square root and cube of a number is greater than the other number,the number is always greater than the other number.
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- Master | Next Rank: 500 Posts
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