COGNIZANT Numbers, decimal fractions and power Questions with Solutions

  1. P is an integer. P is greater than 883 If P -7 is a multiple of 11, then the largest number that will always divide (P+4)(P+15) is

A)242
B)340
C)245
D)178
Answer:A
Explanation: p-7= 11*a (as it is multiple of 11)
p=11*(a+7)
so (p+4)(p+15)= (11a+7+4)(11a+7+15);
= (11a+11)(11a+22);
=11*11(a+1)(a+2);
=121*2
=242

  1. Which pair of rational numbers lie between 1/5 and 2/5 –A. 262/1000, 275/1000

B. 362/1000, 562/1000
C. 451/1000, 552/1000
D. 121/1000,131/1000

Answer:A
Explanation: 1/5=0.2
2/5=0.4
so answer should be in between 0.2 and 0.4
A. 0.262 ,0.275
B. 0.362,0.562
C. 0.451,0.552
D. 0.121,0.131
clearly only option A is the answer

  1. natural numbers between 1 to 100

A)200
B)100
C)50
D)0
Answer:B
Explanation: (1+2+3+4……+100)
tn=a+(n-1)d
100=1+n-1
n=100;

  1. Find the smallest number, which when divided by 3, 5 and 7 leaves a reminder 2 in each case and is divisible by 11A. 737

b. 735
c. 105
d. 107
Answer:D
Explanation: Its Simple, just find the (lcm 3,5,7) + 2 which is remainder given
So lcm of 3,5,7 is 105 + 2 = 107
Therefore, the answer is 107

5. The number 2594* is completely divisible by 6 The smallest value of * can be

A)0
B)2
C)4
D)6
AnswerD
Explanation: to divisible by six it must divisible by 2 and 3. for divisible by 2 last digit must be even number, from given options all are even. so next to divisible by 3 sum of numbers must be divisible by 3. so in * place by keeping 4 sum of total is 24 which is divisible by 3 and last number also even. so by keeping 4 it divisible by 6.

  1. If 22n-1 = (1 / 8n-3) then the value of n is:

A: 3
B: 2
C 3: 0
D: -2
Answer:B
Explanation: 2^2n-1=1 / (8^n-3)
=8 ^ -(n-3)
=2 ^ -(3n-9)
bases are equal so,2n-1= – (3n-9) ==>n=2

  1. What is the value of: (33*812*20)/95 ?

A: 0
B: 3
C :1/3
D: None of these
Answer:B
Explanation: (3^3*81^2*2^0)/9^5?
=> (3*3*3*81*81*1)/(9*9*9*9*9)
=> 3

  1. what is the largest power of 20 conatined in 100!?

a)56
b)1
c)24
d)2
Answer:C
Explanation: 20=5*4
power of 4 in 100!= 100/4+100/16=31.25
power of 5 in 100!= 100/5+100/25=24
so, power of 20 in 100!=(4)^31*(5)^24=24

  1. Rahul purchased 7 dvds each of which costs rs.17. he gave a five hundred rupee note to the shopkeeper .the amount returned to him is divisible by:

a) 3
b)7
c)9
d)11
Answer:a
Explanation: 7*17=119
500-119=381
3+8+1=12 which is divisible by 3 also

  1. There are four prime numbers written in ascending order of magnitude. The product of first three is 385 and that of last three is 1001. Find the first number:

A): 5
B): 7
C): 11
D): 17
Answer:A
Explanation: two middle numbers are common in these 2 products whose product is equal to HCF of 385 and 1001.
HCF = 77
largest number = 1001/77 =13
smallest number = 385/77 =5

  1. The difference between two numbers is 1365. When larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is ?

A)265
B)270
C)150
D)none
Answer:B
Explanation:
Let the numbers be x and 1365+x
Then 1365+x = 6x+15
=> x = 270

  1. 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :

A) 24
B) 34
C) 44
D) 54
Answer: B) 34
Explanation:
Let the two parts be (54 – x) and x.
Then, 10 (54 – x) + 22x = 780
=> 12x = 240
=>  x = 20.
Bigger part = (54 – x)  = 34.

  1. There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is :

A) 3
B) 6
C) 9
D) 12
Answer: C) 9
Explanation:
Let the numbers be x and y. Then, 2x + 3y = 39…(i)and 3x + 2y = 30 …(ii)
On solving (i) and (ii), we get :  x = 6 and y = 9.
larger number = 9

  1. The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?

A) 12
B) 15
C) 17
D) none of these answers can be determined

Answer: D) none of these answers can be determined
Explanation:
Let the ten’s digit be x and unit’s digit be y.
Then, (10x + y) – (10y + x) = 63
=>  9 (x – y) = 63
=> x – y = 7.
Thus, none of the numbers can be deermined

  1. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is :

A) 253
B) 263
C) 273
D) 283
Answer: A) 253
Explanation:
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352
Since the number increases on reversing the digits, so the hundred’s digit is smaller than the unit’s digit.
Hence, required number = 253.

  1. The product of three consecutive even numbers when divided by 8 is 720. The product of their square roots is :

A) 12 sqrt(10)
B) 24 sqrt(10)
C) 120
D) none of these
Answer: B) 24 sqrt(10)
Explanation:
Let the numbers be x, x + 2 and X + 4.
Then, x(x + 2)(x +4) / 8 = 720 => x(x + 2)(x +4) = 5760.
√x  *  √(x + 2) * √(x +4) = √x(x +2)(x + 4 ) = √5760  =  24√10.

  1. If 2x = 3y = 6-z, then (1/x + 1/y + 1/z) is equal to

A)2
B)0
C)3
D)1
Answer:B
Explanation: 2x = 6 -z Þ 2 = 6-z/x ————-(i)
3y = 6 -z Þ 3 = 6-z/y ————-(ii)
Multiplying (i)and(ii)
2×3 = 6-z/x x 6-z/y
6 = 6(1-z/x) *6(1-z/y)
1 = (-z/x) +(-z/y)
1= -z(1/x +1/y)
1/-z = 1/x +1/y
1/x + 1/y + 1/z = 0

  1. What is the value of 500?

A)1
B)3
C)4
D)0
Answer:A
Explanation: any number with power “0” is always “1”.

19. If x^y = y^x and x = 2y, the value of y is:

A)1
B)2
C)3
D)4
Answer:B
Explanation: Ans: 2
sub X = 2Y in 1st eqn
( 2Y )^Y = Y^(2Y)
2^Y * Y^Y = Y^Y * Y^Y
2^Y = Y^Y
powers are equal so equate the bases
.”. Y = 2

  1. Class P has 30 students of which 20 like Music. In class Q, 10 students like Music. Find the number of students in Class Q if the average number of students who like Music in a class is 16

A)10
B)20
C)35
D)none
Answer:B
Explanation:solution will be :: ((30*20)+(x*10))/(30+x)=16
solving equation ans will be x=20.