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The points P(2.8, 4.2) and Q(4,y) lie on a straight line passing through the origin. What is the value of y?

Correct Answer: 6

Explanation:

Since P and Q lie on the same line, the slopes of PO and QO will be equal, where O is the origin.
Slope of PO = (4.2-0)/(2.8-0)
= 3/2
Slope of QO = (y-0)/(4-0)
= y/4
Equating the two we get, y = 6

Question: 2

Evaluate 64^(1/5)*512^(1/5)*[{729^(1/2)}^(1/3)]
[x^(1/5) = Fifth root of x]

A number increases by 30%. What is the percent increase in the square of the number?

Correct Answer: 69%

Explanation:

Let the number be x. The square of the number will be x^2
Percentage increase in the number = 30%
New number = x+30% of x
= x+30*x/100
= 130x/100

The square of the new number = (130x/100)^2
= 16900x^2/10000
= 1.69x^2

Percentage increase in square = (1.69x^2-x^2)/x^2*100
= 69%

[x^2=x*x]

Question: 4

Two trains of lengths 250m and 260m are running in opposite directions and cross each other in 18 seconds. What is the speed of the slower train in km/hr if the faster train is running at speed 62 km/hr?

Correct Answer: 40

Explanation:

Let the speed of the faster train be x km/hr.
Relative speed = (x+62) km/hr
Total distance = 260+250 = 510m = 0.51km
Total time = 18 seconds = 18/(60*60) = 0.005 hr
Speed = Distance/time
x+62 = 0.51/0.005
x+62 = 102
x = 102 - 62 = 40
The speed of the slower train is 40 km/hr

Question: 5

If the probability that a hunter shoots two white rabbits in a certain part of a jungle where only white and black rabbits thrive is 2/11 and there are 5 white rabbits in that part of the jungle, then what is the total number of rabbits in that part of the jungle?

Correct Answer: 11

Explanation:

Let the number of black rabbits be x
Total rabbits = x+5
Required probability = 5/(x+5) * 4/(x+4) = 2/11
20/[(x+5)(x+4)] = 2/11
20*11 = 2(x^2+9x+20)
110 = x^2 + 9x +20
x^2 + 9x -90 = 0
x^2 +15x-6x -90 =0
x(x+15)-6(x+15)=0
x = 6 as x cannot be negative.
There are x+5 = 6+5 = 11 rabbits in the jungle.

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