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

Question

(A) 1,199^2
(B) 2,687^2
(C) 3,425^2
(D) 3,597^2
(E) 4,820^2

Source: Advanced Quant Manhattan Prep 2020

Anubhav23 · Answer

Pls check the options as this will always give 9 at the unit place

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rakshitsood21 · Answer

Anubhav23 
Thanks for pointing out. Corrected the typo!

IanStewart · Answer

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.

lchen21 · Answer

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.

nick1816 · Answer

(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

Fdambro294 · Answer

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-

Abhishek009 · Answer

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)

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

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GMAT Problem Solving (PS) Questions

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

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