sportypk wrote:

I always have trouble with these... does any one have cheatsheets for how to solve these kinds?

1. Is x less than y?

(1) x-y+1<0

(2) x-y-1<0

OA is A.

2. If b is an integer, is an integer?

(1) a^2 + b^2 is an integer.

(2) a^2 – 3b^2 = 0

OA is B

3. If x≠0, is |x| <1?

(1) x^2<1

(2) |x| < 1/x

OA is D

Hey there..

Will answer one by one.

1) x-y+1<0

which means x < y-1

Which means x is clearly less than y.

for eg y=5

this means x<4 which is less than 5. right? SO, A is sufficient !

Option B says

x-y-1<0

which means x<y+1

Now in this case x could be less than y or greater than Y. I'll show you how

Lets say Y= 5. Now x<(5+1) ie x<6

Now x could be 4 which is less than Y. But, x could also be 5.5. right?

Hence B is not sufficient !

Therefore A !

2) A says

a^2 + b^2 is an integer.

since b is an integer , b^2 is obviously an integer.

If a is an integer, a^2 will be an integer.

Even if a is not an integer(lets say a is sqrt(3) , then a^2 will be 3) a^2 could end up an integer.

Hence A is not sufficient.

coming to B

a^2 – 3b^2 = 0

which means a^2=3b^2

this means a=sqrt(3)b (+ or -)

which means a cant be an integer .as we r multiplying by sqrt(3). right?

Hence B is sufficient !

3)x^2<1

means -1<x<1

which means |x| <1 (this expression means -1<x<1)

Hence A is sufficient

Now B

|x| < 1/x

since x is an integer (excluding zero)

(1/any integer) would be less than 1

Hence B sufficient

Therefor D would be the answer !!

BTW: whats a cheat sheet.m pretty new here

Please shoot any questions or doubts you might have !

Cheers!!

Hi Zeenie, welcome to the club.

which makes a an integer. As per your working a can also be non integer.