Hard GMATPrep problems - Help!

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Hard GMATPrep problems - Help!

by GMAT blows » Tue Aug 21, 2007 10:04 am
There were a few PS questions I could not solve on my own and would appreciate if anyone can help. Thanks!

1. If n is a multiple of 5 and n=p^2q , where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2
b) q^2
c) p*q
d) p^2*q^2
e)p^3*q

24. A certain stock exchange designates each stock w/ one-, two-, three- letter code, where each letter is selected from 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order consistutes a different code, how many different stocks is possible to uniquesly designate with these codes?
a) 2951
b) 8125
c) 15600
d) 16302
e) 18278

Any additional insights for doing combination problems will be appreciated also :)
Source: — Problem Solving |

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Re: Hard GMATPrep problems - Help!

by givemeanid » Tue Aug 21, 2007 10:34 am
GMAT blows wrote:There were a few PS questions I could not solve on my own and would appreciate if anyone can help. Thanks!

1. If n is a multiple of 5 and n=p^2q , where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2
b) q^2
c) p*q
d) p^2*q^2
e)p^3*q
n = p*p*q
If n is a multiple of 5, then 5 is a factor of either p or q. So, either p^2 or q^2 is a multiple of 25. Hence p^2*q^2 will definitely be a multiple of 25. Answer is D.


GMAT blows wrote:24. A certain stock exchange designates each stock w/ one-, two-, three- letter code, where each letter is selected from 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order consistutes a different code, how many different stocks is possible to uniquesly designate with these codes?
a) 2951
b) 8125
c) 15600
d) 16302
e) 18278

Any additional insights for doing combination problems will be appreciated also :)
1 letter code -> 26 symbols
2 letter code -> The first letter can be one of the 26 and same for the second letter. So, total = 26*26
3 letter code -> 26*26*26
Total = 26 + 26*26 + 26*26*26.
To find the total, note that each of the terms has a unit digit of 6. So, the unit digit of sum would be unit digit of 6+6+6 that is unit digit of 18 = 8. Answer is E.
So It Goes