Olympiad Verbal - Mathematical Reasoning
Exam Duration: 45 Mins Total Questions : 30
Find the number which replaces the "?",
- (a)
75
- (b)
26
- (c)
25
- (d)
20
In the first figure, 22 + 42 = 20.
In the second figure, 32 + 92 = 9 + 81 = 90.
\(\therefore\) Similarly, in the third figure, 12 + 52 = 26. So, the answer is (8).
Find the number which replaces the "?",
1 | 4 | 9 | ? |
1 | 2 | 3 | 4 |
2 | 4 | 6 | ? |
- (a)
16, 8
- (b)
49, 7
- (c)
36, 4
- (d)
25, 5
Numbers in the first row = (squares of respective numbers of the second row) 12, 22, 32, 42.
Numbers in the third row = (2 X respective numbers of the second row) = 2, 4, 6, 8.
\(\therefore\) The missing numbers = 16, 8.
Find the number which replaces the "?",
1 | \({1\over 2}\) | \({3\over 2}\) |
2 | \({2\over 3}\) | \({8\over 3}\) |
3 | ? | \({19\over 5}\) |
- (a)
\({1\over 2}\)
- (b)
\({2\over 3}\)
- (c)
\({3\over 4}\)
- (d)
\({4\over 5}\)
From 1st row, \(1+{1\over 2}={3\over2}\)
From 2nd row, \(2+{2\over 3}={8\over 3}\)
\(\therefore\) In 3rd row, \(3+?={19\over5}\)
\(\therefore\) The missing number \(={19\over 5}-3={4\over 5}.\)
Find the number which replaces the "?",
- (a)
16
- (b)
9
- (c)
85
- (d)
112
From the figure, (1)2 + (2)2 = 5
(5)2 + (4)2 = 41
(6)2 + (7)2 = 85
Hence, the number which replaces the question mark is 85.
If P denotes \(\div\) , Q denotes X R denotes + and S denotes - then find the value of 18Q 12P 4R 5 5 6 when simplified
- (a)
36
- (b)
53
- (c)
59
- (d)
65
Using correct symbols, we have
Given expression = 18 X 2 \(\div\) 4 + 5 - 6
= 18 X 3 + 5 - 6 = 54 + 5 - 6 = 53.
So, the answer is option (B).
If x denotes 'greater than', \(\phi\) denotes 'equal to', < denotes 'not less than', \(\bot\) denotes 'not equal to', \(\triangle\) denotes 'less than' and + denotes 'not greater than', then choose the correct statement for the statement a x b \(\triangle\) c.
- (a)
a \(\phi\) c \(\triangle \) b
- (b)
b < a X c
- (c)
a < b + c
- (d)
c + b < a
Using the usual notations, we have:
(A) The statement a > b < c \(\Rightarrow\) a = c < b, which is false.
(B) The statement a > b < c \(\Rightarrow\) b \(\nless\). a \(\ngtr\) c, which is false.
(C) The statement a > b < c \(\Rightarrow\) a \(\nless\). b \(\ngtr\) c, which is true.
(D) The statement a > b < c \(\Rightarrow\) c \(\ngtr\) b \(\nless\). c, which is false.
Hence, the statement in option (C) is true.
So, the answer is option (C).
If 7 * 1 = 64; and 3 * 9 = 144, then what is the value of 5 * 6?
- (a)
22
- (b)
55
- (c)
66
- (d)
121
Rule is a * b = ( a + b )2
\(\therefore\) 5 * 6 = ( 5 + 6 )2 = 121
Find the number which replaces the "?',
If 84 \(\oplus\) 72 = 45; 63 \(\oplus\) 41 = 33; then 94 \(\oplus\) 82 = ?
- (a)
45
- (b)
59
- (c)
56
- (d)
65
The rule is to write the differences of the digits of the two numbers side by side.
84 \(\oplus\) 72 = ( 8 - 4 )( 7 - 2 ) = 45
63 \(\oplus\) 41 = ( 6 - 3 ) ( 4 - 1 ) = 33
\(\therefore\) 94 \(\oplus\) 82 = ( 9 - 4 ) (8 - 2 ) = 56
If A means -, B means \(\div\) . C means + and D means x , then, 15 B 3 C 24 A 12 D = ?
