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 ABC be the isosceles triangle, the AD be the altitude 

Let AB = AC = x then BC= 32-2x       [because parameter = 2 (side) + Base] 

since in an isoceles triange the altitude bisects the base so 

BD = DC = 16-x 

In a triangle ADC, AC2=AD2+DC2 

x2=82+16-x2 ⇒x=10 

BC = 32-2x = 32-20 = 12 cm 

Hence, required area = 12*BC*AD= 12*12*10 = 60 sq cm

By the rule of alligation:
Cost of 1 kg rice of 1st kind                  Cost of 1 kg rice of 2nd kind 

  Required ratio = 60 : 90 = 2 : 3

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

Angle traced by hour hand in214 21 hrs = 36012×2140 =157102 

Angle traced by min. hand in 15 min = 36012×150 = 900 

 Required Angle = 157120-900 = 67102

let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then, 

Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300

 x*5*3100+1500-x*8*3100=300 

 x=800

Required ratio =  x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15

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