Inequalities

In each question below is given a statement followed by two conclusions numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows beyond a reasonable doubt from the information given in the statement.

Statement: K$\ge$P, M$>$J, C$=$P, K$=$J

Conclusions: I. C$=$K
                     II. K$>$C

If '$÷$' means '$+$'; '$\times$' means '$-$', '$+$' means '$\times$' and '$-$' means '$÷$', then

$455-5÷15\times 32+13 = ?$

In the following questions, the symbols $@$,$\#$,$\$$,$\%$, $*$ are used with the following meanings:
A@B means A is not smaller than B.
A#B means A is greater than B.
A$B means A is smaller than B.
A%B means A is neither greater nor smaller than B.
A*B means A is not greater than B.
In each of the following questions, assuming the given statements to be true, find which of the following options holds true:
Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true
($5$) if both conclusions I and II are true.

Statements: Q$\%$L, C$\$$O, Q$\$$O, U$*$C
Conclusions: I. Q$\#$C II. O$\#$U

In the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I} \mathrm{and} \mathrm{II}$ given below is/are definitely true.

Statement: $3<4\ge 6=M=R>T>S>U$

Conclusions:

$$\begin{gathered} \mathrm{I}. 3<6 \\ \mathrm{II}. 6>U \end{gathered}$$

In the questions given below, certain symbols are used with the following meanings:
P$\#$Q means P is neither equal to nor smaller than Q.
P$\%$Q means P is not smaller than Q.
P$\$$Q means P is neither greater nor smaller than Q.
P and Q means P is neither greater than nor equal to Q.
P$@$Q means P is not greater than 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 is / are definitely true.
Give answer
($1$) If only conclusion I is true
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I and II are true.
($5$) If both conclusions I and II are true.

Statements:
K$\#$L, N$@$O,
L$\$$O
Conclusions:
I. L$\#$N
II. N$\$$L

In the following questions, the symbols $>$, $=$,$\ge$ and $<$ are used with the following meaning.

A$>$B means A is neither greater than nor smaller than B.
A$\ge$B means A is not greater than B.
A$<$B means A is neither smaller than nor equal to B.
A$=$B means A is neither greater than nor equal to B.
Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true. Given answer
($1$) If only conclusion I is true. 
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I nor II is true.
($5$) If both conclusion I and II are true.

Statements: P$=$E , Q$\ge$P
Conclusions: I. E$<$P , II. E$>$P

In the following question, the symbols $\#,\$,@, and$ and $*$are used with the following meaning as illustrated below:

'$P\#Q$' means '$P$is neither greater nor less than $Q$'

'$P\$Q$' means '$P$ is either less than or equal to $Q$'

'$P@Q$' means '$P$ is less than $Q$'

'$PandQ$' means '$P$ is greater than $Q$'

'$P*Q$' means '$P$ is either greater than or equal to $Q$'.

Now, in the following question assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true and give your answer accordingly.

Statements: $X\$K$, $KandM$, $M\$X$
Conclusions: I. $K*M$ II. $M\#K$

Following questions are based on the five three-digit numbers given below.

685 739 581 456 964

If all the numbers are arranged in descending order from left to right then which of the following will be sum of all the three digits of the number which is third from the left?

In the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I} \mathrm{and} \mathrm{II}$ given below is/are definitely true.

Statements: $S=K, K>D, D<B$

Conclusions:

$$\begin{gathered} \mathrm{I}. S<B \\ \mathrm{II}. S>D \end{gathered}$$

In the following questions, the symbols $@$,$\#$, $\$$, $\%$, $*$ are used with the following meanings:
A$@$B means A is not smaller than B.
A$\#$B means A is greater than B.
A$\$$B means A is smaller than B.
A$\%$B means A is neither greater nor smaller than B.
A$*$B means A is not greater than B.
In each of the following questions, assuming the given statements to be true, find which of the following options holds true:
Give answer—
($1$) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true.
($5$) if both conclusions I and II are true.

Statements: C$@$R, T$\%$I, Y$\$$C, T$*$R
Conclusions: I. R$\#$T II. Y$\#$T

In the following questions, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true.
Given answer
($1$) If only conclusion I is true.
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I nor II is true.
($5$) If both conclusion I and II are true.

Statements:
A$>$B,
B$\ge$C,
C$<$D
Conclusion:
I. A$>$C
II. A$=$C

In the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I} \mathrm{and} \mathrm{II}$ given below is/are definitely true.

Statement: $H>M>2=1<N=3$

Conclusions:

$$\begin{gathered} \mathrm{I}. H>1 \\ \mathrm{II}. 2<3 \end{gathered}$$

In the questions given below, certain symbols are used with the following meanings.
P$\#$Q means P is neither equal to nor smaller than Q.
P$\%$Q means P is not smaller than Q.
P$\$$Q means P is neither greater nor smaller than Q.
P $\&$ Q means P is neither greater than nor equal to Q.
P$@$Q means P is not greater than Q.
In the following question, assuming the given statements to be true, find which of the two conclusions I and II given them is/are definitely true.

