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OTI365 - NTSE - X Standard
NTSE Mental Ability Test - Mathematical Operations Sample Questions with Answer

NTSE Mental Ability Test - Mathematical Operations

Exam Duration: 45 Mins Total Questions : 30

1 )

If $\times$ means +, - means $\div $, $\div $ means - and + means $\times$ then the value of the equation 25+9$\times$45-15 $\div $23 will be

(a)
205
(b)
262
(c)
203
(d)
227

Solution :

25 $\times$ 9 + 45 $\div$15 - 23 = 205

2 )

If $ means $\div$, # means $\times$, % means + and @ means - then the value of the equation 56%78 @ 55$ 11# 8 will be

(a)
94
(b)
86
(c)
104
(d)
82

Solution :

56 + 78 - 55$\div$11 $\times$ 8 = 94

3 )

If $ means $\div$ . # mean X, %means + and @ means - then which of the following equations will be correct

(a)
5 $ 20 @ 8 # 50 % 4 = -75
(b)
5 @ 20 # 8 $ 50 % 4 = -75
(c)
5 % 20 @ 8 # 50 $ 4 = -75
(d)
5 $ 20 @ 8 # 50 % 4 = 75

Solution :

5 + 20 - 8 $\times$ 50 $\div$4 = -75

4 )

5 $\div$ 4 $\times$ 2 + 3 -1 =12

(a)
$\times$ and $\div$
(b)
+ and -
(c)
$\div$ and -
(d)
$\times$ and +

Solution :

Interchanging and in the given equation we get
= 5 $\times$ 4 $\div$ 2 + 3-1
=5$\times$2+3-1
= 10 + 3 - 1
= 13 - 1 = 12

5 )

7 $\div$ 14 $\times$ 16 - 32 + 6 = 34

(a)
$\times$and +
(b)
+ and -
(c)
$\div$ and -
(d)
$\times$ and $\div$

Solution :

7 $\div$ 14$\times$16 + 32 - 6 = 34

6 )

220 + 110 - 11 $\times$ 2 $\div$ 4 = 236

(a)
$\times$and +
(b)
+ and -
(c)
$\div$ and -
(d)
$\times$ and $\div$

Solution :

220 + 110 $\div$11 $\times$ 2 - 4 = 236

7 )

169 $\div$ 13 $\times$ 6 - 4 + 5 = -1

(a)
$\times$and +
(b)
+ and -
(c)
$\div$ and -
(d)
$\times$ and $\div$

Solution :

169 $\div$ 13 + 6 - 4 $\times$5 = -1

8 )

Interchanges:
Signs: $\times$ and -
Numbers: 7 and 2

(a)
2 $\times$ 5 - 7 = 2
(b)
5 - 2 $\times$ 7 = 9
(c)
7 $\times$ 5 - 2 = 3
(d)
7 - 5 $\times$ 2 = 3

Solution :

2 $\times$ 5 - 7 = 3

9 )

Interchanges:
Signs: + and $\div$
Numbers: 7 and 9

(a)
3 + 9 $\div$ 7 = 10
(b)
9 $\div$ 7 + 3 = 10
(c)
9 + 7 $\div$ 3 = 10
(d)
7 + 9 $\div$ 3 = 10

Solution :

'7+ 9 $\div$ 3 = 10

10 )

Interchanges:
Signs: + and -
Numbers: 5 and 3

(a)
1 + 5 - 3 = 7
(b)
3 - 5 + 1 = 7
(c)
5 + 3 - 1 = 7
(d)
3 + 5 - 1 = 7

Solution :

5 + 3 - 1 = 7

11 )

If 4% 2 = 12,5% 3 = 16and 8 %6 = 28 then find the value of 9 %7

(a)
24
(b)
28
(c)
32
(d)
34

Solution :

Subtract square of 2^nd number from that of first, hence 9 % 7 = 81 49 = 32

12 )

If 4 # 6 = 40,8 # 9 = 136 and 7 # 5 = 84 then findthe value of4 # 9

(a)
22
(b)
42
(c)
32
(d)
52

Solution :

Rule is a # b = a² + ab , hence 4 # 9 = 4² + 4 $\times$ 9 = 52

13 )

If 24 72 = 32, 18 48 = 22 and 36 42 = 26 then find the value of 48 78

(a)
32
(b)
38
(c)
42
(d)
48

Solution :

The rule works as follows
48 78=$\frac{48+78}{3}$=42

14 )

If '+' means 'divided by', '-' means 'multiplied. 'x' means 'minus' and '7' means 'plus', which the following will be the value of the expressi 16 $\div$ 8 - 4 + 2 $\times$ 4 ?

(a)
16
(b)
28
(c)
32
(d)
44

Solution :

Putting the proper signs in the given expressi
we get:
16 + 8 x 4 $\div$ 2 - 4 = 16 + 16 - 4
= 32 - 4 = 28.
So, the answer is (b).

15 )

If + means $\div$, - means x, $\div$ means + and means -, then
36 x 12 + 4 $\div$ 6 + 2 - 3 = ?

(a)
2
(b)
18
(c)
42
(d)
$6\frac{1}{2}$

Solution :

Using the proper signs, we get:
36 - 12 $\div$ 4 + 6 $\div$ 2 x 3 = 36 - 3 + 3 x 3
= 36 - 3 + 9
= 45 - 3 = 42
So, the correct answer is (c).

