Explanation
:: Explanation ::
Here are the Explanation of the Questions
(1)
:The value of P, when 4864 x 9P2 is divisible by 12, is
a. 2
b. 5
c. 8
d. None of these
The correct answer is: D
Explanation
Since 4864 is divisible by 4, so 9P2 must be divisible by 3
Therefore (11+P) must be divisible by 3
Therefore least value of P is 1
(2)
:The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is
a. 7
b. 29
c. 41
d. 67
The correct answer is: D
Explanation
x+(x+36)+y=100 => 2x+y=64
Therefore y must be even prime, which is 2
Therefore 2x+2=64 => x=31
Third prime number= (x+36)= (31+36)= 67
(3)
?How many of the following numbers are divisible by 132
264, 396, 462, 792, 968, 2178, 5184, 6336
a. 4
b. 5
c. 6
d. 7
The correct answer is: A
Explanation
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4
Also, 5184 is not divisible by 11
Each one of remaining 4 is divisible by each one of 11, 3 and 4 and therefore, by 132
(4)
:The number 311311311311311311311 is
a. divisible by 3 but not by 11
b. divisible by 11 but not by3
c. divisible by both 3 and 11
d. neither divisible by 3 nor by 11
The correct answer is: D
Explanation
Sum of digits= 35 and so it is not divisible by 3
(Sum of digits at odd places) (Sum of digits at even places)= 1916=3, not divisible by 11
So, the given number is neither divided by 3 nor by 11
(5)
:The largest natural number which exactly divides the product of any four consecutive natural numbers is
a. 6
b. 12
c. 24
d. 120
The correct answer is: C
Explanation
Required number= 1*2*3*4=24
