If I am not clear in the above examples,
below is one more question
Question
https://postimg.cc/image/m0aac64cp/full/

In the above link should we analyse whether option 1 & 2 hleps to find whether n > 24 or
n >24 or not.

Uva@90 wrote:Hi All,
I have basic problem in understanding the Data Sufficiency problem. I have given example below,

Ist Problem,

If n is a positive integer, is x+5 even?
1) x=n+1
2) n=13

In the above mentioned probelm what should I infer whether x+5 is even from option 1 & 2 or whether option 1& 2 helps to find whether x+5 is even or odd ?

Your goal is to be able to answer the question with only one answer i.e x+5 is EVEN or x+5 is ODD. If you can reach to one of these conclusions then the statement(s) are sufficient.

Statement 1 tells you
x = n+1
which means either
n is odd and x is even
OR
n is even and x is odd

This results in different answers to the question Is x+5 even? ==> Insufficient

Example
n = 1 ; x = 2 ==> x + 5 = 7 (ODD)
n = 2 ; x = 3 ==> x + 5 = 8 (EVEN)

If you get multiple answers from the same statement it is always INSUFFICIENT.

Statement 2:
n = 13
No infomration about x ==> Insufficient

Statements 1 & 2 Together

you can tell the value of x which is 14 and answer the question is x+5 is even? 14+5 = 19 which is DEFINITELY NOT EVEN.

Hope that helps.

Is x=y?
1) (x-50)^2 = (y-50)^2
2) (x+y)(1/x + 1/y) =4


For this question-

1) (x-50)^2 = (y-50)^2

(x-50)^2-(y-50)^2=0
(x-50-y+50)(x+y-100)=0
So either (x-y)=0 or (x+y-100)=0

So (1) is INSUFFICIENT to answer the question

2) (x+y)(1/x + 1/y) =4
(x+y)(x+Y)=4xy
x^2+y^2+2xy-4xy=0
(x-y)^2=0

So (2) is SUFFICIENT to answer the question

Hence the Answer will be B.