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GMAT TIGER, so which answer will you opt for? Since x is +ve and y is -ve and both have the same numerical value, x can be > or < than y^2, depending on whether the numerical value is <or> than 1. That's why I think the answer should be (E).
GMAT TIGER, so which answer will you opt for? Since x is +ve and y is -ve and both have the same numerical value, x can be > or < than y^2, depending on whether the numerical value is <or> than 1. That's why I think the answer should be (E).
Quote:
Is x > y^2?
(1) x > y + 5 (2) x^2 - y^2 = 0
x^2 - y^2 = 0 is possible only when either x = y or x = -y but since x > y+5, x must be +ve and therefore y is -ve.
x > y+5
x - y > 5
- y - y > 5
y < -2.5
suppose, y = - 3, x = 6, which is grater than -3+5 = 2.
2) insuff. this statement means (x+y) (x-y)=0
therefore:
x=y or
x=-y
statement 2 alone would be true if we know at least that the variables are integers, however, we weren't told that they are integers. Therefore they could be fractions, which can mess up the whole logic and give different results.
Both statement together
worst case scenario:
scenario a: if y=1/2, then x is at least 6
6>1/4 true
scenario b: if y=-1/2, then x is at least 5
5> 1/4 true
Firstly, looking at the statement: y^2 will always be positive, unless y = 0. Therefore, for x > y^2, one of the conditions is that x must be > 0.
Looking at the statements:
1) INSUFFICIENT: we cannot determine from this equation whether x is > 0. For example: -5 > -11 + 5 AND 5 > -11 + 5
2) x^2 - y^2 = 0, therefore (x-y)(x+y) = 0, therefore x = -y OR + y
INSUFFICIENT: we cannot determine from this equation whether x is > 0. All we know is that x = y OR x is equal to y * -1
1) & 2) Together:
Subsitute x = y into the equation in Statement 1: y > y + 5 This cannot be true. Therefore, x is NOT equal to y! Therefore x = -y
Substitute x = -y into the equation in Statement 1:
-y > y + 5
-2y > 5
-y > 5/2.... x > 5/2
y < -5/2 Because y is <1 and x = -y, as x gets bigger, y gets smaller. Therefore y^2 will always be greater than x. The answer to the question "Is x > y^2" is NO. Therefore it's C.
OE
when we combine the two statements, we see that the absolute values of x and y are equal and that x > y , implying that x is positive and y is negative and neither is equal to zero. Therefore, x > y2 is true.
(1) or (2) alone is not sufficient
Together we have lxl = lyl and x>y+5
so x= -y and y<-2.5
thus x>2.5 and x<x2 = y2
The answer is with (1)(2) together we have x<y2