Mathematical Operations
Exam Duration: 45 Mins Total Questions : 30
If Q means 'add to' , J means 'multiply by' ,T means' subtracted from' and K means 'divide by' then 30 K 2 Q 3 J 6 T 5 = ?
- (a)
18
- (b)
28
- (c)
31
- (d)
108
- (e)
None of these
(b) using the correct symbols, we have :
Given Expression =\(30\div 2+3\times 6-5=15+18-5=28\)
IF P denotes \(\div\),Q denotes \(\times\), R denotes + and S denotes -, then what is the value of 18 Q 12 P 4 R 5 S 6 ?
- (a)
53
- (b)
59
- (c)
63
- (d)
65
(a) using the correct symbols, we have :
Given Expression = \(18\times 12\div 4+5-6=18\times 3+5-6\\ =54+5-6=59-6=53\)
If P denotes 'multiplied by' ,T denotes 'subtracted from' , M denotes 'added to' and B denotes 'divided by' then 28 B 7 P 8 T 6 M 4 ?
- (a)
\(-\frac{3}{2}\)
- (b)
30
- (c)
32
- (d)
34
- (e)
None of these
(b) using the correct symbols, we have :
Given Expression \(=28\div 7\times 8-6+4=4\times 8-6+4\\ =32-6+4=36-6=30\)
In an imaginery language,the digits 0,1,2,3,4,5,6,7,8 and 9 are substituted by a,b,c,d,e,f,g,h,i and j.And 10 is written as ba. dc \(\times\) f - ( bf - d) \(\times\)d is equal to
- (a)
abb
- (b)
abe
- (c)
bce
- (d)
bcf
(c) using the correct symbols, we have :
Given Expression \(=32\times 5-\left( 15-3 \right) \times 3\\ =160-12\times 3=160-36=124=bce\)
If '+' stands for 'division', '+' for 'multiplication' , '\(\div\)' stands for 'multiplication', 'x' for 'addition' , then which for 'addition', which one of the following is correct ?
- (a)
18 \(\div\)6\(\times\)7+5 -2 = 22
- (b)
18\(\times\) 6+7+5 -2 = 16
- (c)
18 \(\div\)6 - 7+5\(\times\) 2 = 20
- (d)
18 +6\(\div\)7+5 -2 = 18
(d) using the proper notations in (d), we get the statement as :
\(18\div 6\times 7-5+2=3\times 7-5+2=21-5+2=18\)
If the given interchanges are made in signs and numbers, which one of the four equations would be correct?
Given interchnages : Signs + and \(\times \) and numbers 4 and 5.
- (a)
5 \(\times \) 4 + 20 = 40
- (b)
5 \(\times \) 4 + 20 = 85
- (c)
5 \(\times \) 4 + 20 = 104
- (d)
5 \(\times \) 4 + 20 = 95
(c) : On interchaging + and \(\times \) and 4 and 5 in (c), we get the equation as :
4 + 5 \(\times \) 20 = 104 or 104 = 104, which is true.
If the given interchanges are made in signs and numbers, which one of the four equations would be correct?
Given interchanges : Signs - and \(\times \) and numbers 3 and 6
- (a)
6 - 3 \(\times \) 2 = 9
- (b)
3 - 6 \(\times \) 8 = 10
- (c)
6 \(\times \) 3 - 4 = 15
- (d)
3 \(\times \) 6 - 7 = 33
(b) : On interchanging - and \(\times \) and 3 and 6 in (b), we get the equation as :
6 \(\times \) 3 - 8 = 10 or 18 - 8 = 10 or 10 = 10, which is true.
If '+' stands for 'greater than' , 'x' stands for 'addition' , '+' stands for 'division' , '-' stands for 'equal to' , '>' stands for 'multiplication' , '=' stands for 'less than' and '<' stands for 'minus' , then which of the following alternatives is correct ?
- (a)
5 > 2 < 1 - 3 \(\times\) 4 \(\times\) 1
- (b)
5 < 2 \(\times\) 1 + 3 > 4 \(\times\) 1
- (c)
5 > 2 \(\times\) 1 -3 > 4 < 1
- (d)
5 + 2 \(\times\) 1 = 3 + 4 > 1
(c) using the proper notations in (c), we get the statement as :
\(5\times 2+1=3\times 4-1\quad or\quad 10+1=12-1\quad or\quad 11=11,\quad which\quad is\quad true\)
If A + B = 2C and C + D = 2 A, then
- (a)
A + C = B + D
- (b)
A + C = 2D
- (c)
A + D = B + C
- (d)
A + C = 2B
(a) Given : A + B = 2C ... (i) and C + D = 2A
Adding (i) and (ii) ,we get : A + B + C + D = 2C + 2A \( \Rightarrow \)B + D = A + C
The given equation becomes correct due to the interchanges of two signs. One of the four alternatives under is specifies the interchange of signs in the equation which when made will make the equation correct.Find the correct alternative.