Statements: T$\%$U, Q$@$R, R$\&$U
Conclusions:
I. T$\#$Q
II. R$@$T

In the following question, assuming the given statements to be true, find which of the following options holds true:
Give answer:
($1$1) if only conclusion I is true.
($2$) if only conclusion II is true.
($3$) if either conclusion I or conclusion II is true.
($4$) if neither conclusion I nor conclusion II is true
($5$) if both conclusions I and II are true.

Statements: P$\ge$K, B$\ge$N, P$\le$N, T$>$B
Conclusions:  I. N$<$T  II.P$>$T

In the following questions some symbols$@, \copyright , \$, \%, \#$, are used with the following meaning as illustrated below:

'A $@$ Z' means 'A is neither greater than nor equal to Z'.
'A $\copyright$ Z' means 'A is neither smaller than nor equal to Z.
'A $\$$ Z' means 'A is not smaller than Z'.
'A $\%$ Z' means 'A is not greater than Z'.
'A $\#$ Z' means 'A is neither smaller than nor greater than Z'.

Now in each of the following questions assuming the given statements to be true, find which of the three conclusions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$, given below them is/are definitely true and give your answer accordingly.

Statements : W $\#$ K, K $\copyright$F, F $\$$ M

Conclusions : $\mathrm{I}$. M $\copyright$ K $\mathrm{II}$. W $@$ F $\mathrm{III}$. F $@$ W

In these questions, relationship between different elements is shown in the statements. These statements are followed by two conclusions.
Mark answer
($1$) If only conclusion I follows.
($2$) If only conclusion II follows.
($3$) If either conclusion I or II follows.
($4$) If neither conclusion I nor II follows.
($5$) If both conclusions I and II follow.

Statement: S$<$T, T$<$U, U$=$W, W$<$X
Conclusion: I. S$\ge$W   II. W$\ge$T

In the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I} \mathrm{and} \mathrm{II}$ given below is/are definitely true.

Statement: $3<4\ge 6=M=R>T>S>U$

Conclusions:

$$\begin{gathered} \mathrm{I}. 6=T \\ \mathrm{II}. 6=S \end{gathered}$$

In the question given below, certain symbols are used with the following meaning :

$\mathrm{A}@\mathrm{B}$ means '$\mathrm{A}$ is not greater than $\mathrm{B}$'.
$\mathrm{A}\copyright \mathrm{B}$ means '$\mathrm{A}$ is not smaller than $\mathrm{B}$'.
$\mathrm{A}\oplus \mathrm{B}$ means '$\mathrm{A}$ is neither greater than nor equal to $\mathrm{B}$'.
$\text{A\%B}$ means '$\mathrm{A}$ is neither smaller than nor equal to $\mathrm{B}$'.
$\mathrm{A}\$\mathrm{B}$' means '$\mathrm{A}$ is neither greater than nor smaller than $\mathrm{B}$'.
Now in each of the following question, assuming the given statements to be true, find which of the two conclusions I and II given below is/are definitely true. Give answers -

Statements : $\mathrm{U}\%\mathrm{V}\copyright \mathrm{W},\mathrm{W}\$\mathrm{X}\%\mathrm{Y}@\mathrm{Z}$
Conclusions :

(I) $\mathrm{Y}\oplus \mathrm{U}$

(II) $\mathrm{X}@\mathrm{V}$

In the questions given below, certain symbols are used with the following meanings:
P$\#$ # Q means P is neither equal to nor smaller than Q.
P$\%$ Q means P is not smaller than Q
P$\$$Q means P is neither greater nor smaller than Q.
P and Q means P is neither greater than nor equal to Q
P$@$Q means P is not greater than 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 is / are definitely true. Give answer
($1$) If only conclusion I is true
($2$) If only conclusion II is true.
($3$) If either conclusion I or II is true.
($4$) If neither conclusion I and II are true.
($5$) If both conclusions I and II are true.

Statements: K$\#$L, N$@$O, L$\$$O
Conclusions:
I. L$\#$N
II. N$\$$L

Symbols $@, \%, \$, \#, \mathrm{and}$are used with following meanings-

$\mathrm{A} @ \mathrm{B}$ means A is smaller than B
$\mathrm{A} \% \mathrm{B}$ means A is greater than B.
$\mathrm{A} \mathrm{and} \mathrm{B}$ means A is neither greater than nor smaller than B
$\mathrm{A} \$ \mathrm{B}$ means A is either smaller than or equal to B
$\mathrm{A} \# \mathrm{B}$ means A is either greater than or equal to B
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 is/are definitely true and give your answer accordingly

Statements :

$\mathrm{G} @ \mathrm{H}, \mathrm{H} \mathrm{and} \mathrm{Q}, \mathrm{Q} \$ \mathrm{M}$
Conclusions :

I.$\mathrm{M} \% \mathrm{G}$
II. $\mathrm{H} \$ \mathrm{M}$