Aptitude Questions and Answers
Find the odd man out:
4, 9, 256, 529, 573
573 is not a perfect square
In a single throw of two dice , find the probability that neither a doublet nor a total of 8 will appear.
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.
A division of a company consists of seven men and five women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
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
What day of the week does May 28 2006 fall on ?
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.
How many days are there in x weeks x days ?
x weeks x days = (7×x)+x=7x+x= 8x days
The calendar for the year 2007 will be the same for the year
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
Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
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
If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth day of the month?
Given that seventh day of a month is three days earlier than Friday
- Seventh day is Tuesday
- 14th is Tuesday
- 19th is Sunday
X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Ratio of the investment = `21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5`
Share of X in the profit = `26400 ** (6/11) = 2400 ** 6 = 14400`
Kamal started a business with Rs.25000 and after 4 months, Kiran joined him with Rs.60000. Kamal received Rs.58000 including 10% of profit as commission for managing the business. What amount did Kiran receive?
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