9 + 5 \(\div \) 4 \(\times \) 3 - 16 = 12
- (a)
+ and \(\times \)
- (b)
\(\div \) and \(\times \)
- (c)
\(\div \) and -
- (d)
+ and -
(c) : On interchanging \(\div \) and -, we get:
Given expression = 9 + 5 - 4 \(\times \) 3 \(\div \) 6 = 9 + 5 - 4 \(\times \) \(\frac { 1 }{ 2 } \) = 9 + 5 - 2 = 12.
If > denotes + , < denotes - , + denotes \(\div\) , ^ denotes x, - denotes = , x denotes > and = denotes < , choose the correct statement in each of the following questions.
- (a)
6 + 3 > 8 = 4 + 2 < 1
- (b)
4 > 6 + 2 \(\times\) 32 + 4 < 1
- (c)
8 < 4 + 2 = 6 < 3
- (d)
14 + 7 > 3 = 6 + 3 > 2
(c) using the proper notations in (c), we get the statement as :
\(8-4\div 2<6+3\quad or\quad 6<9,\quad which\quad is\quad true\quad \)
It being given that : \(\triangle\) denotes 'equal to'; \(\Box\) denotes 'not equal to'; + denotes 'greater than'; - denotes 'less than'; \(\times \) denotes' not greater than'; \(\div\) denotes 'not less than'.
Choose the correct statement in each of the following questions :
a - b - c implies
- (a)
a - b + c
- (b)
b + a - c
- (c)
c \(\times \) b + a
- (d)
b + a \(\div\) c
(b) With usual notations, we have :
(a) a < b < c \(\Rightarrow \quad \)a < b > c , Which is false
(b) a < b < c \(\Rightarrow \quad \)b > a < c , Which is true
(c) a < b < c \(\Rightarrow \quad \)a \(\ngtr \) b > c , Which is false
(d) a < b < c \(\Rightarrow \quad \)a > b\(\nless \) c , Which is false
Different letters stand for various symbols as indicated below :
R :Addition U : Division X : Less than S : Subtraction V : Equal to W : Greater than
Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct one.
- (a)
16 T 2 R 4 U 6 X 8
- (b)
16 R 2 S 4 V 6 R 8
- (c)
16 T 2 U 4 V 6 R 8
- (d)
16 U 2 R 4 S 6 W 8
(b) using the proper notations in (b), we get the statement as :
\(16+2-4=6+8\quad or\quad 14=14,\quad which\quad is\quad true\)
The following questions, different letters stand for various symbols as indicated below :
R :Addition U : Division X : Less than S : Subtraction V : Equal to W : Greater than
Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct one.
- (a)
15 U 5 R 3 V 2 T 3
- (b)
15 U 5 W 3 R 2 T 3
- (c)
15 S 5 T 3 W 2 R 3
- (d)
15 R 5 U 3 V 2 R3
(a) using the proper notations in (a), we get the statement as :
\(15\div 5+3=2\times 3\quad or\quad 6=6,\quad which\quad is\quad true\)
The two expressions on either side of the sign (=) will have the same value if two terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one of the four alternatives under the expressions. find the correct alternative in each case.
7 \(\times \)2 - 3 + 8 \(\div \) 4 = 5 + 6 \(\times \) 2 - 24 \(\div \) 3
- (a)
2, 6
- (b)
6, 5
- (c)
3, 24
- (d)
7, 6
(d) : On interchanging 7 and 6, we get the statement as :
6 \(\times \) 3 + 8 \(\div \) 4 = 5 + 7\(\times \) 2 - 24 \(\div \) 3 or 12 - 3 + 2 = 5 + 14 - 8 or 11 = 11, which is true.
It being given that : \(\triangle \) denotes 'equal to'; \(\Box \) denotes 'not equal to'; + denotes 'greater than'; - denotes 'less than'; \(\times \) denotes' not greater than'; \(\div \) denotes 'not less than'.
Choose the correct statement in each of the following questions :
a + b - c does not imply
- (a)
c+ b -a
- (b)
b- a + c
- (c)
b \(\Box \) a \(\Box \) c
- (d)
None of these
(b) with usual notations, we have :
(a) a > b < c c > b < a, which is false
(b) a > b < c b > a > c , which is true
(c) a > b < c b \(\neq \) a \(\neq \) c , which is false
The two expressions on either side of the sign (=) will have the same value if two terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one of the four alternatives under the expressions. find the correct alternative in each case.
