Which of the following is equal to 5995^2 - 4796^2 ?

The units digit of 5995^2 is 5, and of 4796^2 is 6, so when we subtract, we'll get a units digit of 9. The only answer choices which will produce the correct units digit are B and D.

If we factor, using the difference of squares, we get

5995^2 - 4796^2 = (5995 + 4796)(5995 - 4796) = (10791)(something else)

and if you sum the digits in 10,791, you can see it must be a multiple of 9. So the answer here must be a multiple of 9, and thus must be the square of some multiple of 3. Summing the digits in B and D, only answer D is the square of a multiple of 3, so that must be correct.

Or you could estimate: 5995^2 - 4796^2 is considerably larger than 5995^2 - 5000^2, which will be very close in value to 6000^2 - 5000^2 = (11,000)(1000), using the difference of squares. That's larger than 3000^2, so between B and D, D is the only possible answer.

It's not a realistic GMAT question, because on the GMAT it would always be practical without onerous calculation to arrive at the exact answer, and the only quick way to get the answer here is to use elimination techniques.

5995^2 - 4796^2

I never see that (A+B)(A-B) route. My thought process always goes to factoring.

5995 = 5 * 1199 --> 5995^2 = 5^2 * 1199^2
4796 = 4 * 1199 --> 4796^2 = 4^2 * 1199^2

5995^2 - 4796^2 = (5^2 * 1199^2) - (4^2 * 1199^2)
Factor out the 1199^2 and get 1199^2 (25-16) = 1199^2 * 9

I blanked when answering and chose B because I am looking for something larger than A. However as I write this, I realize if I distribute a 3 to each factor of 1199 you get D.

(5995^2 - 4796^2) mod 5 = 4 mod 5

(5995^2 - 4796^2) = k^2

k= 2 mod 5

Eliminate A, C and E

(5995^2 - 4796^2) mod 11 = 0 mod 11

2687 = 3 mod 11

Eliminate B

D

Long way to do it: Find the Last 2 Digits of the Number, and then Find the A.C. that matches up

5, 995^2 - 4,796^2 = (5, 995 + 4, 796) (5,995 - 4,796) = 10, 791 * 1, 199

Last 2 Digits = ....09


-A-
Last 2 Digits = .... 01

-B-
Last 2 Digits = ....69

-C-
Last 2 Digits = ....25

-D-
Last 2 Digits = ....09

-E-
Last 2 Digits = ....00



Answer must be -D-

\(5995^2 - 4796^2\)

\((5995 - 4796)(5995 + 4796)\)

Or, \(1199*10791\)

NOw check the last digit will be 9 (Only option B & D remains)

Again in (B) 2600*2600 = 6760000 < 1199*10791 hence, Answer must be (D)