The CAT QA section requires speed and accuracy, along with a thorough understanding of the Linear Equations. This article provides a set of MCQs on Linear Equations to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
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CAT MCQs on Linear Equations
1. In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.
| Equations | Conditions | ||
| (a) | 2x2 – 11x + 12 = 0 | (d) | Product of roots is negative |
| (b) | 5x2 21x – 20 = 0 | (e) | Product of roots is completely divisible by 6 |
| ( c) | x2 – 17x + 72 = 0 | (f) | Sum of both roots is positive |
A
(a) – (e) and (f), (b) – (d), (c) – (e)
B
(a) – (e) and (f), (b) – (d) and (f) and (c) – (e) and (f)
C
(a) – (e) and (f), (b) – (d) and (f) and (c) - (d) and (f)
D
(a) – (f), (b) – (d) and (e), (c) – (e) and (f)
2. The digit at the unit place of P would be: Given, P=(6+1) (62+1) (63+1) ......... (6100+1)
A
7
B
9
C
1
D
3
3. In a casino, there are three coloured tokens — Red (₹20), Green (₹50), Blue (₹100). Total worth ₹18,500. On a busy day, all Red tokens were upgraded to ₹200 (no change in Green/Blue). New worth: ₹27,500. Average number of tokens per colour equals the number of Green tokens. Find the total number of tokens.
A
150
B
180
C
270
D
288
4. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and \(x \leq y\) is:
A
7
B
13
C
14
D
18
5. A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
A
Over Rupees 13 but less than Rupees 14
B
Over Rupees 7 but less than Rupees 8
C
Over Rupees 22 but less than Rupees 23
D
Over Rupees 18 but less than Rupees 19
6. The price of Darjeeling tea (in rupees per kilogram) is \( 100 + 0.10n \) on the \( n^{\text{th}} \) day of 2007 (\( n = 1, 2, \ldots, 100 \)), and then remains constant. The price of Ooty tea (in rupees per kilogram) is \( 89 + 0.15n \) on the \( n^{\text{th}} \) day of 2007 (\( n = 1, 2, \ldots, 365 \)). On which date in 2007 will the prices of these two varieties of tea be equal?
A
May 21
B
April 11
C
May 20
D
April 10
7. What is the sum of the series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots\)?
A
1
B
2
C
3
D
4
8. At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?
A
Rs. 31
B
Rs. 41
C
Rs. 21
D
Cannot be determined
9. A change-making machine contains 1-rupee, 2-rupee, and 5-rupee coins. Total coins = 300, total value = Rs. 960. If 1-rupee and 2-rupee coin counts are interchanged, value decreases by Rs. 40. Find the total number of 5-rupee coins.
A
100
B
140
C
60
D
150
10. What is the value of k for which the following system of equations has no solution: \(2x - 8y = 3\) and \(kx + 4y = 10\)
A
-2
B
1
C
-1
D
2
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