SIM - MULTIPLICATION - 4

In this post, we will learn to multiply two numbers whose ending digit is 5 and the sum of the other digits of both numbers is an odd number. For example,

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1) 25 * 75 (Both the numbers end in 5 and the sum of the other digits of the numbers is an odd number, that is, (2 + 7) = 9)

2) 45 * 95 (Ends in 5 & (4 + 9) = 13)

3) 85 * 115 (Ends in 5 & (8 + 11) = 19)

4) 135 * 165 (Ends in 5 & (13 + 16) = 29)

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Let us consider the first example and see the steps for the actual multiplication.

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1) 25 * 75

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a) The answer has two parts LHS and RHS.

b) The answer looks like LHS/RHS.

c) The value of RHS is always 75. That is, RHS = 75.

d) To arrive at the value of the LHS, first we need to multiply the other digits of the numbers besides the ending digit 5. That is, in this case, it is 2 * 7 = 14.

e) Next, we have to halve the sum of those two numbers and take the integer part of the answer. That is, (2+7)/2 = 9/2 = 4.5 = 4.

f) Add the numbers obtained in step (d) & (e). That is, 14 + 4 = 18.

g) The final answer is LHS/RHS = 18/75 = 1875.

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Solved Examples

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2) 45 * 95

= ((4*9)+((4+9)/2))/75

= (36+(13/2))/75

= (36+6)/75

= 42/75

= 4275

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3) 85 * 115

= ((8*11)+((8+11)/2))/75

= (88+(19/2))/75

= (88+9)/75

= 97/75

= 9775

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4) 135 * 165

= ((13*16)+((13+16)/2))/75

= (208+(29/2))/75

= (208+14)/75

= 222/75

= 22275

SIM - MULTIPLICATION - 3

In this post, we will see how to multiply two numbers which end in 5 and the other digits of the two numbers when added gives rise to an even number. For example, the following will make it more clearer.

1) 15 * 55 (Both the numbers end in 5, and the sum of other digits of both the numbers gives rise to an even number, that is, 1 + 5 = 6)

2) 35 * 75 (Ends in 5 & (3 + 7) = 10)

3) 45 * 85 (Ends in 5 & (4 + 8) = 12)

4) 65 * 125 (Ends in 5 & (6 + 12) = 18)

5) 95 * 155 (Ends in 5 & (9 + 15) = 24)

6) 135 * 195 (Ends in 5 & (13 + 19) = 32)

Now, we will take one example and see the steps to follow in order to find the product of those numbers. Let us remember this method works fine for any digit numbers and not restrained only to 2 digit numbers.

1) 15 * 55

a) There are two parts for the answer. They are LHS & RHS.

b) The final answer looks like LHS/RHS.

c) The RHS is always 25. So, RHS = 25.

d) To get the value of the LHS, first multiply the other digits of the number.

That is, 1 * 5 = 5.

e) Next, find half of the sum of the other digits of the numbers.

That is, ((1+5)/2) = (6/2) = 3.

f) Add the numbers obtained in steps (d) & (e).

That is, 5 + 3 = 8.

g) The final answer is LHS/RHS = 8/25 = 825

Solved Examples

2) 35 * 75 = ((3*7)+((3+7)/2))/25 = (21+(10/2))/25 = (21+5)/25 = 26/25 = 2625
3) 45 * 85 = ((4*8)+((4+8)/2))/25 = (32+(12/2))/25 = (32+6)/25 = 38/25 = 3825
4) 65 * 125 = ((6*12)+((6+12)/2))/25 = (72+(18/2))/25 = (72+9)/25 = 81/25 = 8125
5) 95 * 155 = ((9*15)+((9+15)/2))/25 = (135+(24/2))/25 = (135+12)/25 = 14725
6) 135 * 195 = ((13*19)+((13+19)/2))/25 = (247+(32/2))/25 = (247+16)/25 = 26325

SIM - MULTIPLICATION - 2

This shortcut will teach us to multiply two 2 digit numbers whose tens digit add up to 10 and the units digit is same. For example, the following will make things clear for us.

(1) 16 * 96

(2) 27 * 87

(3) 34 * 74

(4) 42 * 62

Suppose we consider the first example, where the tens digit of the given numbers are 1 and 9 which add up to 10 and the units digit of the given numbers are same which is 6. The vedic method of multiplying the numbers is as follows:

(1) 16 * 96

(a) The answer has two parts LHS and RHS.

