Aptitude Questions and Answers

573 is not a perfect square

n(S) = 36

A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

B = { (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) } 

Required probability = `10/36 = 5/18`

 Note: (4,4) occurs in both. Count once.

First, the denominator. We have twelve different people, and we want a combination of two selected from these twelve.  We will use the formula :

`nC2 = (n(n-1))/2`

which, for profound mathematical reasons we need not address here, is also the formula for the sum of the first (n – 1) positive integers.  Here

`12C2 = (12*(11))/2 = 6 * 11 = 66`

That’s the total number of pairs we could pick from the twelve employees.  That’s our denominator.

For the numerator, we want every combination of two from the five female employees.  That’s

`5C2 = (5*(4))/2 = 5 * 2 = 10`

That’s the  number of pairs of female employees we could pick from the five.  That’s our numerator.

probability = `10/66 = 5/33`

Answer = Option D

28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6

Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148

148 days = 21 weeks + 1 day = 1 odd day

Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday

Hence May 28 2006 is Sunday.

x weeks x days = (7×x)+x=7x+x= 8x days

Take the year 2014 given in the choice.

Total odd days in the period 2007-2013 = 5 normal years + 2 leap year
= 5 x 1 + 2 x 2 = 9 odd days
= 2 odd day (As we can reduce multiples of 7 from odd days which will not change anything)

Take the year 2016 given in the choice.

Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 odd days
= 4 odd days
(Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)

Take the year 2017 given in the choice.

Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year
= 7 x 1 + 3 x 2 = 13 odd days
= 6 odd days

Take the year 2018 given in the choice.

Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year
= 8 x 1 + 3 x 2 = 14 odd days
= 0 odd day (As we can reduce multiples of 7 from odd days which will not change anything)

Also, both 2007 and 2018 are not leap years.
Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007

Clearly it can be understood from the question that 9 days ago was a Thursday

Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)

Hence today = (Thursday + 2 odd days) = Saturday

Given that seventh day of a month is three days earlier than Friday

• Seventh day is Tuesday
• 14^th is Tuesday
• 19^th is Sunday

Ratio of the investment = `21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5`

Share of X in the profit = `26400 ** (6/11) = 2400 ** 6 = 14400`

Ratio of the profits = 25000*12 : 60000*8

= 25*12 : 60*8 = 5*3 : 12:2 = 5 : 4*2

= 5:8

Let the total profit = x.

Then Kamal received `(10x)/100 = x/10` as commission for managing the business

Remaining profit = `x- x/10 = (9x)/10` which is shared in the ration 5:8

Kamal's share = `x/10 + ((9x)/10) * (5/13) = 58000`

=> `x + 9x(5/13) = 580000`

=> `x(1 + 45/13) = 580000`

=> `x ( 58/13) = 580000`

=> `x ( 1/13) = 10000`

=> `x = 130000`

Kiran's share = 130000 - 58000 = 72000