2 everywhere

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

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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Source: Beat The GMAT — Problem Solving | Mon Sep 30, 2013 7:02 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Sep 30, 2013 8:03 am

2 x 50 = _ _ 0
Answer {E}

R A H U L

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

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!

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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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

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

R A H U L

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

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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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Mon Sep 30, 2013 8:01 pm

Yes the OA is 8

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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