# Mathematical Reasoning MCQ Quiz - Objective Question with Answer for Mathematical Reasoning - Download Free PDF

Last updated on Feb 23, 2024

## Latest Mathematical Reasoning MCQ Objective Questions

#### Mathematical Reasoning Question 1:

A sum of Rs. 53 is divided among A. B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is :

1. 27 ∶ 20 ∶ 12
2. 27 ∶ 17 ∶ 09
3. 25 ∶ 18 ∶ 10
4. More than one of the above
5. none of the above

Option 3 : 25 ∶ 18 ∶ 10

#### Mathematical Reasoning Question 1 Detailed Solution

Given:

A sum of Rs. 53 is divided among A. B and C

A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets.

Calculation:

Let's assume that C gets x amount of money.

Then, B gets  = x + 8

A gets  = x + 15.

The total amount of money given to all three is

⇒ x + x + 8 + x + 15 = 53.

⇒  3x + 23 = 53

⇒ 3x = 30

⇒ x = 10.

So, C gets 10,

B gets = x + 8 = 10 + 8 =18,

and A gets = x + 15 = 10 + 15 = 25.

The ratio of their shares can be expressed as A : B : C = 25 : 18 : 10.

#### Mathematical Reasoning Question 2:

p ⇒ q is false, if

1. p is true and q is true.
2. p is true and q is false
3. p is false and q is true
4. More than one of the above
5. None of the above

Option 2 : p is true and q is false

#### Mathematical Reasoning Question 2 Detailed Solution

Explanation:

p ⇒ q means i"if p then q"

p ⇒ q is false only when p is true and q is false.

(2) is correct

#### Mathematical Reasoning Question 3:

A sum of Rs. 53 is divided among A. B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is :

1. 27 ∶ 20 ∶ 12
2. 27 ∶ 17 ∶ 09
3. 25 ∶ 18 ∶ 10
4. 23 ∶ 19 ∶ 11

Option 3 : 25 ∶ 18 ∶ 10

#### Mathematical Reasoning Question 3 Detailed Solution

Given:

A sum of Rs. 53 is divided among A. B and C

A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets.

Calculation:

Let's assume that C gets x amount of money.

Then, B gets  = x + 8

A gets  = x + 15.

The total amount of money given to all three is

⇒ x + x + 8 + x + 15 = 53.

⇒  3x + 23 = 53

⇒ 3x = 30

⇒ x = 10.

So, C gets 10,

B gets = x + 8 = 10 + 8 =18,

and A gets = x + 15 = 10 + 15 = 25.

The ratio of their shares can be expressed as A : B : C = 25 : 18 : 10.

#### Mathematical Reasoning Question 4:

Find the principal if the compound interest is charged on the principal at the rate of $$16\frac{2}{3}\%$$ per annum for two years and the sum becomes Rs. 196.

1. Rs. 140
2. Rs. 144
3. Rs. 150
4. Rs. 300

Option 2 : Rs. 144

#### Mathematical Reasoning Question 4 Detailed Solution

Given:

The principal if the compound interest is charged on the principal at the rate of $$16\frac{2}{3}\%$$ per annum for two years.

Formula Used:

A = P x (1 + r/100)n,

where A is the final amount,

P is the principal amount,

r is the interest rate,

and n is the number of compounding periods.

Calculation:

In this case, n = 2 and

r =  $$16\frac{2}{3}\%$$ .

So,
196 = P * (1 + $$16\frac{2}{3}$$ /100)2

⇒ P = 196 / (1 +   $$16\frac{2}{3}$$ /100)2

⇒ P = 196 / (1 + 0.166)2

⇒ P = 196 / 1.34996

⇒ P ≈ 144

So, the principal amount is approximately Rs. 144.

#### Mathematical Reasoning Question 5:

400 students took a mock test: 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?

1. 100
2. 120
3. 150
4. 300

Option 1 : 100

#### Mathematical Reasoning Question 5 Detailed Solution

Given:

400 students took a mock test: 60% of the boys

and 80% of the girls cleared the cut off in the test.

the total percentage of students clearing the cut off in the test is 65%

Calculation:

Let's assume there were b boys and g girls in the test.

According To question:

the total number of students who cleared the cut off = (60/100)b + (80/100)g = 0.65 * 400

the total number of students who took the test =  b + g = 400

⇒ b = 400 - g

Substituting this value of b in the first equation:

(60/100)(400 - g) + (80/100)g = 0.65 * 400

Expanding and simplifying the equation:

240 - 0.6g + 0.8g = 260

0.2g = 20

g = 100

So, 100 girls appeared in the test.

## Top Mathematical Reasoning MCQ Objective Questions

#### Mathematical Reasoning Question 6

The ratio of two numbers a and b is 3 :7. After adding 9 to each number, the ratio becomes 9:17. The numbers a and b are:

1. (8, 42)
2. (9, 21)
3. (15, 35)
4. (18, 42)

Option 4 : (18, 42)

#### Mathematical Reasoning Question 6 Detailed Solution

Given:

Ratio of a and b number is = 3 : 7

Calculation:

let the ratio be x

so, numbers a and b are 3x and 7x repectively.

