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# GRE Quant: The Difference of Squares

If you’ve been studying GRE for some time, you’ve very likely encountered the following:

.

You may, however, only seen the following equation in the context of algebra. Nevertheless, the formula above applies to number properties. Let’s take a look.

While you may be tempted to make a mad dash at it, calculating each of the squares, there is an easier way. Think of the ‘16’ as the ‘x’ and the ‘15’ as the ‘y’. Using the equation above we get:

.

Wow, that was much easier than figuring out the squares of both ‘16’ and ’15.’ Now, let’s try it for the second pair:

That leaves us with (29)(31). I know, you may be balking at my nifty little formula, thinking you still need to do some tedious multiplication. But despair not! We can still use the difference of squares formula:

is simply 3 x 3 add two zeroes: 900. Then we subtract the one and we get 899.

Next our two practice questions. The first question is not very different from the one above. The second one is more challenging and involves exponents.

1. ?

1. 4
2. 36
3. 38
4. 76
5. 224

2. =

1. 7
2. 25
3. 156
4. 175
5. 216

## Explanations:

1.

76 – 72 = 4, Answer (A).

2.

.

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### 6 Responses to GRE Quant: The Difference of Squares

1. Anik May 24, 2014 at 6:25 am #

How many integers between 1 and 300, inclusive, can be expressed as ‘xy’ , where x and y are integers greater than 1?

• Mithun Saha May 19, 2016 at 3:16 am #

64

2. lawal July 24, 2012 at 10:09 am #

hi chris,

for the second question, here is what i did

(4^8/4^4) – (3^8/ 3^4) = 256 -81 = 175

is something wrong with the strategy?

• Chris July 27, 2012 at 3:16 pm #

HI Lawal,

You got the right answer, but technically you cannot express (a + b)/(c + d) as a/c + b/d. You would have to express it as a/(c + d) + b/(c + d).

Hope that makes sense!

3. Aman July 17, 2012 at 11:39 am #

A bit of easy calculation for 1st :(20+18)(20-18)-(19+17)(19-17)
=>2(38)-2(36)
=>2(38-36)=2(2)=4

• Chris July 18, 2012 at 3:54 pm #

Good! That’s definitely a quick and easy way to do it :).

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