**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 (6

^{2}*10

^{2}) = log

_{10 }6

^{2 }+ log

_{10 }10

^{2 }= 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: **log_{4} √(a + b + c) = log_{4 }√(4 + 5 + 7) = = log_{4 }√16 == log_{4 }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 = 2^{5} * 7 *3 *5^{2} =2* 2^{4} * 7 *3 *5^{2}, 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