Here,

Let say total number of apples = 100

Now 45% apples, which weigh more than 81 grams = 45

and

81% apples, weighing less than 145 grams = 81

Lets add both of them = 45 + 81 = 126

But the total no. of apples = 100. This means there is an overlap of 26 apple, which is greater than 81 grams but less than 145 grams

lets asume we have 100 apple, then after basic calculations when have 45 apple which are above 85 grm in weight and 81 apple which are weight less than 145 gm.then why dont we 81-45?

Ok so the way I did this is as follows:
You need to find out how many of the apples that weigh less than 81 grams are also included in the 81% of apples that weigh less than 145 grams.

If 45% of the total apples weigh more than 81 grams, you know 55% of the apples total weigh less than 81 grams, and by default, also weigh less than 145 grams. Subtract the 55% from the 81% to get 26 Percent that weigh more than 81 but less than 145.

Hi,
What makes the problem confusing are the boundary weights (81 grams and 145 grams). It is difficult to process these and the percentages (45% and 81%) simultaneously. It could be a good idea to call 81 grams A and 145 grams B.

The question could be read as 45% weigh more than A and 81% weigh less than B.

Visually:
(The brackets show the the numbers 45% and 81%)
--------------------------A[------------45%--------------------------------------------------] (shows that 45% weigh more than A)
[--------------------------------------------------------81%-----------]B--------------------- (shows that 81% weigh less than B)

The entire line represent 100.
Therefore, not more than A are 55% (because 100-45=55); we can tag A at 55%
Conclusion, between A and B are 81-55 = 26.

Hope this helps.

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.