According to the question,

⇒ (3x + 9)/(7x + 9) = 9/17

⇒ 17 × (3x + 9) = 9 × (7x + 9)

⇒ 51x + 153 = 63x + 81

⇒ 51x - 63x = 81 - 153

⇒ -12x = -72

⇒ x = 6

so, a = 3x = 3 × 6 = 18

⇒ b = 7x = 7 × 6 = 42

∴ Number a and b are 18 and 42

#### Mathematical Reasoning Question 7

Which of the following is not a negation of the statement "A natural number is greater than zero"

1. A natural number is not greater than zero
2.  It is false that a natural number is greater than zero
3. It is false that a natural number is not greater than zero
4. None of these

Option 3 : It is false that a natural number is not greater than zero

#### Mathematical Reasoning Question 7 Detailed Solution

Explanation:

Statement: A natural number is greater than zero

Negation of the statement: A natural number is not greater than zero

As we know the natural number starts from 1.

So, It is false that a natural number is not greater than zero

#### Mathematical Reasoning Question 8

A train leaves Agra at 5 a.m. and reaches Delhi at 9 a.m. Another train leaves Delhi at 7 a.m. and reaches Agra at 10:30 a.m. At what time do the two trains cross each other?

1. 6:36 a.m.
2. 6:56 a.m.
3. 7 a.m.
4. 7:56 a.m.

Option 4 : 7:56 a.m.

#### Mathematical Reasoning Question 8 Detailed Solution

Given:

Train 1 leaves Agra station at 5 a.m. and reaches Delhi at 9 a.m.

Train 2 leaves Delhi station at 7 a.m and reaches Agra at 10.30 a.m

Formula used:

Speed = Distance/time

If two objects move with the speeds u & v in opposite direction, then

Relative speed = u + v

Calculation:

Train 1 travel time = 4 hours

Train 2 travel time is 3.5 = $$\frac{7}{2}$$ hours

We know, speed = Distance/time

Let the distance b/w Agra & Delhi is 28 Km (LCM of 4 & $$\frac{7}{2}$$)

so, speed of 1st train = 28/4 = 7 km/h

⇒ speed of 2nd train = 28/3.5 = 8 km/h

Relative speed = Train 1 speed + Train 2 speed

⇒ Relative speed = 7 + 8 =  15 km

Train 1 travels for 2 hours before train 2 starts.

Remaining distance = 28 - 28/2 = 14 km

Time is taken to cross each other

Time = 14/15 hours or 56 minutes.

Total time taken = 2 hours + 56 minutes

∴ They cross each other at 7 : 56 a.m.

#### Mathematical Reasoning Question 9

If ‘a’ is inversely proportional to ‘b’ and ‘b’ is inversely proportional to c. then

1. ‘a’ is inversely proportional to ‘c’
2. ‘a’ is directly proportional to ‘c’
3. ‘a’ is constant
4. ‘a’ is directly proportional to ‘bc’

Option 2 : ‘a’ is directly proportional to ‘c’

#### Mathematical Reasoning Question 9 Detailed Solution

Given:

a α 1/b      ----(i)

b α 1/c      ----(ii)

Calculation:

If b α 1/c

⇒ b = k/c

Here k is a constant

Put this value of b in equation (i) we get,

a α 1/(k/c)

⇒ a α c/k

⇒ a α c

∴ a is directly proportional to c

#### Mathematical Reasoning Question 10

400 students took a mock test: 60% of the boys and 80% of the girls cleared the cut off in the test. If the total percentage of students clearing the cut off in the test is 65%, then how many girls appeared in the test?

1. 100
2. 120
3. 150
4. 300

Option 1 : 100

#### Mathematical Reasoning Question 10 Detailed Solution

Given:

400 students took a mock test: 60% of the boys

and 80% of the girls cleared the cut off in the test.

the total percentage of students clearing the cut off in the test is 65%

Calculation:

Let's assume there were b boys and g girls in the test.

According To question:

the total number of students who cleared the cut off = (60/100)b + (80/100)g = 0.65 * 400

the total number of students who took the test =  b + g = 400

⇒ b = 400 - g

Substituting this value of b in the first equation:

(60/100)(400 - g) + (80/100)g = 0.65 * 400

Expanding and simplifying the equation:

240 - 0.6g + 0.8g = 260

0.2g = 20

g = 100

So, 100 girls appeared in the test.

#### Mathematical Reasoning Question 11

Which one of the following statements is not a tautology?

1. (p ∨ q) → (p ∨ (~q))
2. (p ∧ q) → (~p) ∨ q
3. p → (p ∨ q)
4. (p ∧ q) → p

Option 1 : (p ∨ q) → (p ∨ (~q))

#### Mathematical Reasoning Question 11 Detailed Solution

Explanation:

 p q ~q p ∨ ~q ~p p ∧ ~q T T F T F F T F T T F T F T F F T F F F T T T F

 p q p ∨ q p → p ∨ q p ∧ q p ∧ q → p T T T T T T T F T T F T F T T T F T F F F T F T

 p q ~p ∨ q (p ∧ q) → (~p) ∨ q (p ∨ q) → (p ∨ (~q)) T T T T T T F F T T F T T T F F F T T T

A tautology is a formula or assertion that is true in every possible interpretation. So, by the truth table (p ∨ q) → (p ∨ (~q)) statement is not a tautology.

