Answers # 6 to 10

question:6=> AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?

(A) 1

(B)3

(C) 7

(D) 9

(E) Cannot be determined
Ans: AB + CD = AAA

Since AB and CD are two digit numbers, then AAA must be 111

case even if ab and cd are the biggest numbers possible even than 96 + 87 = 183.

Therefore 1B + CD = 111

THATS WHY C=9, FOR ALL VALUES OF B.

PROOF: B can assume any value between 3 and 9

If B = 3, then CD = 111-13 = 98 and C = 9

If B = 9, then CD = 111-19 = 92 and C = 9

So for all B between 3 & 9, C = 9

Therefore the correct answer is D (C = 9)

QUESTION:7

1. A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?

(A) 1/4

(B) 1/3

(C) 1/2

(D) 2/3

(E) ¾
Ans: Let X be the fraction of solution that is replaced.

Then X*25% + (1-X)*40% = 35%

Solving, you get X = 1/3

QUESTION:8

A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27

(B) 1/9

(C) 1/3

(D) 4/27

(E) 2/9

Ans:

Case I: Red ball first and then white ball P1 = 3/9*2/9= 2/27

Case 2: White ball first and then red ballP2 = 2/9*3/9 = 2/27

Therefore total probability: p1 + p2 = 4/27

QUESTION:9

What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?

A) 1.4

B) sqrt(2)

C) 1.7

D) sqrt(3)

E) 2.0

Ans:

The equation of the line will be 3x - 4y - 12 = 0.

This crosses the x and y axis at (0,-3) and (4,0)

The circle has the origin at the center and has a radius of 1 unit.

So it is closest to the given line when, a perpendicular is drawn to the line, which passes through the origin.This distance of the line from the origin is 12 / sqrt (9 + 16) which is 2.4
[Length of perpendicular from origin to line ax +by + c = 0 ismod (c / sqrt (a^2 + b^2))]
The radius is 1 unit.

So the shortest distance is 2.4 - 1 unit = 1.4 units

QUESTION:10

In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7

ANSWER:

Since 12w=3x=4y,

w:x=3:12=1:4 and x:y=4:3

so, w = 1x = 4y = 3

the fractional part of the square is shaded:

{(w+x)^2 - [(1/2)wx + (1/2)wx +(1/2)xy + (1/2)w(2w)]}/(w+x)^2

= {(w+x)^2 - [wx + (1/2)xy + w^2)]}/[(w+x)^2]=[(5^2) -(4+6+1)]/(5^2)

= (25 - 11)/25

= 14/25.

Question # 10

In the square above, 12w = 3x = 4y. What fractional part of the square is shaded?

A) 2/3

B) 14/25

C) 5/9

D) 11/25

E) 3/7

INTRODUCTION OF VEDIC MATHEMATICS

• WHAT IS VEDIC MATHEMATICS?

It is an ancient technique, which simplifies multiplication, divisibility,squaring, cubing, square and cube roots.

Even recurring decimals and auxiliary fractions can be handled by Vedic mathematics. Vedic Mathematics forms part of Jyotish Shastra which is one of the six parts of Vedangas. The Jyotish Shastra or Astronomy is made up of three parts called Skandas. A Skanda means the big branch of a tree shooting out of the trunk.

AND THE BEST PART IS - you dont even need a calculator for this purpose.

• What is the basis of Vedic Mathematics?

The basis of Vedic mathematics, are the 16 sutras, which attribute a set of qualities to a
number or a group of numbers. The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras
(Phrases) and 120 words laid down simple steps for solving all mathematical problems in
easy to follow 2 or 3 steps.

Vedic Mental or one or two line methods can be used effectively for solving divisions, reciprocals, factorisation, HCF, squares and square roots, cubes and cube roots, algebraic
equations, multiple simultaneous equations, quadratic equations, cubic equations, biquadratic
equations, higher degree equations, differential calculus, Partial fractions,Integrations, Pythogorus theoram, Apollonius Theoram, Analytical Conics and so on.