x percent of Y

[hiratuka]

I just took my first CAT. I got to the problem named "x percent of y". I don't know if anybody has touched on this yet but there is another way to solve the problem that I think should be at least shown because to me it seems easier and faster. It might not be for everyone, but at least it is another way. Anyways, here is the problem:
x% of y is increased by x%. What is the result in terms of x and y?

A)100xy + x

B)xy + x/100

C)100xy +x /100

D)100xy +xy/100

E)xy(x+100) over 10,000

Here is the explanation given :

The easiest way to solve this problem is to use the VIC method of substituting actual numbers for x and y. The problem asks us to take x% of y and increase it by x%. Since we are dealing with percentages, and the whole (y) is neither given to us nor asked of us, let's set y = 100 and x = 10. Note that this is a variation on the typical method of picking small numbers in VIC problems.

10% of 100 is 10. Increasing that 10 by 10% gives us 10 + 1 = 11. Therefore 11 is our target number. Let's test each answer choice in turn to see which of them matches our target number.

So then they test each answer by plugging in 10 and 100 for each answer to find out which equals 11.

Wouldn't it be a lot easier ( or at least another way to go about it) to just say:

x percent of a number is x/100, so x percent of y is xy/100.
This number is now increased by x percent, so again x percent is x/100 and that's just the increase. The real number would be the increase (x/100) + 100 percent (100/100), which in turn give us (x+100)/100. Now we multiply the number that is increasing with the percentage.That it will be giving us (xy/100)x (x+100)/100. This would give us xy(x+100)/10,000, answer number E. I hope I made sense. Lol!

-Cheers!

[jnelson0612]

You did make sense! Look, it's fantastic if you can easily manipulate algebra like that. For many people that kind of strategy would be much more difficult and prone to error than just plugging numbers. That's why we first suggest plugging numbers. But hey, for those who are algebra wizards feel free to handle these with algebra.

Anyway, thanks for sharing! :-)