Mathematical Reasoning Test

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Mathematical Reasoning Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

The contrapositive of the statement "If it is raining, then I will not come", is :

A
If I will come, then it is not raining.

B
If I will not come, then it is raining.

C
If I will come, then it is raining.

D
If I will not come, then it is not raining.

Solution

Let $$p:$$It is raining
and $$q:$$ I will not come.
Given statement is $$p \rightarrow q$$

Contrapositive of $$p \rightarrow q$$ is $$\sim q \rightarrow \sim p$$
So, $$\sim p$$ : It is not raining.
$$\sim q$$: I will come.

So, the contrapositive statement is "If I will come, then it is not raining."

Question 2

1 / -0

Directions For Questions

Route	Departure time from Hyderabad	Distance (in km)	Fare (in Rs.)
Hyderabad-Vijayawada (via. suryapet)	0300, 0630, 0945, 1100, 1315, 1530, 1630, 1845, 2030, 2215	270	140
Hyderabad-Suryapet	0315, 0645, 1000, 1115, 1330, 1545, 1900	130	70
Hyderabad-Kodad	0700, 1045, 1715, 2130	170	80
Hyderabad-Nandigama	1130	220	115

...view full instructions

How many buses are there for Suryapet from Hyderabad?

$$7$$

$$17$$

$$12$$

$$15$$

Solution

Buses which stops at Suryapet to be consider.

Since, 'via' signifies the stoppage.

No. of buses to Suryapet from Hyderabad $$=$$ Buses to Suryapet $$+$$ Buses which have stop at Suryapet $$= 7 + 10 = 17$$.

Question 3
1 / -0

The converse of "if in a triangle $$ABC, AB>AC$$, then $$\angle C=\angle B$$", is

A
lf in a triangle $$ABC, \angle C=\angle B$$, then $$AB>AC$$.

B
lf in a triangle$$ABC, AB\not\simeq AC$$, then $$\angle C\not\simeq \angle B$$.

C
lf in a triangle $$ABC, \angle C\not\simeq \angle B$$, then $$ AB\not\simeq AC$$.

D
lf in a triangle $$ABC, \angle C\not\simeq \angle B$$, then $$AB>AC$$.

Solution

Take $$p:AB>AC$$
and $$q: \angle C=\angle B$$
So the given statement is symbolically represented as $$p\rightarrow q$$
Now by definition, Converse of a conditional statement $$p\rightarrow q$$ is $$q\rightarrow p$$
Thus $$q\rightarrow p$$ is given by
"If in a $$\triangle ABC, \angle C=\angle B$$ then $$AB>AC$$."
Question 4
1 / -0

The converse of "If $$x$$ has courage, then $$x$$ will win", is

A
If $$x$$ wins, then $$x$$ has courage.

B
If $$x$$ has no courage, then $$x$$ will not win.

C
If $$x$$ will not win, then $$x$$ has no courage.

D
If $$x$$ will not win, then $$x$$ has courage.

Solution

Take $$p:x$$ has courage
and $$q:x$$ will win
So the given conjugation is $$p\Rightarrow q$$
Now we need to find converse of this.
Be definition, Converse will be $$q\Rightarrow p$$
This is symbolic for "If $$x$$ wins then $$x$$ has courage
Question 5
1 / -0

The contrapositive of "if in a triangle $$ABC, AB > AC$$, then $$\angle C>\angle B$$", is

A
lf in a triangle $$ABC, \angle C>\angle B$$, then $$AB>AC$$.

B
lf in a triangle $$ABC, AB\ngtr AC$$, then $$\angle C\ngtr \angle B$$.

C
lf in a triangle $$ABC, \angle C\ngtr \angle B$$, then $$AB > AC$$.

D
lf in a triangle $$ABC, \angle C\ngtr \angle B$$, then $$ AB\ngtr AC$$ .

Solution

Take $$p:AB>AC$$
and $$q:\angle C>\angle B$$
So the given statement is symbolically represented as $$p\rightarrow q$$
Now by definition, Contrapositive of a conditional statement $$p\rightarrow q$$ is $$\sim q\rightarrow \sim p$$
$$\sim p:AB\ngtr AC$$
$$\sim q:\angle C\ngtr \angle B$$
Thus $$\sim q\rightarrow \sim p$$ is given by
"If in a $$\triangle ABC, \angle C\ngtr \angle B$$ then $$AB\ngtr AC$$."
Question 6
1 / -0

Here are some words translated from an artificial language
$$ mie \ pie \ is \ blue \ light$$
$$ mie \ tie \ is \ blue \ berry$$
$$ aie \ tie \ is \ rasp \ berry$$
Which words could possibly mean "light fly"?

