Mathematical operations

The basic approach for the problems of this type is more or less similar to that of coding and decoding. One has to study the symbols or the geometrical figures and their meanings carefully. Then, the meanings are to be used in place of those symbols in answering the questions.

The questions can be categorised into two types Symbols and Notations

Symbols for these types of questions stand for mathematical operations like +, –, ×, ÷, > , <, ³, £, = and #. So, the studentsmust replace the symbols by mathematical operations and apply the BODMAS’ rule to find the value of the given expression. Other symbols which can be used are DÑ, *, @, $, etc, with proper definitions. Some examples are given below

Example 1: If ‘+’ means ‘–’, ‘–’ means ‘×’, ‘×’ means and ‘means’ ‘÷’, and ‘÷’ mean ‘+’ then 15 × 3 ÷ 15 + 5 – 2 = ?
(a) 0 (b) 10
(c) 20 (d) 6

Solution. (b): 15 × 3 = 15 + 5 – 2 after changing the signs = 15 = 3 + 15 – 5 × 2 = 5 + 15 – 10 =10

Example 2: If 2 * 3 = 12, 3 * 4 = 20 and 4 * 5 = 30, then 2 * 6 is
(a) 18 (b) 12
(c) 21 (d) None of these

Solution. (c) The numbers on both sides of * are increased by one and then multiplied to get the answer. 2*6 = 3 × 7 = 21

Example 3: If x $ y = (x + y + xy –1) (x + y + xy + 1), then the value of (4 $ 10) is.
(a) 2915 (b) 2195
(c) 2951 (d) 2955

Solution. (a) As per the definition of $, (4$10) would be (4 + 10 + 4 × 10 - 1) (4 + 10 + 4 × 10 + 1) = 2915. So, answer is (a)

Example 4: If * means “is greater than”, @ means `is less then’; and $ means “is equal to” and if a $ b and b @ c, then
(a) c * b (b) b * c
(c) c * a (d) Both (a) and (c)

Solution. (d) Replace the symbols with the meaning given against them. If a $ b and b @ c would become a = b and b < c, then c > b or c > a ie, c * b, c * a are true from the given options.

Geometrical Figures

These figures will be divided and subdivided into a number of parts, each part is filled with a number or a letter except one part. The numbers or the letters in the figures follow certain pattern. The objective is to identify the pattern and find the missing number or letter. The problems based on geometrical figures are of various types.