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by vinay1983 » Mon Sep 30, 2013 7:02 am
Consider the following sequence : 2,22,222,2222,22222 etc. What is ten's digit of the sum of the first fifty terms of the sequence?

A. 2
B. 8
C. 6
D. 4
E. 0
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Mon Sep 30, 2013 7:50 am
vinay1983 wrote:Consider the following sequence : 2,22,222,2222,22222 etc. What is ten's digit of the sum of the first fifty terms of the sequence?

A. 2
B. 8
C. 6
D. 4
E. 0
EDIT (I originally read it as "units digit)

Rewrite sum as:
2
20 + 2
200 + 20 + 2
2000 + 200 + 20 + 2
20,000 + 2000 + 200 + 20 + 2
200,000 + 20,000 + 2000 + 200 + 20 + 2
.
.
.
+________________________________________

First add units digits (the 2's). When we add (2) fifty times, we get 100.

Now add the 20's
There are forty-nine 20's
(49)(20) = 980


980 + 100 = 1080

So, after adding the 2's and the 20's only, the sum is 1080
At this point, if we add 200's, 2000's etc, the tens digit will remain [spoiler]8[/spoiler].

Answer: B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Sep 30, 2013 8:27 am, edited 1 time in total.
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by theCodeToGMAT » Mon Sep 30, 2013 8:03 am
2 x 50 = _ _ 0
Answer {E}
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by vinay1983 » Mon Sep 30, 2013 8:09 am
Ahem!Brent and Rahul, I think the question asked for ten's digit and NOT unit's digit!
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by theCodeToGMAT » Mon Sep 30, 2013 8:53 am
vinay1983 wrote:Ahem!Brent and Rahul, I think the question asked for ten's digit and NOT unit's digit!
aah.. seems today's long bike ride has really played on my mind..

Is the Answer 8

22*49 + 2 == _ _ 8 0
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by GMATGuruNY » Mon Sep 30, 2013 11:55 am
vinay1983 wrote:Consider the following sequence : 2,22,222,2222,22222 etc. What is ten's digit of the sum of the first fifty terms of the sequence?

A. 2
B. 8
C. 6
D. 4
E. 0
Let K = the sum of the fifty terms.
To determine the tens digit of K, we need examine only the UNITS DIGITS and the TENS DIGITS of the 50 terms:

02 + 22 + 22 + .... + 22 + 22 + 22.

Note that all of the digits are the same except for one: the TENS digit of the first term = 0.

The sum of the 50 units digits = 50*2 = 100.
Thus, the units digit of K = 0.

When we calculate the tens digit of K, we must CARRY 10 from the units place.
The sum of the 50 tens digits + 10 carried from the units place = 0 + 49*2 + 10 = 108.
Thus, the tens digit of K = 8.

The correct answer is B.
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by varun289 » Mon Sep 30, 2013 6:14 pm
Can i try to elaborate little simpler -

2, 22, 222 up to 50 terms ,

so unit digit - 50X 2 = 100 for sure
10 will carry forward
next 2 X 49 = ... 8

so ,,,8 + 10 = always 8 on right side

so ans must be 8

IMO - B
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by vinay1983 » Mon Sep 30, 2013 8:01 pm
Yes the OA is 8
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