Percentage

[vinay1983]

The difference between the value obtained by increasing a number by 12.5% and the value obtained by decreasing the number by 6.25% is 120. What is the original number.

OA: 640

[Brent@GMATPrepNow]

The difference between the value obtained by increasing a number by 12.5% and the value obtained by decreasing the number by 6.25% is 120. What is the original number.

OA: 640

Here's one approach:

12.5% = 1/8
Since 6.25% is half as big as 12.5%, we can conclude that 6.25% = 1/16

Let x be the original number.
Increasing x by 12.5% is the same as increasing x by 1/8, so we get (9/8)x
Decreasing x by 6.25% is the same as decreasing x by 1/16, so we get (15/16)x

If the difference is 120, we can write: (9/8)x - (15/16)x = 120
Eliminate the fractions by multiplying both sides by 16: 18x - 15x = 1920
Simplify: 3x = 1920
Solve: x = 640
Cheers,
Brent

[Brent@GMATPrepNow]

The difference between the value obtained by increasing a number by 12.5% and the value obtained by decreasing the number by 6.25% is 120. What is the original number.

OA: 640

Slightly different approach:

Let x be the original number

IMPORTANT: The difference of 120 is equal to 12.5% of x PLUS 6.25% of x

12.5% = 1/8
6.25% = 1/16

So, we get: (1/8)x + (1/16)x = 120
Eliminate the fractions by multiplying both sides by 16: 2x + x = 1920
Simplify: 3x = 1920
Solve: x = 640

Cheers,
Brent

[vinay1983]

The difference between the value obtained by increasing a number by 12.5% and the value obtained by decreasing the number by 6.25% is 120. What is the original number.

OA: 640

Slightly different approach:

Let x be the original number

IMPORTANT: The difference of 120 is equal to 12.5% of x PLUS 6.25% of x

12.5% = 1/8
6.25% = 1/16

So, we get: (1/8)x + (1/16)x = 120
Eliminate the fractions by multiplying both sides by 16: 2x + x = 1920
Simplify: 3x = 1920
Solve: x = 640

Cheers,
Brent

Thank you Brent

Actually instead of this:

The difference of 120 is equal to 12.5% of x PLUS 6.25% of x

I inserted the negative sign in between.

But tell me, isn't difference meant to be one value MINUS another value?

Thanks!

[Brent@GMATPrepNow]

Thank you Brent

Actually instead of this:

The difference of 120 is equal to 12.5% of x PLUS 6.25% of x

I inserted the negative sign in between.

But tell me, isn't difference meant to be one value MINUS another value?

Thanks!

Hi Vinay1983,

In my first solution, I used the idea of difference.
So, I took the values that resulted from the increases and decreases, and found their difference.
In my second solution I used the fact that the difference will equal the sum of the actual increases and decreases.

For example, let's say that Joe and Sue both have $100.
If we increase Joe's money by 10% and decrease Sue's money by 5%, we can use two different approaches to find the difference between Joe and Sue.

#1) We can determine the resulting values ($110 for Joe and $95 for Sue) and then find the difference (110 - 95 = $15).

#2) We can determine the increase and decrease ($10 increase for Joe and $5 decrease for Sue) and then add these values (10 + 5 = $15).

Cheers,
Brent