tonebeeze wrote:
Is x > y^2?
(1) x > y+5
(2) x^2-y^2 = 0
First, analyze the question: when a number (x) is greater than square of another number (y)?
condition: x must be positive [
if you can find any negative/zero value for x, that's a NO to the main question], y can be positive, negative or zero.
in two situation, a number (x) can be greater than square of another number (y).
situation 1: x=y [when x and y both are positive proper fraction (0<x<1)] i.e. (1/2)>(1/2)^2.
Situation 2: x is greater than the squared value of y. [when x >1] i.e. 10>(-2)^2 or 10>(2)^2.
Statement 1: x>y+5 or x-y>5 or x-y=6 (for simplicity)
for such difference cases, six scenarios are possible.
1. both x & y are negatives. [x=-1, y=-7] thus
NO to main question cause it breaks the primary condition that x must be positive.
2. x=0 , y=negative. [x=0, y=-6] thus
NO to main question cause it breaks the primary condition that x must be positive.
3. x=Positive, y=negative [x=1, y=-5] thus NO to main question cause x is less than the squared value of y.
4. x=Positive, y=negative [x=5, y=-1] thus yes to main question cause x is greater than the squared value of y.
5. x=Positive, y=zero[x=6, y=0] thus
yes to main question cause x is greater than the squared value of y.
6. x=Positive, y=positive [x=7, y=1] thus
yes to main question cause x is greater than the squared value of y.
So statement 1 is insufficient.
Statement 2: x^2-y^2 = 0 or x^=-y^2 or IxI=IyI or x=y or x=-y
in other words, x and y are same numerical value either in same direction or in opposite direction.
1. if x is negative [i.e. -5], y can be positive [i.e. 5] or negative [-5]. but,
NO to main question cause it breaks the primary condition that x must be positive.
2. if x is zero, y must be zero. but,
NO to main question cause it breaks the primary condition that x must be positive.
3. if x is positive proper fraction, y can be positive or negative proper fraction. thus
yes to main question cause x is greater than the squared value of y. i.e. (1/2)>(1/2)^2
4. if x is 1, y can be 1 or -1, thus NO to main question cause x equal the squared value of y.
5. if x is greater than 1, y would be greater than 1 or less than -1. thus
NO to main question cause x is less than the squared value of y. i.e. (1/2)>(1/2)^2
So statement 2 is insufficient.
Combining:
statement 1 says difference between x & y is more than 5 units.
so scenarios 2,3,4 from statement 2 are cancelled out. because
2. if x is zero & y is zero, no difference between x & y.
3. if x is positive or negative proper fraction & y is positive or negative proper fraction, maximum difference between x & y is 1 unit.
4. if x is 1 & y is 1, difference between x & y is 2 unit.
The remaining scenario 1 & 5 say
NO to main question cause x is less than the squared value of y.
So, My answer is C