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M09-14

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M09-14  [#permalink]

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New post 15 Sep 2014, 23:39
1
1
00:00
A
B
C
D
E

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(N/A)

Question Stats:

78% (00:55) correct 22% (03:03) wrong based on 97 sessions

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Re M09-14  [#permalink]

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New post 15 Sep 2014, 23:39
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Re: M09-14  [#permalink]

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New post 04 Nov 2014, 16:59
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.

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Re: M09-14  [#permalink]

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New post 17 Mar 2016, 08:17
Thanks Brunnel! That was a great breakdown of using the difference of two squares to solve this problem!
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New post 24 May 2017, 02:59
I think this is a high-quality question. Another approach - 987 x 987 = (1000-13) x (1000-13) = (1000-13)^2
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Re: M09-14  [#permalink]

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New post 30 Jan 2018, 02:51
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
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M09-14  [#permalink]

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New post 25 Oct 2018, 02:57
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 &nbs [#permalink] 25 Oct 2018, 02:57
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