Percent

[vinay1983]

12 is added to a single digit number. The resulting number is increased by the same percent as was done initially to the single digit number to obtain a result of 75. What was the single digit number?

OA: 3

[ganeshrkamath]

12 is added to a single digit number. The resulting number is increased by the same percent as was done initially to the single digit number to obtain a result of 75. What was the single digit number?

OA: 3

Let the single digit number be x.

x is increased by 12:
Percentage increase = ((12+x)-x)/x * 100% = (1200/x)%

The resultant number is increased by the same percentage to get 75:
(12+x)(100 + 1200/x)/100 = 75
(12+x)(1+12/x) = 75
(12+x)(x+12)/x = 75
(12+x)^2 = 75x
144 + 24x + x^2 = 75x
x^2 - 51x + 144 = 0
(x-48)(x-3)=0
So x = 48 or x = 3
Since x is a single digit number,
[spoiler]x = 3[/spoiler]

Cheers[/i]

[Brent@GMATPrepNow]

12 is added to a single digit number. The resulting number is increased by the same percent as was done initially to the single digit number to obtain a result of 75. What was the single digit number?

OA: 3

This one takes a fair bit of work.

If this were a regular GMAT PS question, there would be 5 answer choices, in which case it might be faster to test each answer choice to see which one meets the given criteria.

For example, if one of the answer choices were 2, we could test it.
2 + 12 = 14.
An increase from 2 to 14 represents a 600% increase.
If we take 14 and increase it by 600%, do we get 75? No.
So, 2 would not be the correct answer.


What about 3? Let's test it.
3 + 12 = 15.
An increase from 3 to 15 represents a 400% increase.
If we take 15 and increase it by 400%, do we get 75? YES!
So, 3 is the correct answer.

Cheers,
Brent