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MATHEMATICAL OPERATION
Under this type of problem, usually mathematical symbol are EXAMPLE 3. Select correct combination of mathematical sign
converted into another form by either interchanging the symbol to replace ‘*’ sign to balance the equation.
or using different symbol in place of usual symbol and then 9 * 4 * 22 * 14
calculate the equation according to the given condition. (a) × = – (b) × – =
EXAMPLE 1. If ‘+’ stands for division, ‘×’ stands for addition, (c) = – × (d) – × =
Sol. (b) 9 * 4 * 22 * 14
‘–’ stands for multiplication, and ‘¸’ stands for subtraction, then
9 × 4 – 22 = 14
which of the following equation is correct?
(a) 36 × 6 + 7 ¸ 2 – 6 = 20 EXAMPLE 4. ® means is ‘bigger than’
(b) 36 + 6 – 3 × 5 ¸ 3 = 24 ® means is ‘smaller than’
(c) 36 ¸ 6 + 3 × 5 – 3 = 45 ® means is ‘equal to’
(d) 36 – 6 + 3 × 5 ¸ 3 = 74 × ® means ‘plus’
Sol. (d) 36 × 6 ¸ 3 + 5 – 3 = ® means ‘minus’
Þ 36 × 2 + 5 – 3 = 74
If a c and b× d c, then
EXAMPLE 2. If P denotes ‘+’, Q denotes ‘–’, R denotes ‘×’
(a) d a (b) a d
and S denotes ‘¸’ then, which of the following statement is correct?
(a) 16 R 12 P 49 S 7 Q 9 = 200 (c) b c (d) d a
(b) 32 S 8 R 9 = 160 Q 12 R 12 Sol. (d) a > c and b + d = c
(c) 8 R 8 P 8 S 8 Q = 57 Þ a > b + d and this is true only if, d < a.
(d) 36 R 4 S 8 Q 7 P 4 = 10 Þ d a
Sol. (c) 8 R 8 P 8 S 8 Q EXAMPLE 5. Given interchange : sign ‘+’ and ‘–’and numbers
=8×8+8¸8–8 5 and 8. Which of the following is correct?
8 (a) 82 – 35 + 55 = 2 (b) 82 – 35 + 55 = 102
=8×8+ –8
8 (c) 85 – 38 + 85 = 132 (d) 52 – 35 + 55 = 72
= 64 + 1 – 8 = 57 Sol. (a) 52 + 38 – 88 = 2

1. If ‘+’ means ‘–’ ‘–’ means ‘×’ ‘¸’ means ‘+’ and ‘×’ means ‘¸’, 4. If > = ¸, Ú = ×, < = +, Ù = –, + = <, × = =, – = >
then (a) 6 > 2 > 3 Ù 8 Ú 4 + 13 (b) 6 Ù 2 < 3 > 8 < 4 – 13
10 × 5 ¸ 3 – 2 + 3 = ? (c) 6 Ú 2 < 3 Ù 8 > 4 × 13 (d) 6 > 2 Ú 3 < 8 Ù 4 + 13
53 5. Find out the correct answer for the unsolved equation on
(a) 5 (b) 21 (c) (d) 18 the basis of the given equations.
3 If 6 * 5 = 91, 8 * 7 = 169, 10 * 7 = 211, then11 * 10 = ?
2. If ‘+’ means ‘¸’ , ‘–’ means ‘×’, ‘¸’ means ‘+’ and ‘×’ means (a) 331 (b) 993 (c) 678 (d) 845
‘–’, then 63 × 24 + 8 ¸ 4 + 2 – 3 = ? 6. If ‘–’ stands for division, ‘+’ for multiplication ‘¸’for
(a) 54 (b) 66 (c) 186 (d) 48 subtraction and ‘×’ for addition. Which one of the following
3. Which one of the following is correct? equation is correct?
6 * 4 * 9 * 15 (a) 6 ¸ 20 × 12 + 7 – 1 = 70 (b) 6 + 20 – 20 ¸ 7 × 1 = 62
(a) ×, = , – (b) ×, –, = (c) =, ×, – (d) –, ×, = (c) 6 – 20 ¸ 12 × 7 + 1 = 57 (d) 6 + 20 – 20 ¸ 7 – 1 = 38

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7. In an imaginary mathematical operation ‘+’ means 20. If ‘20 – 10’ means 200, ‘8 ÷ 4’ means 12, ‘6 × 2’ means 4 and
multiplication, ‘×’ means subtraction, ‘¸’means addition and ‘12 + 3’ means 4, then
‘–’ means division. All other rules in mathematical operation 100 – 10 × 1000 ÷ 1000 + 100 × 10 = ?