- (a)
34
- (b)
2
- (c)
\({5\over 9}\)
- (d)
5
Given expression = 15 \(\div\) 3 + 24 - 12 x 2
= 5 + 24 - 24 = 5
Identify the rule and find the missing number in place of the question mark.
13 | 4 | 165 |
3 | 2 | 7 |
? | 11 | 14 |
- (a)
25
- (b)
7
- (c)
5
- (d)
2
(165 + 4)1/2 = 13; (7 + 2)1/2= 3; (11 + 14)1/2 = 5.
Identify the rule and find the missing number in place of the question mark.
21 | 56 | 70 |
45 | 87 | 84 |
115 | 180 | ? |
- (a)
130
- (b)
195
- (c)
295
- (d)
150
The rule is that in each row, the difference of first two numbers is doubled i.e., (56 - 21) x 2 = 70. Hence the required number is (180 - 115) x 2 = 130.
Identify the rule and find the missing number in place of the question mark.
256 | 128 | 32 |
112 | 56 | 14 |
800 | 400 | ? |
- (a)
200
- (b)
100
- (c)
25
- (d)
50
In a row, divide the first number by 2 and then by 4. thus
800 \(\div\) 2 = 400,
400 + 4= 100.
Identify the rule and find the missing number in place of the question mark.
5 | 11 | 96 |
9 | 13 | 88 |
8 | 17 | ? |
- (a)
225
- (b)
165
- (c)
185
- (d)
250
112 - 52 = 96, 132 - 92 = 88 Similarly 172 - 82 = 225
Identify the rule and find the missing number in place of the question mark.
9 | ? | 16 |
64 | 10 | 36 |
144 | 20 | 256 |
- (a)
20
- (b)
40
- (c)
5
- (d)
0
(144 + 256)1/2 = 20, (36 + 64)1/2 = 10,
(9 + 16)1/2 = 5.
Identify the rule and find the missing number in place of the question mark.
41 | 43 | 4 |
47 | 53 | 36 |
? | 61 | 4 |
- (a)
57
- (b)
59
- (c)
63
- (d)
67
The rule is \(43-\sqrt{4}=41,53-\sqrt{36}=47.\)
Identify the rule and find the missing number in place of the question mark.
5 | 11 | 96 |
3 | 6 | 69 |
8 | 17 | ? |
- (a)
225
- (b)
165
- (c)
185
- (d)
250
B - 5 = 3,17 -11 = 16 Similarly 96 + 69 = 165.
Identify the rule and find the missing number in place of the question mark.
6 | 15 | 35 |
77 | 143 | 221 |
323 | 427 | ? |
- (a)
657
- (b)
663
- (c)
667
- (d)
700
This is a series of numbers each number is obtained by multiplying the two successive prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.
The number required is 23 X 29 = 667.
Find the number which replaces the question mark.
- (a)
24
- (b)
25
- (c)
23
- (d)
31
\(\sqrt{36}+\sqrt{49}+\sqrt{64}+\sqrt{25}=26\)
\(\sqrt{9}+\sqrt{25}+\sqrt{16}+\sqrt{81}=21\)
Similarly \(\sqrt{25}+\sqrt{144}+\sqrt{36}+\sqrt{64}=31\)
Find the number which replaces the question mark.
- (a)
7
- (b)
9
- (c)
13
- (d)
15
\(\sqrt{7+5+9+4}=5\)
\(\sqrt{14+35+20+75}=12\)
Similarly \(\sqrt{9+45+45+65}=13\)
Identify the rule and find the missing number.
- (a)
11
- (b)
14
- (c)
10
- (d)
12
(10 - 12) + (15 - 9 ) = 4
(28 - 20) + (16 -12) = 12
(23 - 16) + (1 5 - 11) = 11
Which two signs are to be interchanged to make the equation below true?