16 )

It being given that: > denotes +, < denotes -, + denotes $\div$, - dentotes =, = denotes 'less than' and x denotes 'greater than', find which of the • following is a correct statement

(a)
3 + 2 > 4 = 9 + 3 < 2
(b)
3 > 2 > 4 = 18 + 3 < 1
(c)
3 > 2 < 4 x 8 + 4 < 2
(d)
3 + 2 < 4 x 9 + 3 < 3

Solution :

Using proper notations, we have :
(a) Given statement is 3 $\div$ 2 + 4 < 9 $\div$ 3 - 2
or $\frac{11}{2}<1$ which is not true.
(b) Given statement is 3 + 2 + 4 < 18 $\div$ 3 - 1
or 9 < 5, which is not true.
(c) Given statement is 3 + 2 - 4 > 8 $\div$ 4 - 2
or 1 > 0, which is true.
(d) Given statement is 3 + 2 - 4 > 9 $\div$ 3 -
or $-\frac{5}{2}>0$ which is not true.
So, the statement (c) is true.

17 )

It being given that x denotes 'greater than', $\phi$ denotes 'equal to', < denotes 'not less than',$\bot$ denotes 'not equal to', $\Delta$ denotes 'less than' and + denotes 'not greater than', choose the correct statement from the following: If a x b $\Delta$ c, it follows that

(a)
a $\phi$ c $\Delta$ b
(b)
b < a x c
(c)
a < b + c
(d)
b < a $\phi$ c

18 )

Which of the following two signs need to be interchanged to make the given equation correct?
10 + 10 $\div$ 10 - 10 x 10 = 10

(a)
+ and -
(b)
+ and $\div$
(c)
+ and x
(d)
$\div$ and +

Solution :

On interchanging + and <, we get the equation as
10 x 10 $\div$ 10 - 10 + 10 = 10
or 10 x 1 - 10 + 10 = 10
or 10 = 10, which is true.

19 )

$\frac { 50 }{ ? } =\frac { ? }{ 12 \frac { 1 }{ 2 } } $

(a)
25/2
(b)
4/25
(c)
25
(d)
5/25

20 )

$\frac { \sqrt{625} }{ ? } =\frac { ? }{ 16 } $

(a)
0.025
(b)
2.05
(c)
0.025
(d)
20.0

21 )

Find the correct inference according to given
premises and symbols:
A: Not greater than
B: Greater than
C: Not equal to
D: Equal to
E: Not less than
F: Less than
Premises: (RCm) and (RAm)

(a)
$\ell$Bm
(b)
$\ell$Dm
(c)
$\ell$Em
(d)
$\ell$Fm

22 )

It being given that D denotes 'equal to '; .. denotes 'not equal to '; + denotes 'greater than '; - denotes 'less than', x denotes 'not greater than '; -i- denotes 'not less than '. Choose the correct statement in each of the following questions:
a + b + c does not imply

(a)
b - a + c
(b)
c - b - a
(c)
c - a + b
(d)
b - a - c

23 )

The following questions, $\Delta$ means 'is greater than', % means 'is lesser than', means 'is equal to' = means 'is not equal to', + means 'is a little more than', x means 'is a little less than'. Choose the correct alternative in each of the following question.
If c % b and b x a, then

(a)
a $\Delta$ c
(b)
c a
(c)
b c
(d)
c $\Delta$ a

24 )

If x means +, $\div$ means -, - means x and + means $\div$, then: 8 x 7 - 8 + 40 $\div$ 2 = ?

(a)
1
(b)
$7\frac{2}{5}$
(c)
$8\frac{3}{5}$
(d)
44

Solution :

Using the correct symbols, we have:
Given expression:
= 8 + 7 x 8 $\div$ 40 - 2
= 8 + 7 $\times\frac{1}{5}-2=8+\frac{7}{5}-2$
= $\frac{37}{5}=7\frac{2}{5}$

25 )

If + stands for 'division', x stands for 'addition', _ stands for 'multiplication' and $\div$ stands for 'subtraction', then which of the following equation is correct:

(a)
36 x 6 + 7 $\div$ 2 - 6 = 20
(b)
36 $\div$ 6 + 3 x 5 - 3 = 45
(c)
36 + 6 - 3 x 5 $\div$ 3 = 24
(d)
36 - 6 + 3 x 5 $\div$ 3 = 74

Solution :

Using the proper notations in (d), we get the statements as :
36 x 6 $\div$ 3 + 5 -3
= 36 -x 2 + 5-3
= 72 + 5 - 3 = 74

26 )

If > denotes +, < denotes =, + denotes =, $\Lambda$ denotes x, - denotes =, x dentotes > and = denotes <, choose the correct statements in each of the following question

(a)
6 + 3 > 8 = 4 + 2 < 1
(b)
4 > 6 + 2 x 32 + 4 < 1
(c)
8 < 4 + 2 = 6 > 3
(d)
14 + 7 > 3 = 6 + 3 > 2

Solution :

Using the proper notations In (c), we get the statements as :
8 - 4 + 2 < 6 + 3
or 6 < 9. which is true.

27 )

In the following questions, arrange the given words in a meaningful sequence and then choose the most appropriate sequence from amongst the alternatives provided below each question.
1. Birth
2. Death
3. Funeral
4. Marriage
5. Education.