Mathematical Reasoning Test

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Mathematical Reasoning Test - 22

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Question 1
1 / -0

Find the negation of the statement, "Some odd numbers are not prime".

A
Some odd numbers are primes.

B
There is an odd number which is not a prime.

C
All odd numbers are primes.

D
Not all odd numbers are primes.

Solution

To find the negation of the statement, we find the opposite of the conclusion.

So, negation of the given statement is " All odd numbers are primes"
Question 2
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He is smart; He is intelligent.
Write the conjunction.

A
He is smart and he is intelligent.

B
He is smart maybe he is intelligent.

C
He is intelligent because He is smart

D
He is not smart and he is not intelligent.

Solution

The conjunction is both the statements together, that is " He is smart and he is intelligent"
Question 3
1 / -0

"If natural numbers are whole numbers, then rational numbers are integers" or "If rational numbers are integers, then natural numbers are whole numbers" is

A
a tautology

B
a contradiction

C
a contingency

D
not a statement

Solution

A tautology is a statement that is always true.
Here, both the statements of the compound statement are False. Hence the compound statement is Tue as a combination of Two False is True.
Hence, the given statement is a tautology.
Question 4
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Find the inverse of the statement, "If $$\triangle{ABC}$$ is equilateral, then it is isosceles".

A
If $$\triangle{ABC}$$ is isosceles, then it is equilateral.

B
If $$\triangle{ABC}$$ is not equilateral, then it is isosceles.

C
If $$\triangle{ABC}$$ is not equilateral, then it is not isosceles.

D
If $$\triangle{ABC}$$ is not isosceles, then it is not equilateral.

Solution

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

So, inverse of the given statement is "If $$ \triangle ABC $$ is not equilateral , then it is not isosceles"
Question 5
1 / -0

In the above network, current flows from T to M, when

A
p closed, q closed and r opened.

B
p closed, q opened and r closed.

C
p opened; q closed and r closed.

D
All the above

Solution

For current to flow from $$ T $$ to $$ M $$, the line from T to M should be completely connected.

This can happen when both $$ p, q $$ are closed irrespective of $$ r $$ open or close.
And can happen when $$ r $$ is closed, and either of $$ p , q $$ is closed or open.
So All of the given options are answers.
Question 6
1 / -0

The compound statement, "If you won the race; then you did not run faster than others" is equivalent to

A
"If you won the race, then you ran faster than others".

B
"If you ran faster than others, then you won the race".

C
"If you did not win the race, then you did not run faster than others".

D
"If you ran faster than others, then you did not win the race".

Solution

Two equivalent statements are those which have the same meaning.

From the given options, we can see that the compound statement, "If you ran faster than others, then you did not win the race" hss the same meaning as the given statement.
Question 7
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Which of the following is negation of the statement "All birds can fly".

A
"Some birds cannot fly".

B
"All the birds cannot fly".

C
"There is at least one bird which can fly".

D
All the above

Solution

To find the negation of the statement, we find the opposite of the conclusion.

So, negation of the given statement is " Some birds cannot fly"
Question 8
1 / -0

Find the counter example of the .statement "Every natural number is either prime or composite''.

A
5

B
1

C
6

D
None of these

Solution

As $$ 1 $$ is neither prime nor composite, it is a counter example to the statement, "Every natural number is either prime or composite ".
Question 9
1 / -0

The statement "$$x>5$$ or $$x<3$$" is true, if x equals

A
$$1$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

For "or" to be true either (or both) of the conditions must be true.

The only value that makes either of the conditions true is when $$x=1$$
For $$x>5$$ i.e $$1>5$$ is not true
but For $$x<3$$ i.e $$1<3$$ is true.

When $$x=3$$
For $$x>5$$ is not true
also For $$x<3$$ is not true.
Both the conditions are False.

When $$x=4$$
For $$x>5$$ is not true
also For $$x<3$$ is not true.
Both the conditions are False

When $$x=5$$
For $$x>5$$ is not true
also For $$x<3$$ is not true.
Both the conditions are False

Option A is correct.
Question 10
1 / -0

Which statement represents the inverse of the statement "If it is snowing then Skeeter wears a sweater"?

A
If Skeeter wears a sweater then it is snowing

B
If Skeeter does not wear a sweater then it is not snowing

C
If it is not snowing then Skeeter does not wear a sweater

D
If it is not snowing then Skeeter wears a sweater

Solution

Remember: to form the INVERSE of a statement insert "NOT" into the "If" and the "then" sections of the sentence.
Hence, option C is correct.

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Re-Attempt Weekly Quiz Competition

Mathematical Reasoning Test - 22

Result

Mathematical Reasoning Test - 22

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SHARING IS CARING

Question 1

Some odd numbers are primes.

There is an odd number which is not a prime.

All odd numbers are primes.

Not all odd numbers are primes.

Solution

Question 2

He is smart and he is intelligent.

He is smart maybe he is intelligent.

He is intelligent because He is smart

He is not smart and he is not intelligent.

Solution

Question 3

a tautology

a contradiction

a contingency

not a statement

Solution

Question 4

If $$\triangle{ABC}$$ is isosceles, then it is equilateral.

If $$\triangle{ABC}$$ is not equilateral, then it is isosceles.

If $$\triangle{ABC}$$ is not equilateral, then it is not isosceles.

If $$\triangle{ABC}$$ is not isosceles, then it is not equilateral.

Solution

Question 5

p closed, q closed and r opened.

p closed, q opened and r closed.

p opened; q closed and r closed.

All the above

Solution

Question 6

"If you won the race, then you ran faster than others".

"If you ran faster than others, then you won the race".

"If you did not win the race, then you did not run faster than others".

"If you ran faster than others, then you did not win the race".

Solution

Question 7

"Some birds cannot fly".

"All the birds cannot fly".

"There is at least one bird which can fly".

All the above

Solution

Question 8

5

1

6

None of these

Solution

Question 9

$$1$$

$$3$$

$$4$$

$$5$$

Solution

Question 10

If Skeeter wears a sweater then it is snowing

If Skeeter does not wear a sweater then it is not snowing

If it is not snowing then Skeeter does not wear a sweater

If it is not snowing then Skeeter wears a sweater

Solution

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