I always have trouble with these... does any one have cheatsheets for how to solve these kinds?
1. Is x less than y?
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?
(2) |x| < 1/x
OA is D
Will answer one by one.
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
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 !
which means |x| <1 (this expression means -1<x<1)
Hence A is sufficient
|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 !