Problem Solving MCQ Quiz - 1 - UPSC MCQ

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.
US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2. 
Now US : Indian = 25 : 10, and Indian : British = 10 : 2
Hence the two ratios can be combined and US : British = 25 : 2

Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3, 4, 5 triangle, and is therefore, 5.
Circumference = π.diameter = 5π

If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as
n + (n + 1) + (n + 2) + (n + 3 ) and
(n + 3) + (n + 4) + (n + 5) + (n + 6)
Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12

(Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral
9 - (2 x ½ x 3 x 1.5) = 4.5

Remember that n could be positive negative or a fraction. Try out a few cases:
In case I, if n is -1, then 2n is less than n.
In case II, if n is a fraction such as ½ then n² will be less than n.
In case III, if n is 2, then 2-n = 0, which is less than n.
Therefore, none of the choices must be greater than n

The smallest value for n such that 5n is a square is 5.
75np can now be written as 75 x 5 x p.
This gives prime factors.... 3 x 5 x 5 x 5 x p
To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9
n + p = 5 + 9 = 14

Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11, but anywhere in between is possible.

1 < 4n + 7 < 200
n can be 0, or -1
n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1.
The largest value for n will be an integer < (200 - 7) /4
193/4 = 48.25, hence 48
The number of integers between -1 and 48 inclusive is 50

Total volume of water = 12 liters = 12 x 1000 cm³
The base of the aquarium is 50 x 30 = 1500cm²
Base of tank x height of water = volume of water
1500 x height = 12000; height = 12000 / 1500 = 8

Let Ben's age now be B
Anita's age now is A.
(A - 6) = P(B - 6)
But A is 17 and therefore 11 = P(B - 6)
11/P = B-6
(11/P) + 6 = B