alphabetic-to-numerical coding

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed May 02, 2012 4:52 am

In an alphabetic-to-numerical coding system, the single letters A-Z are given values of 0-25 respectively. In a three-letter word, the first letter has value µ, the second letter has value ß, and the third letter has value ∂. The value of a three-letter word is computed as follows:

word value = µ·26^2 + ß·26^1 + ∂·26^0

Example: CAT = 2 x 26^2 + 0 x 26^1 + 19 x 26^0 = 1371

What word has the value 783?
(A) ASK
(B) BED
(C) CUP
(D) DOG
(E) ELF

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Source: Beat The GMAT — Problem Solving | Wed May 02, 2012 4:52 am

klmehta03: Senior | Next Rank: 100 Posts; Posts: 74; Joined: Sun Sep 05, 2010 3:11 pm; Thanked: 3 times

by klmehta03 » Wed May 02, 2012 5:09 am

IMO B .
BED= (1*26^2)+(4*26^1)+(3* 26^0)
= 783
took me 30 sec to get the answer but 2 min to undertsand the problem.
OA pls?

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed May 02, 2012 5:23 am

klmehta03 wrote:IMO B .
BED= (1*26^2)+(4*26^1)+(3* 26^0)
= 783
took me 30 sec to get the answer but 2 min to undertsand the problem.
OA pls?

Since, the one’s place of the word value is 3, which is obtained by ∂•26^0 = ∂•1 = ∂; hence, ∂ must represent D. Only one choice shows D in one’s place, and that’s [spoiler]B[/spoiler].

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

spartacus1412: Master | Next Rank: 500 Posts; Posts: 110; Joined: Wed Feb 22, 2012 11:28 pmFollowed by: 1 member; Location: India; Thanked: 13 times

by spartacus1412 » Wed May 02, 2012 8:17 pm

the hundreds place in 783 has to be 1.
as , 0*26^2 will not make the number sum 783

and if hundreds place is 2 then 2*26^2 is greater than 783.

so, the hundreds place is 1.

now from CAT c is numbered 2, A is numbered 0.

so I suppose B is numbered 1. hence, optionB

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