15 + 3 \(\times \) 4 - 8 \(\div \) 2 = 8 \(\times \) 5 + 16 \(\div \) 2 - 1
- (a)
3, 5
- (b)
15, 5
- (c)
15, 16
- (d)
3, 1
(a) : On interchanging 3 and 5,we get the statement as :
15 + 5 \(\times \) 4 - 8 \(\div \) 2 = 8 \(\times \) 3 + 16 \(\div \) 2 - 1 or 15 + 20 - 4 = 24 + 8 - 1 or 31 = 31, which is true.
The two expressions on either side of the sign (=) will have the same value if two terms on either side or on the same side are interchanged. The correct terms to be interchanged have been given as one of the four alternatives under the expressions. find the correct alternative in each case.
8 \(\div \) 2 \(\times \) 5 - 11 + 9 = 6 \(\times \) 2 - 5 + 4 \(\div \) 2
- (a)
5, 2
- (b)
8, 5
- (c)
9, 6
- (d)
11, 5
(c) : On interchanging 9 and 6,we get the statement as :
8 \(\div \) 2 \(\times \) 5 - 11 + 6 = 9 \(\times \) 2 - 5 + 4 \(\div \) 2 or 4 \(\times \) 5 - 11 + 6 = 18 - 5 + 2 or 15 = 15, which is true.
By applying which of the following meanings of arithmetical signs, will the value of \( 700 - 10 \div {1\over2} \times 35 + 70\) be zero?
- (a)
x means \(\div\) , + means x , \(\div\) means + , - means -
- (b)
x means \(\div\) , + means - , \(\div\) means x , - means x
- (c)
x means + , + means - , \(\div\) means x , - means \(\div\)
- (d)
x means \(\div\) , + means - , \(\div\) means x , - means +
- (e)
None of these
Using the operations given in (c) , we get the given expression as :
\(700 \div 10 \times {1\over 2} + 35 - 70 = 70 \times {1\over 2} + 35 - 70 = 35 + 35 - 70 = 0.\)
In the following questions, the symbols @,#,$,%,* are used with the following meanings as illustrated below:
'A @ B' means 'A is not greater than B';
'A # B' means 'A is greater than or equal to B';
'A $ B' means 'A is neither greater than nor less than B';
'A % B' means 'A is less than B';
'A * B' means 'A is neither less than nor equal to B';
Now, in each of the following questions, assuming the given statements to be true, find which of the three conclusion I,II and III given below them is/are definitely true.
Statements :D $ T ,\(T\ast P\), M @ P
conclusions : I. \(D\ast M\) II. M % T III.D # P
- (a)
Only I is true
- (b)
Only I and II are true
- (c)
Only I and III are true
- (d)
All are true
- (e)
None of these
(b) Given statements : D = T, T > P, M \(\le \) P
I. Relation between D and M :
D = T, T > P, P \(\ge \) M \(\Rightarrow \) D = T > P \(\ge \) M \(\Rightarrow \) D > M i.e \(D\ast M\)
II. Relation between M and T :
M \(\le \) P, P > T \(\Rightarrow \) M \(\le \) P < T \(\Rightarrow \) M > T i.e M % T
III. Relation between D and P :
D = T, T > P\(\Rightarrow \) D = T > P\(\Rightarrow \) D > P i.e \(D\ast P\)
So only I and II and are true
The greek letter standing for arithmetical operations aregiven..Find the relationship which can definitely be deduced from the two relationships given at the top
operations : \(\alpha \) is ' greater than ', \(\beta \) is 'less than', \(\gamma\) is 'not greater than', \(\delta \) is 'not less than', \(\theta \) is ' equal to '
If B \(\theta \) 2C and 3C \(\gamma\) A , then
- (a)
B \(\gamma\) 2A
- (b)
B \(\theta \) A
- (c)
3B \(\alpha \)2A
- (d)
B \(\beta \) A
Some symbols have been used for some mathematical operations as indicated below:
\(\times\) for 'greater than'; \(\triangle\) for 'less than'.
Using these symbols, choose the correct alternative in each of the following questions.
If a © b \(\times\) c, it implies that
- (a)
a © b \(\phi \) c
- (b)
a \(\triangle\) b © c
- (c)
a \(\times\) c + b
- (d)
c \(\times\) b \(\times\) a
The Greek letter standing for arithmetical operations are given. Find the relationship which can definitely be deduced from the two relationships given at the top.
Operations: \(\alpha \) is ' greater than ', \(\beta \) is 'less than', \(\gamma\) is 'not greater than', \(\delta \) is 'not less than', \(\theta \) is ' equal to '.