are the same as in the existing system. (a) 1090 (b) 0 (c) 1900 (d) 20
Which one of the following gives the result of 21. If ‘+’ means ‘×’ ; ‘–’ means ‘÷’ ; ‘ ×’ means ‘–’ and ‘÷’ means
175 – 25 ¸ 5 + 20 × 3 + 10 = ? ‘+’ then 9 + 8 ÷ 8 – 4 × 9 = ?
(a) 160 (b) 2370 (c) 7 7 (d) 240 (a) 26 (b) 17 (c) 65 (d) 11
8. If L stands for +, M stands for –, N stands for ×, P stands for 22. If ‘÷’ means ‘+’ ; ‘–’ means ‘×’ ; ‘+’ means ‘÷’ and ‘×’ means
¸, then 14 N 10 L 42 P 2 M 8 = ? ‘–’ then 20 ÷ 12 × 4 + 8 – 6 = ?
(a) 153 (b) 216 (c) 248 (d) 251
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9. It being given that: > denotes +, < denotes –, + denotes ¸, – (a) 8 (b) 29 (c) 32 (d) 26
denotes =, = denotes ‘less than’ and × denotes ‘greater 3
than’. Find which of the following is a correct statement. 23. If ® stands for ‘addition’ ¬ stands for ‘subtraction’ ­
(a) 3 + 2 > 4 = 9 + 3 < 2 (b) 3 > 2 > 4 = 18 + 3 < 1
stands for ‘division ; ¯ stands for’ multiplication' Z stands
(c) 3 > 2 < 4 × 8 + 4 < 2 (d) 3 + 2 < 4 × 9 + 3 < 3
10. If ‘–’ stand for addition, ‘+’ stands for subtraction, ‘÷’ stands for equal to' then which of the following alternatives is
for multiplication and ‘×’ stands for division, then which correct?
one of the following equations is correct? (a) 7 ¬ 43 ­ 6 ¯ 1 Z 4
(a) 25 × 5 ÷ 20 – 27 + 7 = 120 (b) 3 ¯ 6 ­ 2 ® 3 ¬ 6 Z 5
(b) 25 + 5 × 20 – 27 ÷ 7 = 128
(c) 25 + 5 – 20 + 27 × 7 = 95 (c) 5 ® 7 ¬ 3 ­ 2 Z 5
(d) 25 – 5 + 20 × 27 ÷ 7 = 100 (d) 2 ¯ 5 ¬ 6 ® 2 Z 6
11. If ‘×’ stands for ‘addition’, ‘<’ for substraction, + for division, 24. If ‘×’ Stands for ‘ addition’ ‘<’ for subtraction’ ‘+’ for division'
> for multiplication, – for ‘equal to’, ¸ for ‘greater than’ and > for multiplication’ ‘–’ for equal to’ ‘+’ for ‘ greater than’
‘=’ for ‘less than’, then state which of the following is true? and '=' for ' less than' state which of the following is true. ?
(a) 3 × 4 > 2 – 9 + 3 < 3 (b) 5 × 3 < 7 ¸ 8 + 4 × 1 (a) 3 × 4 > 2 – 9 + 3 < 3 (b) 5 × 3 < 7 ¸ 8 + 4 × 1
(c) 5 > 2 + 2 = 10 < 4 × 8 (d) 3 × 2 < 4 ¸ 16 > 2 + 4 (c) 5 > 2 + 2 = 10 < 4 × 8 (d) 3 × 2 < 4 ¸ 16 > 2 + 4
DIRECTIONS (Qs. 12 - 15): In an imaginary language, the digits 25. If ¸ means + – means ÷ × means – and + means × then
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are substituted by a, b, c, d, e, f, g, h, (36 x 4 ) - 8 x 4
i and j. And 10 is written as ba. =?
