Modern Mathematics Questions for the CAT exam are part of the Syllabus in the CAT exam. Through Modern Maths questions, aspirants are tested on concepts related to Formula, Concepts, Probability, Permutations. The difficulty level of the Algebra questions can be easy to moderate.

## Tips to improve Modern Mathematics Questions for CAT?

- Ensure you have a clear understanding of fundamental concepts and definitions of each topic.
- Solve a variety of practice questions from different difficulty levels.
- Use CAT preparation books, online resources, and study guides specifically designed for Modern Mathematics.

## Modern Mathematics Questions Tricks for the CAT Exam

- Ensure clarity on fundamental concepts like permutations (arrangements) and combinations (selections).
- Solve many kinds of ratio and percentage questions that are asked, as well as their type of difficulty, by solving and analyzing questions from previous CAT examinations.
- Utilize ratios to solve percentage problems, especially those involving comparisons or distributions of quantities.

## Modern Mathematics Questions Concepts for the CAT Exam

- Problems involving seating arrangements, committee formations, and selection of groups are common.
- Problems involving coin tosses, dice throws, card selections, and conditional probability scenarios.
- Problems involving factors, multiples, divisibility tests, and prime factorization.
- Problems involving revenue, profit, cost functions, growth models, and optimization.

**Modern Mathematics Practice Questions for CAT exam**

**Q1.** The sum of the perimeters of an equilateral triangle and a rectangle is 90cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfy the relationship. If the sides of the rectangle are in the ratio 1:3, then the length, in cm, of the longer side of the rectangle, is

A. 27

B. 21

C. 24

D. 18

**Level: Moderate**

**Answer.** Option (A)

**Q2**. Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

A. 8.8

B. 7.8

C. 6.6

D. 7.2

**Level: Difficult**

**Answer.** Option (A)

**Q3.** The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

**Level: Difficult**

**Answer.** 250π/9)

**Q4.** The points (2,1) and (-3,-4) are opposite vertices of a parallelogram.If the other two vertices lie on the line x + 9y + c = 0, then c is

A. 12

B. 13

C. 15

D. 14

**Level: Difficult**

**Answer.** Option (D)

**Q5**. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

Answer:

**Level: Moderate**

**What are the must-do Modern Mathematics questions for the CAT exam?**

**Q 6.** Find the lowest common multiple of 24, 36 and 40.

(a) 120

(b) 240

(c) 360

(d) 480

**Level: Easy**

**Answer.** Option (C)

**Q 7.** The L.C.M. of 22, 54, 108, 135 and 198 is

(a) 330

(b) 1980

(c) 5940

(d) 11880

**Level: Moderate**

**Answer.** Option (C)

**Q 8**. The L.C.M. of 148 and 185 is

(a) 680

(b) 740

(c) 2960

(d) 3700

**Level: Difficult**

**Answer.** Option (C)

**Q 9.** Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is

(a) 75

(b) 81

(c) 85

(d) 89

**Level: Easy**

**Answer.** Option (A)

**Q 10.** Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is

(a) 40

(b) 80

(c) 120

(d) 200

**Level: Easy**

**Answer.** Option (A)

**What are the most important Modern Mathematics questions for the CAT 2024 exam?**

**Q 11.** The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is

(a) 91

(b) 910

(c) 1001

(d) 1911

**Level: Moderate**

**Answer.** Option (B)

**Q 12**. What value will replace the question mark in the following equations?

(i) 5172.49 + 378.352 +? = 9318.678

(ii) ? – 7328.96 = 5169.38

**Level: Moderate**

**Answer.**(i) Let 5172.49 + 378.352 + x = 9318.678.

Then, x = 9318.678 – (5172.49 + 378.352)

= 9318.678 – 5550.842 = 3767.836.

(ii) Let x – 7328.96 = 5169.38.

Then, x = 5169.38 + 7328.96 = 12498.34.