A tautology is a statement that is always true, no matter what. If you construct a truth table for a statement and all of the column values for the statement are true (T), then the statement is a tautology because it's always true!

#### Mathematical Reasoning Question 12

The negation of the statement "All continuous functions are differentiable."

1. All continuous functions are not differentiable.
2. Some continuous functions are differentiable.
3. Some continuous functions are not differentiable.
4. All differentiable functions are continuous

Option 3 : Some continuous functions are not differentiable.

#### Mathematical Reasoning Question 12 Detailed Solution

Calculation:

Always all differentiable functions are continuous. But all continuous functions are not differentiable.

So, the negation of the given statement is some continuous functions are not differentiable.

Hence, option (3) is correct.

#### Mathematical Reasoning Question 13

The Boolean expression ~(p ⇒ (~q)) is equivalent to:

1. p ∧ q
2. q ⇒ ~p
3. p ∨ q
4. (~p) ⇒ q

Option 1 : p ∧ q

#### Mathematical Reasoning Question 13 Detailed Solution

From question, the Boolean expression given is:

~(p ⇒ (~q))

The truth table for the above expression is given below:

 p q ~q P ⇒ (~q) ~(p ⇒ (~q)) T T F F T T F T T F F T F T F F F T T F

Now, we need to consider the options:

Option (a) p ∧ q:

 p q P ∧ q T T T T F F F T F F F F

Option (b) q ⇒ ~p:

 p q ~p q ⇒ ~p T T F F T F F F F T T T F F T T

Option (c) p ∨ q:

 p q P ∨ q T T T T F T F T T F F F

Option (d) (~p) ⇒ q:

 p q ~p (~p) ⇒ q T T F T T F F T F T T T F F T F

On comparing the truth values of expression and truth values in options. The truth values in option is same and option (a) is the correct answer.

#### Mathematical Reasoning Question 14

A solid is in the form of a cylinder with hemispherical ends. The diameter of the cylinder is 1/3 of its height (excluding the hemispherical ends). The total length of the solid including the hemispherical ends is 56 cm. What is the surface area of the solid?

1. 3080 cm2
2. 2464 cm2
3. 2772 cm2
4. 2156 cm2

Option 2 : 2464 cm2

#### Mathematical Reasoning Question 14 Detailed Solution

Given:

The diameter of the cylinder = Height/3

Total length = 56 cm

Formula:

Surface area of cylinder = 2πrh

Surface area of hemisphere = 2πr2

Calculation:

Let the diameter be 2x

Height of the cylinder = 6x

The total length of the solid including the hemispherical ends = 56 cm

⇒ 6x + 2x = 56

⇒ x = 7 cm

The surface area of cylinder = 2π × 7 × 42

The surface area of cylinder = 1848 cm2

Surface area of one hemisphere = 2π × 49 = 308 cm2

Surface area of two hemisphere = 308 × 2 = 616 cm2

∴ The surface area of the solid = 1848 + 616 = 2464 cm2

#### Mathematical Reasoning Question 15

In a class of 35 students, Rajan is placed seventh from the bottom whereas Karan is placed ninth from the top. Divya is placed exactly in between the two. What is the difference in the positions of Rajan and Divya?

1. 9
2. 10
3. 11
4. 13

Option 2 : 10

#### Mathematical Reasoning Question 15 Detailed Solution

Given

Total students = 35

Rajan is 7th from bottom, Karan is 9th from top and Divya is exactly between Karan and Rajan

Concept Used

n position from bottom = (Total + 1 - n) position from top

Calculation

Rajan = 7th from bottom = (35 + 1 - 7)the from top = 29th from top

Karan = 9th from top

Divya is placed exactly in between Rajan and Karan.

Total students between Karan and Rajan = 35 - (9 + 7) = 35 - 16 = 19

Thus, Divya's position from Karan = $$\frac{19\;+\;1}{2}=\frac{20}{2}=10$$

Divya's position from top = 9 + 10 = 19,

Hence, differences in the positions of Rajan and Divya = 29 - 19 = 10  i.e total 10 seats.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://testbook.com/objective-questions/mcq-on-mathematical-reasoning--5eea6a1439140f30f369f0f0", "fetch_time": 1716493228000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-22/segments/1715971058653.47/warc/CC-MAIN-20240523173456-20240523203456-00144.warc.gz", "warc_record_offset": 487302294, "warc_record_length": 68038, "token_count": 4251, "char_count": 12990, "score": 4.40625, "int_score": 4, "crawl": "CC-MAIN-2024-22", "snapshot_type": "latest", "language": "en", "language_score": 0.8509347438812256, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00045-of-00064.parquet"}