12. (cd + ef) × bc is equal to 4 + 8 x 2 + 16 + 1
(a) 684 (b) 816 (c) 916 (d) 1564 (a) 0 (b) 8 (c) 12 (d) 16
13. dc × f – (bf – d) × d is equal to 26. If × means +, – means × , ÷ means + and + means – then
(a) abb (b) abe (c) bce (d) bcf (3 – 15 ÷ 19) × 8 + 6 = ?
14. baf + fg – (ca × h/be) is equal to (a) – 1 (b) 2 (c) 4 (d) 8
(a) 141 (b) 145 (c) 151 (d) 161 27. If + means ¸ , – means ×, × means +, ¸ means –, then
15. baf ¸ bf × d is equal to 90 + 18 – 6 × 30 ¸ 4 = ?
(a) df (b) cb (c) be (d) d (a) 64 (b) 65 (c) 56 (d) 48
16. In the following question, some relationship have been 28. Given below are numbers in the first line and symbols in the
expressed through symbols which are second line. Numbers and symbols are code for each other.
× = greater than q = not less than Choose the correct code for given symbols.
÷ = less than b = not greater than 1 2 3 4 5 6 7 8 9
+ = equal to f = not equal to, + – × ¸ ¹ ­ ® b
then A q B × C implies Which number can be decoded from the following :
(a) B q C (b) A ÷ C (c) A f C (d) B b C
17. If the given interchanges namely : signs + and ÷ and ¹ ­ ×®
numbers 2 and 4 are made in signs and numbers, which one (a) 5 8 6 3 7 (b) 5 6 8 7 3
of the following four equations would be correct ? (c) 5 7 8 6 3 (d) 5 8 3 6 7
(a) 2 + 4 ÷ 3 = 3 (b) 4 + 2 ÷ 6 = 1.5 29. If '–' stands for '+', '+' stands for '×', '×' stands for '–' then
which one of the following is not correct ?
(c) 4 ÷ 2 + 3 = 4 (d) 2 + 4 ÷ 6 = 8.
(a) 22 + 7 – 3 × 9 = 148 (b) 33 × 5 – 10 + 20 = 228
18. If L denotes ×, M denotes ÷ , P denotes + and Q denotes
(c) 7 + 28 –3 × 52 = 127 (d) 44 – 9 + 6 × 11 = 87
–, than 8 P 36 M 6 Q 6 M 2 L 3 = ?
30. Some equations are solved on the basis of a certain system.
13 1 1 Find the correct answer for the unsolved equation on that
(a) (b) – (c) 14 (d) 5
6 6 2 basis.
19. If × stands for ‘addition’, < for ‘substraction’, + stands for 5 * 6 = 35, 8 * 44 = 28, 6 * 8 = ?
‘division’, > for ‘multiplication’, –, stands for ‘equal to’, (a) 46 (b) 34 (c) 23 (d) 38
¸ for ‘greater than’ and = stands for ‘less than’, state which 31. Select the correct combination of mathematical signs to
of the following is true ? replace * signs and to balance the following equation.