A
pie zie

B
pie mie

C
aie zie

D
aie mie

Solution

It is clear that pie means light. So there can be only $$2$$ correct options, either pie zie or pie mie.
But mie means blue as it is common in the first two statements.
Hence, correct option is pie zie.
Question 7
1 / -0

Denial of a statement is called its

A
negation

B
converse

C
inverse

D
truth value

Solution

It is a fundamental concept that, denial of a mathematical statement is called its negation.
Question 8
1 / -0

The contrapositive of "if $$x$$ has courage then $$x$$ will win", is

A
If $$x$$ will in, then $$x$$ has courage.

B
If $$x$$ has no courage, then $$x$$ will not win.

C
If $$x$$ will not win, then $$x$$ has no courage.

D
If $$x$$ will not win, then $$x$$ has courage.

Solution

Take $$p:x$$ has courage
and $$q:x$$ will win
So the given conjugation is $$p\Rightarrow q$$
Now we need to find Contrapositive of this.
Be definition, Contrapositive of $$p\Rightarrow q$$ is $$\sim q\longrightarrow \sim p$$
$$\sim q:x$$ will not win and
$$\sim p:x$$ has no courage
Thus the Contrapositive $$\sim q\longrightarrow \sim p$$ is symbolic for "if $$x$$ will not win, then $$x$$ has no courge"
Question 9
1 / -0

The contrapositive of "If $$x\in A\cup B$$, then $$x\in A$$ or $$x\in B$$", is

A
If $$x\in A$$ or $$x\in B$$, then $$x\in A\cup B$$.

B
If $$x\not\in A\cup B$$, then $$x\not\in A$$ and $$x\not\in B$$.

C
If $$x\not\in A$$ and $$x\not\in B$$, then $$x\not\in A\cup B$$.

D
If $$x\not\in A$$ and $$x\not\in B$$, then $$x\in A\cup B$$.

Solution

Contrapositive of statement "If P then Q" is "If not Q then not P"
Hence, C.
Question 10
1 / -0

Earth is a planet. Choose the option that is a negation of this statement.

A
Earth is round

B
Earth is not round

C
Earth revolves round the sun

D
Earth is not a planet

Solution

Negation of statement "P" is "not P"

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Mathematical Reasoning Test - 10

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Question 1

If I will come, then it is not raining.

If I will not come, then it is raining.

If I will come, then it is raining.

If I will not come, then it is not raining.

Solution

Question 2

$$7$$

$$17$$

$$12$$

$$15$$

Solution

Question 3

lf in a triangle $$ABC, \angle C=\angle B$$, then $$AB>AC$$.

lf in a triangle$$ABC, AB\not\simeq AC$$, then $$\angle C\not\simeq \angle B$$.

lf in a triangle $$ABC, \angle C\not\simeq \angle B$$, then $$ AB\not\simeq AC$$.

lf in a triangle $$ABC, \angle C\not\simeq \angle B$$, then $$AB>AC$$.

Solution

Question 4

If $$x$$ wins, then $$x$$ has courage.

If $$x$$ has no courage, then $$x$$ will not win.

If $$x$$ will not win, then $$x$$ has no courage.

If $$x$$ will not win, then $$x$$ has courage.

Solution

Question 5

lf in a triangle $$ABC, \angle C>\angle B$$, then $$AB>AC$$.

lf in a triangle $$ABC, AB\ngtr AC$$, then $$\angle C\ngtr \angle B$$.

lf in a triangle $$ABC, \angle C\ngtr \angle B$$, then $$AB > AC$$.

lf in a triangle $$ABC, \angle C\ngtr \angle B$$, then $$ AB\ngtr AC$$ .

Solution

Question 6

pie zie

pie mie

aie zie

aie mie

Solution

Question 7

negation

converse

inverse

truth value

Solution

Question 8

If $$x$$ will in, then $$x$$ has courage.

If $$x$$ has no courage, then $$x$$ will not win.

If $$x$$ will not win, then $$x$$ has no courage.

If $$x$$ will not win, then $$x$$ has courage.

Solution

Question 9

If $$x\in A$$ or $$x\in B$$, then $$x\in A\cup B$$.

If $$x\not\in A\cup B$$, then $$x\not\in A$$ and $$x\not\in B$$.

If $$x\not\in A$$ and $$x\not\in B$$, then $$x\not\in A\cup B$$.

If $$x\not\in A$$ and $$x\not\in B$$, then $$x\in A\cup B$$.

Solution

Question 10

Earth is round

Earth is not round

Earth revolves round the sun

Earth is not a planet

Solution

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