3 - 9 X 27 + 9 \(\div\) 3 = 15
- (a)
+ and -
- (b)
X and +
- (c)
X and +
- (d)
- and +
If we interchange - and +, the equation changes into 3 + 9 X 27 + 9 - 3 = 9 + 9 - 3 = 18 - 3 = 15. Hence option (D) is the correct answer.
Which two signs are to be interchanged to make the equation below true?
5 X 15 \(\div\) 7 - 20 + 4 = 77
- (a)
- and \(\div\)
- (b)
x and \(\div\)
- (c)
+ and \(\div\)
- (d)
+ and x
If we interchange signs + and +. then the equation changes to 5 x 15 + 7 - 20 \(\div\) 4 = 75 + 7 - 5 = 77
Which two signs are to be interchanged to make the equation below true?
51 \(\div\) 3 x 12 - 6 + 3 = 11
- (a)
+ and \(\div\)
- (b)
- and +
- (c)
x and \(\div\)
- (d)
+ and x
If we interchange signs + and +. then the equation results
into 51 \(\div\) 3 + 12 - 6 X 3 =11
Hence, option (D) is the correct answer.
If '+' means 'x', '-' means '\(\div\)", '\(\div\)' means '+' and 'x' means '- then what will be the value of 16 \(\div\) 64 - 4 x 4 + 3?
- (a)
20
- (b)
15. 12
- (c)
52
- (d)
12
61 + 64 + 4 -4 x 3 = 16 + 16 - 12 = 20
If '+' means 'x', '-' means' \(\div\)' , 'x' means '-' and '+' means '\(\div\)', then what will be the value of 12 \(\div\) 48 - 8 x 4 + 4?
- (a)
8
- (b)
4
- (c)
2
- (d)
6
12 + 48 \(\div\) 8 - 4 X 4 = 12 +16 - 16 = 2
If the digits '4' and '8', signs '+' and '-' are interchanged, then which one of the four equations would be correct?
- (a)
4 + 8 - 12 = 16
- (b)
4 - 8 + 12 = 0
- (c)
8 + 4 -12 = 24
- (d)
8 - 4 + 12 = 8
On interchanging + and -, and 4 and 8 we get the equation 8 - 4 + 12 = 4 + 12 = 16 which is true.
If the signs '\(\div\)' and '+' and the digits '6' and '3' are interchanged, then which one of the four equations would be correct?
- (a)
3 + 6 \(\div\) 2 = 5
- (b)
6 \(\div\) 3 + 2 = 8
- (c)
3 + 6 \(\div\) 5 = 7
- (d)
3 \(\div\) 6 + 1 = 6
On interchanging -i- and + and 6 and 3 in (c), we get the, equation as 6 +3 + 5 = 7 or 2 + 5 = 7 which is true
If the signs '\(\div\)' and '+' and the digits '9' and '3' are interchanged, then which one of the four equations would be correct?
- (a)
3 + 9 \(\div\) 4 = 8
- (b)
3 \(\div\) 3 + 9 = 13
- (c)
3 + 9 \(\div\) 2 = 5
- (d)
3 + 9 \(\div\) 9 = 2
On interchanging \(\div\) and + numbers 9 and 3 in (c), we get the equation 9 \(\div\) 3 + 2 = 5 or 3 + 2 = 5 which is true.
If 15 x 20 x 60 = 20 x 60 x 15 and 21 x 42 x 63 = 42 x 63 x 21 then 19 x 17 x 41 = ?
- (a)
17 x 19 x 41
- (b)
17 x 41 x 19
- (c)
19 x 41 x 17
- (d)
41 x 19 x 17
In the given expression, middle number is written first, last number in the middle and first number is written in the last.
19 X 17 X 41 = 17 X 41 X 19
If 11 x 12 x 13 = 234, 24 x 23 x 35 = 658 , then 31 x 43 x 54 = ?
- (a)
497
- (b)
974
- (c)
749
- (d)
479
11 x 12 x 13 = (1 + 1) (1 + 2)(1 + 3) = 234
and 24 x 23 x 35 = (2 + 4)(2 + 3)(3 + 5) = 658
Similarly,
31 x 43 x 54 = (3 + 1)(4 + 3)(5 + 4) = 479.