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M16-16

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Math Expert
Joined: 02 Sep 2009
Posts: 52390

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15 Sep 2014, 23:59
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:46) correct 15% (00:30) wrong based on 71 sessions

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What is $$8988*9012$$ ?

A. 80998866
B. 80998956
C. 80999856
D. 80999986
E. 80999996

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52390

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15 Sep 2014, 23:59
1
Official Solution:

What is $$8988*9012$$ ?

A. 80998866
B. 80998956
C. 80999856
D. 80999986
E. 80999996

$$8988*9012 = (9000 - 12)(9000 + 12) = 9000^2 - 12^2 = 81000000 - 144 = 80999856$$.

_________________
Intern
Joined: 29 Sep 2016
Posts: 16
Location: United States
Concentration: Finance, Economics
GPA: 3.01

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06 Nov 2016, 14:44
1
Referencing The GMAT Club Math Book (pg.13)

To find the n of last digits of the product = product of n digits of the integers.

By looking at the answer choices, the answers very at the hundred digit places.
A = 866, B =956, C=856, D= 986, E = 996.

Thus we want to find the last 3 digits of the product in order to find the answer.

8988 * 12 = 10856. (note that it's not necessary for you to calculate beyond 856). Thus the only answer that contains 856 is C.
Intern
Joined: 27 Jan 2017
Posts: 30

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09 Mar 2017, 07:24
2
I think the official answer here is the best way of looking at the problem.

When I first approached this question, however, I didn't notice that 8988 could be re-written as (9000-12).

I was still able to solve the question in under 1:30 seconds, though. I figured rather than trying to spend 30 seconds trying to think of a way to solve this, I could actually just multiply the two numbers quickly on paper. And quickly noticed I didn't have to solve the whole thing to find the answer.

8988
*
9012
------
17976
89880
000
0000
------
xx856

After adding the last two digits (76+80) I noticed the answer must end in 56. This eliminated everything but B and C. Then adding the last three digits 976+880+000 shows the answer must be 856.

I am not posting this because this is the most efficient way, but another way of looking at the problem because sometimes instead of losing precious time trying to find the easiest way to do something it might be quicker to just grind it out.
Re: M16-16 &nbs [#permalink] 09 Mar 2017, 07:24
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