Quantitative Aptitude - Arithmetic Ability Questions

The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:

= 6*6*6*6=64

n(S) = 64

Let X be the event that all dice show the same face. 

X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}

n(X) = 6

Hence required probability = n(X)n(S)=664 =1216

Let the number  be 476ab0 

476ab0 is divisible by 3 

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2, 

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2, 

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5, 

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5, 

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

Let original consumption = 100 kg and new consumption = x kg, 

So, 100 * 6 = x * 7.50 => x = 80kg 

Reduction in consumption = 20%.

(Place value of 7)-(face value of 7)
=7000-7=6993.

Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m

Cost of painting = Rs. 158 x 3 = Rs. 474

The given number series 8, 18, 56, 232, 1165 

8

8 x 2 + 2 = 18

18 x 3 + 3 = 57 (not 56)

57 x 4 + 4 = 232

232 x 5 + 5 = 1165

Hence, the odd man in the given series is 56.