Chaitanya_1986 wrote:please help

no. of 1 letter word that can be formed out of 26 letter is 26;
no. of 2 letter word that can be formed out of 26 letter word is 26*26( because here repetition of words is allowed and AA,BB..etc forms a different unique code)=676 ;
no. of 3 letter word than can be formed out of 26 letter word is 26*26*26( here also AAA,BBB,CCC... will form a unique and also repetition of digits is allowed)=17576;

hence total no. of different stocks that can be uniquely designated with these codes can be 26+676+17576=18278 hence E

manpsingh87 wrote:

Chaitanya_1986 wrote:please help

no. of 1 letter word that can be formed out of 26 letter is 26;
no. of 2 letter word that can be formed out of 26 letter word is 26*26( because here repetition of words is allowed and AA,BB..etc forms a different unique code)=676 ;
no. of 3 letter word than can be formed out of 26 letter word is 26*26*26( here also AAA,BBB,CCC... will form a unique and also repetition of digits is allowed)=17576;

hence total no. of different stocks that can be uniquely designated with these codes can be 26+676+17576=18278 hence E

Completely agree with analysis, would just like to present a quick approach to finding the answer instead of actually calculating 26^3:

focus on the units digits.
when 6 is raised to higher powers, the units digit always ends with a 6.
6^2 = 36 - ends with a 6
6^3 = 36*6 = (30+6)*6 = 30*6 + 6*6 = 360 + 36 = ends with a 6.
etc.
so 26^2 = 26*26 and 26^3 = 26*26*26 will also end with a 6 - the units digit is just a higher power of 6.

This means that 26 + 26^2 + 26^3 will end with the units digit of 6+6+6 = 18 - ends with an 8 - which only E does.

Geva@MasterGMAT wrote:

manpsingh87 wrote:

Chaitanya_1986 wrote:please help

no. of 1 letter word that can be formed out of 26 letter is 26;
no. of 2 letter word that can be formed out of 26 letter word is 26*26( because here repetition of words is allowed and AA,BB..etc forms a different unique code)=676 ;
no. of 3 letter word than can be formed out of 26 letter word is 26*26*26( here also AAA,BBB,CCC... will form a unique and also repetition of digits is allowed)=17576;

hence total no. of different stocks that can be uniquely designated with these codes can be 26+676+17576=18278 hence E

Completely agree with analysis, would just like to present a quick approach to finding the answer instead of actually calculating 26^3:

focus on the units digits.
when 6 is raised to higher powers, the units digit always ends with a 6.
6^2 = 36 - ends with a 6
6^3 = 36*6 = (30+6)*6 = 30*6 + 6*6 = 360 + 36 = ends with a 6.
etc.
so 26^2 = 26*26 and 26^3 = 26*26*26 will also end with a 6 - the units digit is just a higher power of 6.

This means that 26 + 26^2 + 26^3 will end with the units digit of 6+6+6 = 18 - ends with an 8 - which only E does.

yep.. completely agree with you sir.. thanks a lot for sharing an alternative way of dealing with the problem....!!