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What is 987*987?

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What is 987*987? [#permalink]

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New post Updated on: 21 Dec 2013, 05:19
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A
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Difficulty:

  15% (low)

Question Stats:

77% (01:06) correct 23% (01:08) wrong based on 314 sessions

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What is 987*987?

(A) 974,169
(B) 974,219
(C) 974,549
(D) 975,019
(E) 975,369
[Reveal] Spoiler: OA

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Originally posted by barakhaiev on 05 Sep 2009, 10:37.
Last edited by Bunuel on 21 Dec 2013, 05:19, edited 1 time in total.
Added the OA.
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Re: What is 987*987? [#permalink]

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New post 05 Sep 2009, 10:43
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(1000-13)(1000-13)=(a-b)^2=a^2+b^2-2ab
=1,000,000
+..........169
-......26,000
__________
=1,000,169-26,000=(A)

barakhaiev wrote:
What is 987*987?

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

I wonder, how can this question be solved quickly?

Thanks in advance.

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Re: What is 987*987? [#permalink]

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New post 05 Sep 2009, 18:21
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thanks ..this seems to be a simple one ..

other tedios way is

987 * 987

unit digit comes from multiplying unit terms ( 7 * 7 . so unit digit 9)
10's digit comes from mulitplying tens digit of 1st term and unit digit of 2nd term ( 8 * 7 = 56 ) so tens digit 6


this way , you can trim your answer choices and wil be useful if you are asked to multiply some strange numbers

like 758 * 758 , but will not be useful for the above question as the solution provided by nitya is much easier .
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Re: What is 987*987? [#permalink]

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New post 06 Sep 2009, 00:50
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barakhaiev wrote:
What is 987*987?

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

I wonder, how can this question be solved quickly?

Thanks in advance.


987 is divisible by 3 so 987*987 is divisible by 9 so the sum of the digits is divisible by 9, only A satisfies.
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Re: What is 987*987? [#permalink]

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New post 06 Sep 2009, 00:55
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Hello. Method provided by Snowingreen is not correct.

Is you multiply two numbers then

987 *987

If we go to very basic steps which I had learned in my primary school.
987
*987
-------
06909
7896X
8883XX
---------
974169

Unit digit will come via 7*7 but ten's digit will be multiply by tens digits in this multiplication. ( o + 6+ x) = 6 . Here by luck we are getting 0 in first row because ( 56+ 4 ( carry forward) = 60 so 0 will remain there but 6 will be carry forward). In case if some would have been diffrerent

986
986
----
5916
7888X
8874XX
--------
972196

So here ten's digit is 9 .....

I hope you got it. If not try 2 - 3 sample multilpication and you will get it.
Best way is to use formula. ( a-b) ^2
I hope it will help you.
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Re: What is 987*987? [#permalink]

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New post 06 Sep 2009, 06:24
ahhh..I posted quicky and I didnt mention it .. I didnt mention abt the 0 from the last 2 terms( tenth digit)

sorry guys..let me update my post
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Re: What is 987*987? [#permalink]

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New post 20 Dec 2010, 04:07
Can I please ask someone to take a look at it and solve it algebraically? The method provided by DavidArchuleta is nice but how do you come up with an idea that 987 is divisible by 3?

Thank you.
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Re: What is 987*987? [#permalink]

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New post 20 Dec 2010, 04:23
nonameee wrote:
Can I please ask someone to take a look at it and solve it algebraically? The method provided by DavidArchuleta is nice but how do you come up with an idea that 987 is divisible by 3?

Thank you.


If the sum of numbers is divisible by 3, then the whole number is too.

9+8+7 = 24; 24 is divisible by 3 = 8
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Re: What is 987*987? [#permalink]

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New post 20 Dec 2013, 20:34
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if you take a base of 1000 then 987 is 13 less than 1000

to get the product of 987 x 987 write like this

987- 13( as 13 less than base1000)
987- 13
------------
now 13 x 13 = 169
and 987-13 = 974

so 987 x 987 = 974169 ... (bingo the answer is A . you can even have a shortcut ...... 13 x 13 = 169 ... only answer choice has last three digits as 169.. so no need to calculate 987-13 . after you get 13 x 13 you can straight way pick answer choice A.

now try the same method for 986x 984 ... and let me know if u get the correct answer in less than 10 seconds or not !
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Re: What is 987*987? [#permalink]

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New post 27 Dec 2013, 21:28
barakhaiev wrote:
What is 987*987?

