[Official] Quant Thread for 2015!

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Approach plz :

1 and 8 are the first two natural numbers for which 1+2+3+.......+n is a perfect square . which number is fourth such number ?

For how many integers n is (n^4+6n) less than (6n^3 +n^2 ) 

Anyone here took AIMCAT advance pakage of test series ? They mention online section test as 180 during enrollemnt but i have only 90 available  ..is same with others too ?

For how many pairs (a,b) of natural numbers is the LCM of a and b is  2^3*5^7*11^13?

Find sum of all two digit positive integers which exceeds product of their digits by 12 . approach plz

For how many prime numbers p is( p ^2 + 3p -1 )a prime number ?

The no :of positive integers n in the range 12 less than or equals to n less than or equals to 40 such that the product (n-1 )(n-2).......3.2.1. is not divisible by n is ? . 

How many divisors of 21600 are perfect squares

six positive numbers are taken at random and multiplied together . then what is the probability that the product ends in an odd digit other than 5.                         Answer 0.4 or 0.4^6. Confusing answers. Approach pls. 

Given a^1/3 = 7^1/3 +26^1/3 + 63^1/3. Find the value of a.

 A bus, moving from Delhi to Jaipur overtakes a scooter at 2:00 pm. The bus reaches Jaipur at 4:00 pm and rests for 1 hr. When the bus returns it meets with the scooter again at 5:30 pm. When will the scooter reach Jaipur?

PnC : 

In how many ways can 21 identical white balls and 19 identical black balls be arranged in a row so that no 2 black balls are together ?

PnC : In how many ways numbers 1 to 12 can be arranged on a sides of squares (5 places on each sides i.e 20 places total) leaving 8 places empty.  ?

b)Here first number can be placed in how many ways ? 5 or 3 ?