(b) The answer will look like LHS/RHS.

(c) To get the value of the RHS, multiply the units digit of the two given numbers. Here, it is, RHS = 6 * 6 = 36.

(d) To get the value of the LHS, multiply the tens digit of the two given numbers and then add the value of the tens digit to the product obtained. Here, it is,

LHS = (1 * 9) + 6 = 9 + 6 = 15

(e) The answer is = LHS/RHS = 15/36 = 1536.

SIM - MULTIPLICATION - 1

This is my first posting on shortcuts in maths (SIM). In this post, we will see how to multiply two 2 digit numbers whose units digit add up to 10 and the tens digit are same. For example,

(1) 62 * 68
(2) 34 * 36
(3) 71 * 79
(4) 23 * 27

In all the above examples, you can observe that the units digit add to 10 and the tens digit are the same. Now, we all know the classic method of doing this since childhood. But, how do we do this in the vedic method. The process is as follows:

(1) 62 * 68

(a) There are two parts to the answer, which we call the LHS and the RHS.
(b) So, our answer looks like LHS/RHS.
(c) To get the RHS, multiply the units digit of the given numbers.
Here, it is, RHS = 2 * 8 = 16
(d) To get the LHS, multiply the tens digit of the given number by one more than it. Here, it is, LHS = 6 * (6 + 1) = 6 * 7 = 42.
(e) The final answer as above is LHS/RHS = 42/16 = 4216

CURRICULUM FOR ENGLISH

This can also be called as Verbal Reasoning. This is one of the most important area in the aptitude tests and is becoming tougher day by day. The following are some of the types of questions generally asked.

Verbal Reasoning

• Spotting the errors
• Fill in the blanks
• Synonyms
• Antonyms
• One word substitution
• Improvement of sentences
• Ordering of sentences
• Rearrangement of sentences
• Spelling
• Idioms & Phrases
• Active & Passive voices
• Cloze type passages
• Reading Comprehension

CURRICULUM FOR REASONING

Reasoning in aptitude tests can be divided into four categories. This classification is based on my research and personal bias.

1) Analytical Reasoning

• Linear Arrangement
• Complex Arrangement
• Comparison of Ranks
• Blood Relations
• Family Tree
• Conditions & Grouping
• Quantitative Analysis
• Miscellaneous

2) Logical Reasoning

• Syllogism
• Statement & Assumption
• Statement & Conclusion
• Passage & Conclusion
• Statement & Argument
• Statement & Course of action
• Punchline

3) Non Verbal Reasoning

• Series
• Coding-Decoding
• Repeating series
• Odd one out
• Mathematical systems
• Cubes
• Analogy

CURRICULUM FOR APTITUDE

As promised in my previous post, this post talks about the content to be followed for any aptitude test conducted in India and abroad. The following content is with respect to mathematical aptitude.

1) SIM (Shortcuts In Maths)

• Addition
• Subtraction
• Multiplication
• Division
• Squares
• Square Roots
• Cubes
• Cube Roots

2) Algebra

• Surds
• Indices
• Logarithms
• Expressions
• Polynomials
• Progressions
• Equations
• Set Theory
• Functions
• Graphs

3) Arithmetic

• Numbers & Systems
• Decimals & Fractions
• Simplifications & Approximations
• Percentages & Averages
• ProfitLoss & Partnerships
• Ratios & Proportions
• Mixtures & Alligations
• Time & Distance
• Trains & Tracks
• Boats & Streams
• Races & Games
• Time & Work
• Work & Wages
• Pipes & Cisterns
• Ages & Eras
• Clocks & Calendars

4) Banking

• Simple Interest
• Compound Interest
• Bankers Discount
• True Discount
• Annuties
• Stocks

5) Trigonometry

• Heights
• Distances
• T-Ratios
• Identities
• Inequalities

6) Mensuration

• Two dimensional figures
• Perimeters
• Areas
• Three dimensional figures
• Surface areas
• Volumes

7) Geometry

• Points & Locus
• Lines & Angles
• Circles & Arcs
• Triangles & Types

8) Statistics

• Permutation
• Combination
• Probability
• Statistics

9) Datum

• Data Analysis
• Data Interpretation
• Data Sufficiency