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# gamma+delta

Author Message
Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38

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20 Sep 2011, 05:04
00:00

Difficulty:

(N/A)

Question Stats:

56% (02:18) correct 44% (00:34) wrong based on 9 sessions

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Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of a gamma raised to the seventh power and a delta raised to the seventh power?

(A)alpha
(B)beta
(C)gamma
(D)delta
(E)epsilon
[Reveal] Spoiler: OA

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Manager
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Joined: 29 Jun 2010
Posts: 121
WE: Information Technology (Consulting)

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20 Sep 2011, 09:51
1
KUDOS
Looking at the units digit is the key here

First find the units digit, There is a pattern :

If the result ends with a 0 or a 5, it is an alpha (our answer)
If the result ends with a 1 or 6, it is a beta
If the result ends with a 2 or 7, it is a gamma
so on...

Hope this helps
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GC24

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Senior Manager
Joined: 03 Mar 2010
Posts: 440
Schools: Simon '16 (M)

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20 Sep 2011, 10:24
alpha--beta--gamma--delta--epsilon
0--1--2--3--4
5--6--7--8--9

Now (gamma)^7+(delta)^7
=2^7+3^7
=last digit of 2^7 + last digit of 3^7
= 8+7=5(last digit of sum)--alpha

One more case
= 7^7 + 8^7
=last digit of 7^7 + last digit of 8^7
= 3+2=5(last digit of sum)--alpha.

OA A.
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Director
Joined: 01 Feb 2011
Posts: 755

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20 Sep 2011, 17:29
A-B-G-D-E
0-1-2-3-4 ----->second row
5-6-7-8-9

In the above sequence we can see that every number can be expressed as a multiple of 5 and some remainder.

eg 0 = 0*5
6= 5*1+1

so if we can figure out whats the remainder when the number is divided by 5, we can figure out what label it belongs to by looking at the second row.

remainder of (G^7+D^7)/5 = ?

lets pick G=2, D=3

=remainder of (2^7+3^7)/5

last digit of 2^7 is 8 and last digit of 3^7 = 7

=> remainder will be 0

i.e label A or Alpha.

Manager
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Joined: 16 Aug 2011
Posts: 179
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37
GMAT 2: 620 Q49 V27
GMAT 3: 700 Q49 V36
WE: Other (Other)

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21 Sep 2011, 01:57
gmatcracker24 wrote:
Looking at the units digit is the key here

First find the units digit, There is a pattern :

If the result ends with a 0 or a 5, it is an alpha (our answer)
If the result ends with a 1 or 6, it is a beta
If the result ends with a 2 or 7, it is a gamma
so on...

Hope this helps

Good explanation. Kudos to you.
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Re: gamma+delta   [#permalink] 21 Sep 2011, 01:57
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