(a) 3 × 2 < 4 ¸ 16 > 2 + 4 (b) 5 > 2 + 2 = 10 < 4 × 2 12 * 3 * 4 = 6 * 8 * 8
(c) 3 × 4 > 2 – 9 + 3 < 3 (d) 5 × 3 < 7 ¸ 8 + 4 × 1
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(a) +, ×, –, × (b) ×, +, –, × replace the * sings and to balance the following equation :
(c) ×, +, ×, – (d) ×, –, ×, + (45*3*6)*6*15
32. Which of the following interchange of signs would the (a) + × ¸ = (b) + ¸ × =
equation correct ? (c) + × – = (d) ¸ × ¸ =
6 × 4+2=16 34. Select the correct combination of mathematical sings to
(a) + and ×, 2 & 4 (b) +and ×, 4 & 6 replace * sings and to balance the following equation :
(c) + and ×, 2 & 6 (d) +and ×, 3 & 4 8 *5 * 10 * 2 * 25
33. Select the correct combination of mathematical sings to (a) + × ¸ = (b) + ¸ – =
(c) × + = × (d) × – = ×

ANSWER KEY
1 (a) 6 (a) 11 (c) 16 (a) 21 (c) 26 (b) 31 (c)
2 (b) 7 (c) 12 (b) 17 (d) 22 (b) 27 (c) 32 (b)
3 (b) 8 (a) 13 (c) 18 (d) 23 (d) 28 (a) 33 (d)
4 (c) 9 (c) 14 (c) 19 (b) 24 (c) 29 (c) 34 (c)
5 (a) 10 (a) 15 (b) 20 (b) 25 (a) 30 (a)

HINTS & SOLUTIONS

+Þ – – Þ´ 7. (c) + Þ ´, ´ Þ –
1. (a) ¸Þ + ´Þ¸ ¸ Þ +, – Þ ¸
10 × 5 ¸ 3 – 2 + 3 = ? Given expression ® 175 – 25 ¸ 5 + 20 × 3 + 10
or, ? = 10 ¸ 5 + 3 × 2 – 3 After conversion Þ 175 ¸ 25 + 5 × 20 – 3 × 10
or, ?= 2+6–3 =5 = 7 + 100 – 30
= 77
+Þ ¸ – Þ´ 8. (a) Using the proper signs, we get
2. (b)
¸Þ+ ´Þ – Given expression = 14 × 10 + 42 ¸ 2 – 8
= 140 + 21 – 8
63 × 24 + 8 ¸ 4 + 2 – 3 = ?
= 153
or, ? = 63 – 24 ¸ 8 + 4 ¸ 2 × 3
9. (c) Using proper notations, we have:
or, ? = 63 – 3 + 2 × 3
or, ? = 66 11
(a) Given statement is 3 ¸ 2 + 4 < 9 ¸ 3 – 2 or < 1 not true
3. (b) 6 × 4 – 9 = 15 2
4. (c) (b) 3 + 2 + 4 < 18 ¸ 3 – 1 or 9 < 5, which is not true.
>Þ ¸ ÚÞ´ <Þ + -Þ> (c) 3 + 2 – 4 > 8 ¸ 4 – 2 or 1 > 0, which is true
ÙÞ- + Þ< ´ Þ<
5
6 × 2 + 3 – 8 ¸ 4 = 13 (d) 3 ¸ 2 – 4 > 9 ¸ 3 – 3 or - > 0, which is not true.
2
6 × 2 + 3 – 2 = 13
10. (a) Solve by options, we can check all the options one by
12 + 3 – 2 = 13
one.
15 – 2 = 13
25 ¸ 5 × 20 + 27 – 7 Þ 5 × 20 + 27 – 7 Þ 100 + 27 – 7
5. (a) 6 × 5 = 30, 30 × 3 + 1 = 91, 8 × 7 = 56, 56 × 3 + 1 =
120 = 120
169, 10 × 7 = 70, 70 × 3 + 1 = 211
11. (c) Using the proper notations in (c), we get the statement
Similarly 11 × 10 = 110, 110 × 3 + 1 = 331
as:-
6. (a) – Þ ¸, + Þ ´ 5 × 2 ¸ 2 < 10 – 4 + 8
or, 5 × 1 < 18 – 4
¸ Þ –, ´ Þ +
or 5 < 12 ® which is true.
Option (a) : 6 ¸ 20 × 12 + 7 – 1 = 70 12. (b) Using the correct symbols, we have
L.H.S. = 6 – 20 + 12 × 7 ¸ 1 Given expression = (23 + 45) × 12 = 68 × 12 = 816.