If B \(\theta \) 2 C and 3C \(\gamma\) A, then
- (a)
B \(\delta \) 2A
- (b)
B \(\theta\) A
- (c)
3 B \(\alpha\) 2A
- (d)
B \(\beta\) A
B \(\theta\) 2C and 3C \(\gamma\) A \(\Rightarrow \) B = 2C and 3C \(\ngtr \) A \(\Rightarrow \) B = 2C and 3C \(\le \) A
\(\Rightarrow \) B = 2C < 3C \(\le \) A \(\Rightarrow \) B < Ai.e. B \(\beta\) A.
These \(\alpha\) stands for 'equal to'; \(\beta\) for 'greater than'; \(\gamma \) for 'not equal to'.
If ax \(\gamma \) by, bx \(\alpha\) cz and \(b^{2}\) \(\alpha\) ac, then
- (a)
ax \(\beta\)cy
- (b)
ay \(\alpha\) cz
- (c)
y \(\gamma \) z
- (d)
y \(\beta\) z
These \(\alpha\) stands for 'equal to'; \(\beta\) for 'greater than'; \(\gamma \) for 'not equal to'.
If bcy \(\gamma \) ax, cy \(\alpha\) bz and \(a^{2}\) \(\gamma \) bc, then
- (a)
\(cx \ \alpha \ abz\)
- (b)
\(cx \ \gamma \ abz\)
- (c)
\(cx \ \delta \ abz\)
- (d)
\(c^{2}x \ \gamma \ a^{2} z\)
These symbols\(\bigstar\), %, $, # and © are used with the following meanings as illustratbelow:w :
'P $ Q' means 'P is smaller than Q';
'P \(\bigstar\) Q' means 'P is neither smaller than nor greater than Q';
'P # Q' means 'P is either greater than or equal to Q';
'P % Q' means 'P is greater than Q';
'P © Q' means 'P is either smaller than or equal to Q'.
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them islare definitely true ?
Statement : B # D, D \(\bigstar\) F, F % H
Conclusion : I. F \(\bigstar\) B II. F $ B
- (a)
if only conclusion I is true
- (b)
if only conclusion II is true
- (c)
if either conclusion I or II is true
- (d)
if neither conclusion I nor II is true
- (e)
if both conclusions I and II are true.
'P Q' means 'P is neither smaller than nor greater than Q';
'P # Q' means 'P is either greater than or equal to Q';
'P % Q' means 'P is greater than Q';
'P © Q' means 'P is either smaller than or equal to Q'.
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them islare definitely true ?
Statement : M % K, K # T, T \(\bigstar\) J
Conclusion : I. J © K II. T $ M
- (a)
if only conclusion I is true
- (b)
if only conclusion II is true
- (c)
if either conclusion I or II is true
- (d)
if neither conclusion I nor II is true
- (e)
if both conclusions I and II are true.
'P Q' means 'P is neither smaller than nor greater than Q';
'P # Q' means 'P is either greater than or equal to Q';
'P % Q' means 'P is greater than Q';
'P © Q' means 'P is either smaller than or equal to Q'.
Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them islare definitely true ?
Statement : W © F, F % R, R # K
Conclusion : I. W $ K II. K \(\bigstar\) W
- (a)
if only conclusion I is true
- (b)
if only conclusion II is true
- (c)
if either conclusion I or II is true
- (d)
if neither conclusion I nor II is true
- (e)
if both conclusions I and II are true.
These symbols @, %, #, $, © are used with different meanings as explained below::
'P @ Q' means 'P is not greater than Q';
'P % Q' means 'P is neither greater than nor equal to Q';
'P # Q' means 'P is neither than nor equal to Q';
'P $ Q' means 'P is neither smaller than nor greater than Q';
'P © Q' means 'P is not smaller than Q'.
In each question, three statements showing relationship have been given, which are followed by two conclusion I and II. Assuming that the given statement are true, find out which of the conclusions is/are definitely true.
Statements : W @ V, V # X, Y © V
Statements : I. X % Y II. X $ W
- (a)
If only conclusion I is true
- (b)
if only conclusion II is true
- (c)
if either conclusion I or II is true
- (d)
if neither conclusion I nor II is true
- (e)
if both conclusions I and II are true.
These symbols $, #, %, and @ are used with the following meanings as illustrated below:
'X $ Y' means 'X is not greater than Y';
'X # Y' means 'X is neither greater than nor smaller than Y';
'X % Y' means 'X is not smaller than Y';
'X Y' means 'X is neither smaller than nor equal to Y';
'X @ Y' means 'X is neither greater than nor equal to Y';
Now, in each of the following questions, assuming the given statements to be true, find which of the three conclusion I, II and III given below them is/are definitely true.
Statements : F # M, M \(\bigstar\) J, P % F
Conclusions : I. P \(\bigstar\) J II. P % J III. P # M
- (a)
Only I is true
- (b)
Only I and II are true
- (c)
Only I and III are true
- (d)
Only II and III or I are true
- (e)
None of these