Dear Reader, Below are few questions from numeric and algebraic sections. Most of the questions are simple to answer but could be time consuming if not practiced well.

Question 1

The average of seven consecutive even numbers P,Q,R,S,T,U,V is 64. What is the product of P and V?

a) 4060 b) 3860 c) 4260 d) 4440

Answer : a) 4060.

Reason :

In case the average of the given seven consecutive numbers is 64, logically it should be equal to the number exactly equidistant from both ends which is S.

(For example consider 2,4,6,8,10,12,14. In this case average is 2+4+6+8+10+12+14/7 = 56/7 = 8. This is nothing but the middle number 8 which is fourth in position from both the ends. Note: This method of finding average can be applied to any consecutive even number series when the number of terms is an odd number.)

Therefore S = 64.

If S is 64, then P must be 58 and V is 70. Product of 58 and 70 is 4060.

Question 2

If the numerator of a fraction is increased by 200% and the denominator is increased by 250% the resultant fraction is 3/14. What is the original fraction?

a) 1/2 b) 3/4 c) 1/4 d) 1/8

Answer : c) 1/4

Reason :

Let P and Q be the original numerator and denominator respectively.

P when increased by 200% becomes, P + P(200/100) = P (100 + 200)/100 = 300P/100

Q when increased by 250% becomes, Q + Q(250/100) = Q (100 + 250)/100 = 350Q/100

According to the question, (300P/100) / (350Q/100) = 3/14

Or 300P/350Q = 3/14

Or P/Q = (3/14) x (350/300) = 25/100 = 1/4

Question 3

How many number in between 1 and 100 are there each of which is not only exactly divisible by 4 but does not have 4 as a digit?

a) 18 b) 17 c) 7 `d) 20

Answer : b) 17.

Reason :

100 divided by 4 will give us 25. This not only means 4 times 25 is 100, but also means that there can be 25 numbers divisible by 4 from 1 to 100. Since the question is about numbers in between 1 and 100, 100 is to be excluded. So we have 24 numbers falling between 1 and 100 divisible by four. The question is the number should be divisible by 4 but it should not have 4 as a digit. Numbers fulfilling this condition are: 8,12,16,20,28,31,36,52,56,60,68,72,76,80,88,92,96.

Question 4

If the remainder obtained by subtracting a number from its own square is 6 times the number, what is the number?

a)4 b) 3 c) 6 d) 7

Answer : d) 7

Reason :

This is a very simple question. Solution is as follows.

Remainder obtained by subtracting the number from its own square is 6 times the number.

That means X² - X = 6 X

X² = 7 X.

X = 7

Question 5

Three-fourth of a number is equal to 60% of another number and the difference between the two numbers is 20. What is the sum of the two numbers?

a) 220 b) 180 c) 170 d) 320

Answer : b) 180.

Solution :

This is another simple question dealing with algebraic equations. Solution is as follows.

Let the numbers be X and Y.

3/4 X = 60/100 Y = 3/5Y

3/5 Y = 3/4 X

12Y = 15X

12Y - 15 X = 0 ----(i)

But from the question, Y- X = 20. Multiplying LHS and RHS by 12 we get,
12Y – 12 X = 240 ---- (ii)

Simplifying both the equations, 12Y-15 X -12Y+12X = 0-240

-3X = -240

X = 80 & Y = 80 + 20 = 100

Sum of the two numbers = 80 + 100 = 180