Doubt With OA

[Fatehdeep Singh]

x > y^2 ?

I) x>y+5
II)x^2 - y^2 =0

OA after some discussions?

[cans]

IMO C

[sivaelectric]

IMO A

[cans]

x>y^2?

I) x>y+5 - suppose y=1, x>6 and x>1^2
if y=9, x>14 we can't say that x>81.
Thus A insufficient.

II)x^2 - y^2 =0
=> either x=y or x=-y
now if x=y, and x=y=1, x>y^2 not true
x=y=0.5, x>y^2 true,
Thus B alone not sufficient.

A&B together,
x>y+5 => x not equal to y, thus x=-y
x>-x+5 => x>5/2
Now to find if x>y^2 or to find if x>(-x)^2 or to find if x > x^2
As x>2.5, thus x < x^2
Thus not true. Sufficient
Hence C.

[Anurag@Gurome]

x > y^2 ?

I) x>y+5
II)x^2 - y^2 =0

OA after some discussions?

Solution:
Consider first I alone.
Let x = 5 and y = -1.
Here (x = 5) > (y+5 = -1+5 = 4) and (x = 5) > (y^2 = 1).
Next let x = -1/3 and y = -6.
Now, -1/3 = x > -6+5 = -1.
But x = -1/3 < y^2 = 36.
So, nothing definite can be said from (1) alone.
Next consider II) alone.
Let x = -1 and y = 1.
So, x = -1 < y^2 = 1.
Next, let x = 1/2 and y = 1/2.
So, x = ½ > y^2 = ¼.
Again, nothing definite can be said from (2) alone.
Lastly, combine both statements and check.
If x > y+5, we get that x > y.
Or x is not equal to y.
Now II means that (x+y)(x-y) = 0.
This means that x = -y.
Now, x > y+5 means that -y > y+5 or y < -5/2.
Now x > y^2 means that -y > y^2 or y^2+y < 0 or -1<y<0.
This is not possible because y <-5/2.
So, the answer to the main question is "no".
Or, both statements together are sufficient to answer the question.

The correct answer is (C).

[sivaelectric]

x > y^2 ?

I) x>y+5
II)x^2 - y^2 =0

OA after some discussions?

Can someone please explain why this procedure is wrong?

X>Y+5
X-Y>5, we can take X=7 and Y=1 so that X-Y more than 5. now X = 7 > Y^2 = 1

@Anurag Sir, can you please correct me?

[Anurag@Gurome]

x > y^2 ?

I) x>y+5
II)x^2 - y^2 =0

OA after some discussions?

Can someone please explain why this procedure is wrong?

X>Y+5
X-Y>5, we can take X=7 and Y=1 so that X-Y more than 5. now X = 7 > Y^2 = 1

@Anurag Sir, can you please correct me?

If you are just considering statement I, this example is fine but if you are combining and checking, then x^2 = 49 is not equal to y^2 = 1. So condition in II is not being satisfied.
This example will not hold then.

[sivaelectric]

Sir, But when you get an answer with the first one itself, should you have to go for the second one. But as I type this I am also starting to get another doubt about this.

When the first hint gives you an answer, should you check the same values with the second one too? Is it like that?

[Anurag@Gurome]

Sir, But when you get an answer with the first one itself, should you have to go for the second one. But as I type this I am also starting to get another doubt about this.

When the first hint gives you an answer, should you check the same values with the second one too? Is it like that?

You are not going to get the answer with just this example.
Take x =-1/3 and y = -6.
Here also x=-1/3 > y+5 = -1 but x = -1/3 < y^2 = 36.
This means I being true does not mean that x > y^2.
Or I alone is not sufficient.
Now, check II alone.
Take values that satisfy only II and have nothing to do with I.
Again you will not get a definite answer.
This means that II alone is not sufficient.
Next check with values that satisfy both I ans II simultaneously.
Then try to get the answer to the main question.

[sivaelectric]

Great explanation Anurag Sir