1.
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General
Mental Ability
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First we should know some mathematical operations. They are add (+), subtraction
(–), multiply (×) and division (÷), greater than (>), less than (<). This test is set up to
test candidates skill in mathematical operations. The questions involving these
operations are set using artificial symbols. You are required to substitute the real
signs and solve the questions accordingly, to get the answer.
Different Type of Questions
There are three types of questions based on mathematical operations which are
asked in various competitive examinations. They are,
Problem-Solving by Substitution
In such type of questions you have some substitutes for various mathematical
symbols or numerals followed by a question involving calculation of an expression
or choosing the correct/incorrect equation.
Arithmetical Reasoning
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Rule BODMAS
Brackets
Of
Division
Multiplication
Addition
Subtraction
While solving a mathematical operations proceed according to the
BODMAS formula.
Example 1: If ‘+’ means ‘minus’ ‘×’ means ‘divided by’ ‘÷’ means ‘plus’ and ‘–
’means ‘multiplied by’ then which of the following will be the value of
expression 7 × 3.5 ÷ 2 – 4 + 5 ?
(a) 4 (b) 5
(c) 11 (d) None of these
Solution.
(b) Using the proper notations in the given expression, we have
= 7 × 3.5 ÷ 2 – 4 + 5 = 7 + 3.5 + 2 ÷ 4 – 5
= 2 + 2 × 4 – 5 = 2 + 8 – 5 = 10 – 5 = 5
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Example 2: If × means +, + means ÷, – means × and ÷ means –, then 6 × 4 – 5
+ 2 ÷ 1 =?
(a) 10 (b) 11
(c) 12 (d) 15
Solution.
(d) Using the proper notations in the given expression, we have
6 × 4 – 5 + 2 ÷ 1 = 6 + 4 × 5 ÷ 2 – 1
= 6 + 4 × 2.5 – 1
= 6 + 10 – 1
= 16 – 1 = 15
Example 3: If P denotes ‘multiplied by’ T denotes ‘subtracted from, M
denotes ‘added to’ and B denotes ‘divided by’, then
12 P 6 M 15 T 16 B 4
(a) 70 (b) 83
(c) 75 (d) 110
(e) None of these
Solution.
(b) 12 P 6 M 15 T 16 B 4
= 12 × 6 + 15 – 16 ÷ 4 = 12 × 6 + 15 – 4
= 72 + 15 – 4 = 87 – 4 = 83
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Interchanging of Signs and Numbers
This type of question certain signs or numbers interchanging with each other. The
candidate is required to change the given signs or change the given numbers with
each other and select which of the equation is correct of the given alternatives.
Example 4: If signs + and –and numbers 4 and 8 interchanges with each
other, which one of the following four equations would be correct?
(a) 4 – 8 + 12 = 0 (b) 8 – 4 ÷ 12 = 8
(c) 4 ÷ 8 – 12 = 16 (d) 8 ÷ 4 – 12 = 24
Solution.
(a) On interchanging signs + and – and numbers 4 and 8 in equation (a)
8 + 4 – 12 = 0
12 – 12 = 0
0 = 0
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Example 5: Which one of the four interchanges in signs and number would
make the given equation correct?
6 × 4 + 2 = 16
(a) + and ×, 2 and 4 (b) + and ×, 4 and 6
(c) + and ×, 2 and 6 (d) None of the above
Solution.
(b) On interchanging signs + and × and 4 and 6,
4 + 6 × 2 = 4 +12 = 16
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