= 6 – 20 + 84 13. (c) Given expression = 32 × 5 – (15 – 3) × 3
= 90 – 20 = 70 R. H.S. = 160 – 12 × 3
= 160 – 36 = 124 = bce

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14. (c) Given expression = 105 + 56 – (20 × 7/14) 29. (c) By options –
= 105 + 56 – 10 (a) 22 × 7 + 3 – 9 = 148
= 151 154 + 3 – 9
15. (b) Given expression = 105 ¸ 15 × 3 157 – 9 = 148 (correct)
= 7 × 3 = 21 = cb (b) 33 – 5 + 10 × 20 = 228
16. (a) A q B × C 33 – 5 + 200
AqB;B×C 200 + 33 – 5
\ A³ B; B> C 233 – 5 = 228 (correct)
Hence, option (a) implies the given equation. (c) 7 × 28 + 3 – 52 = 127
17. (d) Interchanging (+ and ÷) and (2 and 4), we get :
196 + 3 – 52
(1) 4 ÷ 2 + 3 = 3 or 5 = 3, which is false
199 – 52 = 147 (incorrect)
(2) 2 ÷ 4 + 6 = 1.5 or 6.5 = 1.5, which is false.
(d) 44 + 9 × 6 – 11 = 87
10 44 + 54 – 11
(3) 2 + 4 ÷ 3 = 4 or = 4, which is false.
3 98 – 11 = 87 (correct)
(4) 4 ÷ 2 + 6 = 8 or 8 = 8, which is true. 5 * 6/2 = 3 5
18. (d) Using the correct symbols, we have: 30. (a)
Given expression = 8 + 36 ÷ 6 – 6 ÷ 2 × 3
8 * 4/2 = 2 8
=8+6–3×3=5
19. (b) Using the proper notations in (2), we get the statement
as 5 × 2 ÷ 2 < 10 – 4 + 2 or 5 < 8 , which is true. 6 * 8/2 = 4 6
20. (b) Since, 20 × 10 = 200, therefore, – means ×
8 + 4 = 12, therefore, ÷ means +. 31. (c) By options,
6 – 2 = 4, therefore, × means – . (a) 12 + 3 × 4 = 6 – 8 × 8
and 12 ÷ 3 = 4, therefore, + means ÷. 12 + 12 = 6 – 64
Now, given expression 24 = 58 (incorrect)
= 100 × 10 – 1000 + 1000 ÷ 100 – 10 Q 58 > 24
= 100 0 – 1000 + 10 – 10 = 0 (b) 12 × 3 + 4 = 6 – 8 × 8
21. (c) 9 × 8 + 8 ÷ 4 – 9 = 65 36 + 4 = 6 – 64
22. (b) 20 + 12 – 4 ÷ 8 × 6 = 29 40 = 58 (incorrect)
23. (d) Using the proper notations in (4) we get the statement Q 58 > 48
as 2 × 5 – 6 + 2 = 6 or 10 – 6 + 2 = 6 or 6 = 6, which is (c) 12 × 3 + 4 = 6 × 8 – 8
true.
36 + 4 = 48 – 8
24. (c) Using the proper notations in (3), we get the statement
40 = 40 (correct)
as 5 × 2 ¸ 2 < 10 – 4 + 8 or 5 × 1 < 18 – 4 or 5 < 14,
(d) 12 × 3 – 4 = 6 × 8 + 8
which is true.
25. (a) Using the correct symbols, we have 36 – 4 = 48 + 8
Given expression 32 = 56 (incorrect)
Q 56 > 32
( 36 - 4) ¸ 8 - 4 32 ¸ 8 - 4 4 - 4 32. (b) 4 + 6 ´ 2 = 16
= = = = 0.
4 ´ 8 - 2 ´ 16 + 1 32 - 32 + 1 0 +1 33. (d) (45 ¸ 3 × 6) ¸ 6 = 15
26. (b) Using the correct symbols, we have 34. (c) 8 × 5 + 10 = 2 × 25
Given expression = (3 × 15 + 19) ÷ 8 – 6 50 = 50
= 64 ÷ 8 – 6 = 8 – 6 = 2.
27. (c) 90 ¸ 18 × 6 + 30 – 4 = 56
28. (a) # ­ ´ ®
­ ­ ­ ­ ­
Decoded as ® 5 8 6 3 7

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