Official Quant thread for CAT 2013

If P and Q are prime no. greater than 3 , than P^2 - Q^2 is always divisible by ? Don't know the answer, approach please.

In how many ways 156 be factorised into three factors such that each factor is greater than unity ans atleast two of the three possible pairs of factors are relatively prime. Approach please

Find the no of integer sol for equation 1/x + 1/y = 1/48. Please explain the approach to be used in these type of ques.

In how many ways 5^11 be expressed as product of 3 factors ?

What is the volume of smallest cube that can be made by stacking cuboids of dimension 6 * 3 * 4 ?

Product of 3 consecutive odd natural no is 531117. What is the sum of three num ?
1. 183
2. 213
3. 243
4. 273
Approach please. The answer is 3

NO of ways of 5^11 can be expressed as product of 3 distinct factors. *edit*


How many three letter words can be formed using the letters of the word 'PRACTICES' ?


What is the minimum no of cubes with which one can construct a cuboid of dimension 20 * 16 * 12 ?

N is the sum of squares of 3 consecutive odd no such that all digits of N are same. If N is 4 digit no, the value of N is ?
1. 3333
2. 5555
3. 7777
4. 9999

Ans is 2, please explain the approach

Can anybody pls share some set theory questions (or links for the same) related to maximum and minimum.plsss

18 ^ 2000 + 12 ^ 2000 - 5 ^ 2000 - 1 is divisible by
1. 323
2. 221
3. 299
4. 237



if S =
{ (10^4 + 324) (22^4 + 324) (34 ^ 4 + 324) (46 ^ 4+ 324) (58 ^ 4 + 324)} / { (4^4 + 324) (16 ^ 4+ 324) (28 ^ 4+ 324 ) (40 ^ 4 + 324 ) (52^4 + 324) }, then value of S is :
1. 373
2. 256
3. 504
4. 588

100 people r standing in a row , and are counting off in 5 as (1,2,3,4,5,1,2,3,4,5...........). The person who says 5 is taken out of the line and the procedure is repeated until 4 persons r remaing. What was the original position of the last person to leave ?
1. 93
2. 96
3. 97
4. 98

Any short method ?

An Indian king is born in an yr, which is a perfect square. Lived a square no of yrs , and died in an yr which is also a perfect no. Then the yr he could have born in was ?
1. 1936
2. 1764
3. 1600
4. 1444

Approach please

A no A is a 3 digit perfect square. The no when written in reverse order is also a perfect square. A 4 digit perfect square is formed by repeating the rightmost digit of A. the sum of digits of A
1. perfect square
2. even
3. Prime

it is given that m and n are two smallest natural no satisfying following conditions :
1. 5 2. mn - 3 and mn + 3 are prime
Then m + n is equal to :
1. 15
2. 17
3. 19
4. 21

In a bag, there are some slips with no 13 and 14 written on them. The slips with no 13 are 5 more than slips with no. 14 written on them. Which can be the sum of no in bag:
1. 254
2. 300
3. 327
4. 353

45! is divided by 47....wat wil b the remainder?

kindly solve it