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# M09-14

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Math Expert
Joined: 02 Sep 2009
Posts: 55804

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16 Sep 2014, 00:39
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

77% (00:56) correct 23% (02:51) wrong based on 101 sessions

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What is 987 * 987?

A. 974,169
B. 974,219
C. 974,549
D. 975,019
E. 975,369

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Math Expert
Joined: 02 Sep 2009
Posts: 55804

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16 Sep 2014, 00:39
2
3
Official Solution:

What is 987 * 987?

A. 974,169
B. 974,219
C. 974,549
D. 975,019
E. 975,369

$$987*987 = (987 + 13)*(987 - 13) + 13^2 = 1000*974 + 169 = 974,169$$. We used $$(a + b)(a - b) + b^2 = a^2$$.

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Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
GMAT 1: 650 Q39 V41
WE: Analyst (Commercial Banking)

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04 Nov 2014, 17:59
1
Notice that the 10's digit of all the answer choices is different. Perform regular multiplication till you can calculate what the 10's digit will be.

987
x987
6906 (multiplied 7 in denominator by the numerator)
78960 (multiplied numerator by 8)

No need to multiply by the 9 in the denominator. We can see that the tens digit will be 6. We actually didn't need to multiply the 7 or the 8 all the way across either, but it's simple to do, and may help avoid errors.

Best
Manager
Joined: 12 Mar 2015
Posts: 54
Location: United States
GMAT 1: 670 Q45 V38
GPA: 2.99
WE: Corporate Finance (Aerospace and Defense)

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17 Mar 2016, 09:17
Thanks Brunnel! That was a great breakdown of using the difference of two squares to solve this problem!
Intern
Joined: 09 Jul 2016
Posts: 17
GMAT 1: 730 Q50 V39

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24 May 2017, 03:59
I think this is a high-quality question. Another approach - 987 x 987 = (1000-13) x (1000-13) = (1000-13)^2
Intern
Joined: 01 Aug 2017
Posts: 6
Location: India
Schools: Duke '21
GMAT 1: 750 Q49 V42
GPA: 4

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30 Jan 2018, 03:51
1
The best way to solve this question (What is 987 * 987?) is by elimination method.

we know 987*987 has to be divisible by 9, since 987 is divisible by 3.
Using the divisor rule of 9 in the options: correct answer should be the one whose sum of digits is divisible by 9.

974,169= 36
974,219= 32
974,549= 38
975,019= 31
975,369= 39

only 36 is divisible by 9, so A is correct
Director
Joined: 12 Feb 2015
Posts: 863

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25 Oct 2018, 03:57
Use $$(a-b)^2$$ = $$a^2+b^2-2ab$$ to solve the question.

987 * 987 = (1000-13)*(1000-13) = 1000^2+13^2-2*1000*13 = 1000000 + 169 - 26000 (STOP here) ...Don't solve it further. Just realise that the final solution will have 169 as the last 3 digits. Only option A has it. Correct Ans is A.
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M09-14   [#permalink] 25 Oct 2018, 03:57
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# M09-14

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