| Updated On - Nov 29, 2024
The CAT 2024 Slot 2 Question Paper for Quantitative Ability (QA), along with the answer key and detailed solutions, is now available for download in PDF format. This section, conducted on November 24, 2024, during the 12:30 PM to 2:30 PM time slot, challenged candidates with questions on key mathematical concepts such as arithmetic, algebra, and geometry. With 22 questions contributing to a total of 66 marks, the QA section plays a vital role in shaping the overall exam score. The CAT 2024 slot 2 QA was moderate.
CAT 2024 Slot 2 QA Question Paper with Solutions PDF
| CAT 2024 Slot 2 QA Question Paper with Answer Key | Download | Available Soon |
CAT 2024 Slot 2 Question Paper with Solutions
| Question | Answer | Detailed Solution |
|---|---|---|
| 333³³³ divided by 11, what is the remainder? | 5 | Using modular arithmetic: • 3^1 ≡ 3 (mod 11), 3^2 ≡ 9 (mod 11), 3^3 ≡ 5 (mod 11). The remainders repeat every 5 terms. Since 333 ÷ 5 = 66 R3, we use 3^3 ≡ 5 (mod 11). |
| If Rajesh’s age were Shivani’s, their ratio would be 3:2. What is their present age ratio? | 2:3 | Let Rajesh's age be R and Shivani's age be S. If R = S: R/S = 3/2 ⇒ S/R = 2/3. |
| S invested Rs. 22,000 for 6 years at 4% compounded half-yearly. B invested for 5 years in the same scheme and reinvested for 1 year at 10% simple interest. If their final amounts are equal, what was B's initial investment? | 20,800 | Using compound interest formula for S (A = P(1 + r/100)^n) and simple interest for B: Final amounts are equal. Solving gives B's initial investment as Rs. 20,800. |
| A bus leaves at 9:00 AM, travels at 60 km/h, and reaches 3.5 hours late. If the next day it covers 2/3 of the route in 1/3 of the time and the rest in 40 minutes, when is the normal arrival time? | 1:15 PM | Normal travel time is calculated as 4 hours 15 minutes. Adding to 9:00 AM gives 1:15 PM. |
| A container has acid and water. After adding 2L water, acid becomes 50%. Adding 18L acid raises it to 80%. What is the initial acid-to-water ratio? | 3:2 | Using equations for percentages: Solve A = W + 2 and A + 18 = 0.8(A + W + 20). Initial ratio A:W is 3:2. |
CAT Questions
1. If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).
If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).
3. If Rajesh’s age were to be the present age of Shivani, their age ratio would be \(3:2\). Then what would be their present age ratio?
If Rajesh’s age were to be the present age of Shivani, their age ratio would be \(3:2\). Then what would be their present age ratio?
- 2:3
- 3:2
- 4:2
- 1:2
4. A container has a mixture of acid and water. If 2 liters of water are added, the acid content reaches 50%. After adding 18 liters of acid, the acid content increases to 80%. What was the initial acid to water ratio in the container?
A container has a mixture of acid and water. If 2 liters of water are added, the acid content reaches 50%. After adding 18 liters of acid, the acid content increases to 80%. What was the initial acid to water ratio in the container?
- 4:3
- 3:2
- 4:2
- 1:2
5. Read the Passage carefully and answer the following questions
A health food store specializing in dietary supplements and whole grains recorded the following sales figures (in kilograms) for various food categories last month: Millets (M) = 500 kg at a cost price of 40/kg and selling price of 50/kg; Protein supplements (P) = 300 kg at a cost price of 80/kg and selling price of 100/kg; Vitamin supplements (V) = 200 kg at a cost price of 60/kg and selling price of 80/kg; Carbohydrates (C) = 600 kg at a cost price of 80/kg and selling price of 100/kg; Fats (F) = 100 kg at a cost price of 120/kg and selling price of 150/kg. Additionally, they sold 50 kg of mixed nuts (N) at a cost price of 100/kg and a selling price of 130/kg
Read the Passage carefully and answer the following questions
A health food store specializing in dietary supplements and whole grains recorded the following sales figures (in kilograms) for various food categories last month: Millets (M) = 500 kg at a cost price of 40/kg and selling price of 50/kg; Protein supplements (P) = 300 kg at a cost price of 80/kg and selling price of 100/kg; Vitamin supplements (V) = 200 kg at a cost price of 60/kg and selling price of 80/kg; Carbohydrates (C) = 600 kg at a cost price of 80/kg and selling price of 100/kg; Fats (F) = 100 kg at a cost price of 120/kg and selling price of 150/kg. Additionally, they sold 50 kg of mixed nuts (N) at a cost price of 100/kg and a selling price of 130/kg
A health food store specializing in dietary supplements and whole grains recorded the following sales figures (in kilograms) for various food categories last month: Millets (M) = 500 kg at a cost price of 40/kg and selling price of 50/kg; Protein supplements (P) = 300 kg at a cost price of 80/kg and selling price of 100/kg; Vitamin supplements (V) = 200 kg at a cost price of 60/kg and selling price of 80/kg; Carbohydrates (C) = 600 kg at a cost price of 80/kg and selling price of 100/kg; Fats (F) = 100 kg at a cost price of 120/kg and selling price of 150/kg. Additionally, they sold 50 kg of mixed nuts (N) at a cost price of 100/kg and a selling price of 130/kg
6. The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).
The terms \(x_5 = -4\), \(x_1, x_2, \dots, x_{100}\) are in an arithmetic progression (AP). It is also given that \(2x_6 + 2x_9 = x_{11} + x_{13}\). Find \(x_{100}\).
- -194
- 206
- 204
- -196
Comments