**Q 13.** Find the products:

(i) 6.3204 × 100

(ii) .069 × 10000

**Level: Difficult**

**Answer.** (i) 6.3204 × 100 = 632.04.

(ii) .069 × 10000 = .0690 × 10000 = 690

**Q 14**. Find the quotient:

(i) 0.63 ÷ 9

(ii) 0.0204 ÷ 17

(iii) 3.1603 ÷ 13

**Level: Moderate**

**Answer.** (i) 63 ÷ 9 = 7. Dividend contains 2 places of decimal.

0.63 ÷ 9 = .07.

(ii) 204 ÷ 17 = 12. Dividend contains 4 places of decimal.

0.0204 ÷ 17 = .0012.

(iii) 31603 ÷ 13 = 2431. Dividend contains 4 places of decimal.

3.1603 ÷ 13 = .2431

**Q 15.** Ram went to a shop to buy 50 kg of rice. He buys two varieties of rice which cost him ` 4.50 per kg and 5 per kg. He spends a total of 240. What was the quantity of rice bought which cost him 4.50 per kg?

**Level: Easy**

**Answer.**Let the quantity of rice bought at ` 4.50 per kg be x kg.

Then, quantity of rice bought at ` 5 per kg = (50 – x) kg.

4.50x + 5(50 – x) = 240 ⇒ 250 – 0.5x = 240 ⇒ 0.5x = 10 ⇒ x = 20.

Hence, quantity of rice bought at ` 4.50 per kg = 20 kg)

**Find some previous year Simplification questions from the CAT 2023**

**Q 16. ** How many boxes are required to filling 15 kg of sweet if each box is filled with 250 grams of sweet?

(a) 30

(b) 70

(c) 80

(d) 120

(e) None of these

**Level: Easy**

**Answer.** Option (E)

**Q 17.** A sink contains exactly 12 liters of water. If water is drained from the sink until it holds exactly 6 liters of water less than the quantity drained away, then how many liters of water were drained away?

(a) 2

(b) 3

(c) 6

(d) 9

**Level: Difficult**

**Answer.** Option (D)

**Q 18. **Cost of 8 pens and 4 pencils is ` 176 and the cost of 2 pens and 2 pencils is ` 48. What is the cost of one pen?

(a) 12

(b) 14

(c) 16

(d) 18

(e) None of these

**Level: Moderate**

**Answer.** Option (E)

**Q 19**. The cost of two dozen apples and three dozen bananas is 136. The cost of 5 dozen bananas and one dozen apples is 110. What is the price of one dozen bananas?

(a) 16

(b) 18

(c) 20

(d) 24

(e) None of these

**Level: Easy**

**Answer.** Option (E)

**Q 20**. The cost of one pencil, two pens and four erasers is 22 while the cost of five pencils, four pens and two erasers is 32. How much will three pencils, three pens and three erasers cost?

(a) 21

(b) 24

(c) 27

(d) 30

**Level: Difficult**

**Answer.** Option (C)

**What are the most Repeating Modern Mathematics questions for the CAT 2024?**

**Q 21**. Along a yard 225 metres long, 26 trees are planted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees?

(a) 8 metres

(b) 9 metres

(c) 10 metres

(d) 15 metres

**Level: Difficult**

**Answer.** Option (C)

**Q 22.** In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

(a) 20 m

(b) 22 m

(c) 24 m

(d) 26 m

**Level: Moderate**

**Answer.** Option (B)

**Q 23.** Some students planned a picnic. The budget for food was 500. But, 5 of them failed to go and thus the cost of food for each member increased by 5. How many students attended the picnic?

(a) 15

(b) 20

(c) 25

(d) 30

**Level: Difficult**

**Answer.** Option (C)

**Q 26.** A class decided to have a party at a total cost of 720. Four students decided to stay out of the party. To meet the expenses the remaining students had to increase their share by 9. What is the original cost

per student?

(a) 18

(b) 20

(c) 24

(d) 36

**Level: Easy**

**Answer.** Option (B)

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