Cognizant Qunatitative Ability Questions
Q1) log 3600 is equal to .
A.2 log 6 + 1
B.6 log 2 + 1
C.2 log 6 + 2
D.6 log 2 +2
Answer : Option C
Explanation: Log 3600 = log (62 *102 ) = log10 62 + log10 102 = 2log6 +2
Q2) If a = 4, b = 5, and c = 7, then what is the value of log4 √(a + b + c)?
A.1
B.2
C.3
D.4
Answer : Option A
Explanation: log4 √(a + b + c) = log4 √(4 + 5 + 7) = = log4 √16 == log4 4 = 1
Q3) What is the difference between the LCM and the HCF of the numbers 20, 30, and 40?
A. 100
B. 110
C. 120
D. 130
Answer : Option B
Explanation: LCM of 20,30 and 40 = 120
HCF of 20,30 and 40 = 10
Difference between L.C.M and H.C.F is 120-10 = 110.
Q4) If I have kept six different books on a shell, in how many different ways can I arrange them?
A.6
B.24
C.120
D.720
Answer : Option D
Explanation: six different books on a shell can be arranged in 6P6 6! Ways = 720 ways
Q5) The simple interest earned on a certain amount is double the money when invested for 15 years. What interest rate is offered?
A. 26.66%
B. 12%
C. 30%
D. 13.33%
Answer : Option D
Explanation: Let principal be rs. p
Then simple interest after 15 years will be 2p
Now, Simple Interest = Principal × Rate × Time
2p = p × Rate × 15
2 = Rate × 15
Rate × 15 = 2
Rate = 2/15
rate = 0.1333
So, rate of interest = 13.33%
Q6) What is the largest power of 20 obtained in 100 factorials?
A. 20
B. 25
C. 24
D. 21
Answer : Option C
Explanation: The largest power of 20 contained in 100 factorials.
20=5×2×2
The highest prime factor 20 is 5.
So, number of powers of 20 will only depend on power of 5.
Also, 1005=20,10025=4.
Therefore, the power of 5 is 20+4=24
Hence, the largest power of 20 contained in 100 factorial is 24.
Q7) Rajesh commutes daily by travelling 4/5 of the distance between his home and office by metro train, 3/20 by auto and remaining 1 km on foot. What is the distance between his home and office?
A. 20 km
B. 21 km
C. 29 km
D. 30 km
Answer : Option A
Explanation: The distance travelled by Rajesh from home to office by metro train = 4/5
The distance travelled by auto = 3/20
The distance travelled on Foot = 1 km
Let x be the total distance from the home to the office
Distance travelled
x = [(4/5)x + (3/20)x] + 1
x [1 – (4/5) – (3/20)] =1
x (1/20)=1
x = 20 km
Thus, the total distance travelled by Rajesh from home to the office is 20 km.
Q8) What is least perfect square, which is divisible by 24, 30, 60?
A. 1600
B. 3600
C. 14400
D. 32400
Answer : Option B
Explanation: The LCM is 120
Now to find the smallest square number divisible by 120:
Factors of 120 = 2*2*2*3*5
Now, to form pairs, you have to multiply it by 2*3*5 or 30
120*30 = 3600
Hence, the smallest perfect square number that is divisible by 24, 30, and 60? is 3600 (it is the square of 60).
Q9) In a poultry farm, 50 hens give 200 eggs in 2 days. In how many days will 20 hens give 400 eggs?
A. 15
B. 10
C. 5
D. 8
Answer : Option B
Explanation: Let the no. of hen be H1, no. of eggs E1, no. days D1 separately
Thus,
H1=50, E1=200, D1= 2
We are supposed to find what amount of time will 20 hens require to give 400 eggs
Allow x to be the no. of days
So,
H2= 20, E2= 400, D2=x
Therefore, the formula here will be
(H1 * D1)/E1 = (H2 * D2)/ E2
(50 * 2)/200 = (20 * x)/400
(50 * 2) * 400/(200 * 20) = x
Hence, x = 10
So, we can conclude that 20 hens will take 10 days to lay 400 eggs.
Consequently 20 hens require 10 days to give 400 eggs.
Q10) Rani invested Rs. 20,000 at 8 % p.a. If the interest is compounded half yearly, then total interest earned by Rani at the end of the year is:
A. Rs. 1829
B. Rs. 1632
C. Rs. 1923
D. Rs. 2020
Answer : Option B
Explanation:
Q11) The difference of two numbers is 14. Their L.C.M. and H.C.F. are 441 and 7. Find the numbers.
A. 21, 35
B. 35, 49
C. 49, 63
D. 63, 77
Answer : Option C
Explanation: Going through option verification
Option A – 21 and 35 , L.C.M =105 , Hence wrong option
Option b – 35 and 49 , L.C.M =245 , Hence wrong option
Option c – 49 and 63, L.C.M =441 , and H.C.F is 7 and difference between numbers is 14, hence option C
Q12) Piya sold her car for Rs. 50,000 less than what she bought if for and lost 8%. At what price should she have sold the car, if she wanted to gain as much as she lost in the first transaction?
A. Rs. 6,25,000
B. Rs. 6,50,000
C. Rs. 6,75,000
D. Rs. 6,37,000
Answer : Option C
Explanation: cp = x
Sold at Rs. 50000 less than Rs. x
so, sp = x - 50000
Also, 50000 is 8% of x
so, 50000 = 8/100 of x
or, 50000 = 0.08x
or, x = 50000/0.08 = 625000
So, Piya bought at Rs. 625000.
To gain what she lost in her first transaction I.e., Rs 50000 she should have sold the car at
Rs. 625000 + 50000 = Rs. 6,75,000
Q13) The permutations and combinations of abcd taken 3 at a time are respectively:
A. 12, 2
B. 24, 4
C. 36, 6
D. 48, 8
Answer : Option B
Explanation: The permutations and combinations of abcd taken 3 at a time are respectively 4P3 and 4C3
4P3 = 4! /1! = 24
4C3 = 4!/3! = 4
Q14) The average age of a cricket team of eleven is 22 years. The average age gets increased by 1 year, when the coach age is also included. What is the age of the coach?
A. 34
B. 23
C. 30
D. 40
Answer : Option A
Explanation: Average = sum of elements / no. of elements.
average age of cricket team = sum of ages of players/ no of players
22 = sum of ages of players/ no of players
22 × 11 = sum of ages of players
242 = sum of ages of players
as average age gets increased by 1 year when the coach age is also included
23 = sum of ages of players + age of coach / no of players + 1
23 ( 11 + 1 ) = sum of ages of players + age of coach
23 × 12 = sum of ages of players + age of coach
276 = sum of ages of players + age of coach
Now,
age of coach = sum of ages of players + age of coach - sum of ages of players
age of coach = 276 – 242= 34
Hence, the age of the coach is 34
Q15) What is the least number by which 16,800 must be divided to get a number perfect square?
A. 21
B. 42
C. 24
D. 40
Answer : Option B
Explanation: 16,800 = 168 * 100 = 25 * 7 *3 *52 =2* 24 * 7 *3 *52, hence 2,7 and 3 are the one’s which are not perfect squares , hence the product of 2*3*7 = 42 should be divided