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


987*987 = 987^2 = (1000-13)^2

= 1000^2 - 2*13*1000+13^2
= 1000000-26000+169
= 974169
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Re: What is 987*987? [#permalink]

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New post 27 Dec 2013, 22:44
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barakhaiev wrote:
What is 987*987?

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


Looks weird, but not so tricky.

987*987 ---------> (987*1000) - (987*13) ---------> 987000 - 12831 --------> 974169 -----------> Choice A
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Re: What is 987*987? [#permalink]

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New post 29 Dec 2013, 04:28
What is\(987*987?\)

To find: \(987^2\)

Since, 987 is a 3-digit number, its square will be six digit number XXXYYY.
XXX = 987 - ( 1000-987) Or, XXX = 974
YYY = (1000-987)^2 Or, YYY = 169

Hence, \(987 ^ 2 = 974169\)

Answer: (A)
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Re: What is 987*987? [#permalink]

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barakhaiev wrote:
What is 987*987?

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


GMAT always tests your ability to do something smart. So rather than looking for some esoteric short cuts the student should try to know what is it the test makers really want him to do and try to do that.

In the above example can the numbers be represented in terms of numbers which would greatly simplify the calculation? The answer is yes and 987 can be written as 1000-13

So the problem now boils down to finding (1000-13) ^2
i.e., 1000000+169-26000=974169

These are much easier and fewer computations than if the multiplication were done directly.
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Re: What is 987*987? [#permalink]

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barakhaiev wrote:
What is 987*987?

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


Doesn't look like a typical GMAT question. However, this is easily done in 5 seconds.

Note that the value of the multiplicands are very near to 1000.

All you have to do is :

987 | (1000-13)
987 | (1000-13)

Thus, what you do is subtract 987 from the nearest multiple of 10, and then write the difference \(\to\)

987 | 13
987 | 13

Now you subtract 13 from 987 = 974 and multiply 13*13 = 169
Thus, the answer is 974,169

This is just a brilliant method from Vedic Mathematics.Doubt will be ever useful for GMAT.
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Re: What is 987*987? [#permalink]

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\(987^2\)

\(= (1000 - 13)^2\)

= 1000000 + 169 - 26000

= 1000169 - 26000

Last 3 digits should be 169; only option A fits in

Answer = A
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What is 987*987? [#permalink]

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New post 24 Jul 2015, 11:20

Don't ignore the easy problems! Finding efficient ways to do easy problems is of prime importance because it means that you have more time for hard questions. This problem should take you 30 seconds or less.



Others have mentioned some pretty quick methods - you can use those awesome ways or stick to what you already know if that's what is most comfortable for you.

Thought:
Just multiply 5 pairs of single digit numbers and add two numbers up!

All of the answer choices end in 9. So we can't simply multiply the units digits. There are some tens digits which are the same so the tens and units digits are the same number, but the hundreds digits makes all of the numbers different.

You can start multiplying 987 x 987 the long and tedious way, but stop at the units, tens, and hundreds digit when multiplying and ignore the rest. In other words, don't multiply it all out.


Math: Short, simple, and sweet
* Line 1: \(987 * 987\) = 7*7, 7*8, 7*9 the first three digits are 9, 0, 9 (in order from highest digit to units digit; don't forget to carry over the tens digits like you would normally do)
* Line 2: Then 8*7 and 8*8 the first three digits for the next line is 9, 6, 0
* Line 3: Then for the next line it's just 9*7, so 3, 0, 0

+ Add up the digits accordingly and it's 169 (leave the 2 out since it isn't even necessarily the correct thousand's digit, as it needs to get added to the full multiplication).

Answer is (A).
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Re: What is 987*987? [#permalink]

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Re: What is 987*987?   [#permalink] 19 Dec 2017, 19:40
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