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Pat has a weight problem. He exercises for three months and reduces his weight by 40%. He meets with an accident and fractures his leg, thereby increasing his weight by 50% in two months. What was his weight loss percent at the end of the five-month period?

Correct Answer: 10%

Explanation:

Let his original weight be 100 kg.
Weight after the first three months = 100 kg - 40% of 100 kg
= 100 - 40 = 60 kg
Weight after the next two months = 60 + 50% of 60 kg
= 60 + 30 = 90 kg
Loss % = (Initial weight - final weight)/initial weight*100
= (100-90)/100*100
= 10%
He lost 10% of his weight in five months.

Question: 2

The house of Laura is 60 meters west and 70 meters north of a crossing. The house of Ann is 10 meters west and 50 meters south of the same crossing. What is the distance between their houses in meters?

Correct Answer: 130 meters

Explanation:

The crossing can be considered as an origin and the four directions can be taken as the four axes.
The co-ordinates of the houses of Laura and Ann will be (-60, 70) and (-10, -50).
Distance between the points given = sqrt[(-10+60)^2+(-50-70)^2]
= sqrt[50^2+(-120)^2] = sqrt(2500+14400)
= sqrt(16900) = 130
The distance is 130 meters.
[sqrt(2) = square root of 2,[2^2 = 2*2]

Question: 3

What is the difference between the mean of the first 5 odd numbers and the mean of the first 5 even numbers?

Correct Answer: 1

Explanation:

The mean of the first 5 odd numbers = (1+3+5+7+9)/5
= 25/5 = 5
The mean of the first 5 even numbers = (2+4+6+8+10)/5
= 30/5 = 6
Difference = 6-5 = 1

Question: 4

There are 10 flags of different colours. Tim has to prepare 2 different arrangements, each using 4 flags of different colours. How many different arrangements can he possibly make if the flags of one set cannot be used in the other?

Correct Answer: 1814400

Explanation:

Tim can pick the first four flags from the ten flags in P(10,4) ways.
He will then be left with 6 flags out of which he can pick the next four in P(6,4) ways.
Total number of arrangements = P(10,4)*P(6,4)
= 10!/(10-4)! * 6!/(6-4)!
= 10!/6! * 6!/2!
= 10!/2!
= 1814400

Question: 5

A variable is such that it satisfies the quadratic equation 9x^2-63x-162 = 0. Find the natural number.
[x^2 = x*x]

Correct Answer: 9

Explanation:

9x^2-63x-162 = 0
x^2 -7x -18 = 0
x^2 - 9x + 2x -18 = 0
x(x - 9) + 2(x - 9) = 0
(x-9)(x+2) = 0
x = 9, -2
Since x is a natural number, it is equal to 9

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