gamma+delta

Question

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

gmatcracker24 · Answer

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

jamifahad · Answer

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.

Spidy001 · Answer

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.

Answer is A.

GMATmission · Answer

Good explanation. Kudos to you.

gamma+delta

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