Quantitative Aptitude - Arithmetic Ability Questions

The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520 

(since n = 8)

Number of cubes= (100x100x100) / (10x10x10)= 1000

P(odd) = P (even) =12 1(because there are 50 odd and 50 even numbers)

Sum or the three numbers can be odd only under the following 4 scenarios:

Odd + Odd + Odd = 12*12*12= 18

Odd + Even + Even = 12*12*12=18

Even + Odd + Even = 12*12*12=18

Even + Even + Odd = 12*12*12 = 18

Other combinations of odd and even will give even numbers. 

Adding up the 4 scenarios above:

= 18+ 18+18+ 18 = 48 = 12

Let the cost price = Rs 100
then, Marked price = Rs 135

Required gain = 8%,
So Selling price = Rs 108
Discount = 135 - 108 = 27

Discount% = (27/135)*100 = 20%

Let the third proportional to x2-y2 and x-y be z. Then, 

x2-y2:x-y::x-y:z  

=>x2-y2*z=x-y2  

=> z=x-y2x2-y2=x-yx+y

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

Let the initial number of persons be x. Then,

16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20.

Clearly, any of the three will give us the answer