SNAP 2024 Slot 1 Quant based Questions Ques 1 - 10
Question 1: A sum of ₹12,000 is invested at a rate of 10% per annum for 2 years. Calculate the difference between the compound interest (compounded annually) and the simple interest for the same period.
- 1. ₹120
- 2. ₹150
- 3. ₹180
- 4. ₹200
Solution:
Simple Interest (SI):
\[ SI = \frac{P \times R \times T}{100} = \frac{12000 \times 10 \times 2}{100} = ₹2400 \]
Compound Interest (CI):
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
\[ CI = 12000 \left(1 + \frac{10}{100}\right)^2 - 12000 = 12000 \times 1.1^2 - 12000 \]
\[ CI = 12000 \times 1.21 - 12000 = ₹2520 \]
Difference:
\[ \text{Difference} = CI - SI = 2520 - 2400 = ₹120 \]
Question 2: Find the next number in the series: 2, 6, 12, 20, 30, ...
- 1. 40
- 2. 42
- 3. 44
- 4. 46
Solution:
The differences between consecutive terms are:
\[ 6 - 2 = 4,\ 12 - 6 = 6,\ 20 - 12 = 8,\ 30 - 20 = 10 \]
The differences increase by 2 each time. The next difference will be \(10 + 2 = 12\).
\[ \text{Next term} = 30 + 12 = 42 \]
Question 3: If \(\sin \theta = \frac{3}{5}\), find \(\cos \theta\).
- 1. \(\frac{4}{5}\)
- 2. \(\frac{3}{5}\)
- 3. \(\frac{\sqrt{16}}{5}\)
- 4. \(\frac{1}{5}\)
Solution:
Using the identity \(\sin^2 \theta + \cos^2 \theta = 1\):
\[ \cos^2 \theta = 1 - \sin^2 \theta = 1 - \left(\frac{3}{5}\right)^2 = 1 - \frac{9}{25} = \frac{16}{25} \]
\[ \cos \theta = \sqrt{\frac{16}{25}} = \frac{4}{5} \]
Question 4: A shopkeeper marks an item at ₹500 and offers a discount of 20%. If the cost price is ₹350, find the profit percentage.
- 1. 20%
- 2. 25%
- 3. 15%
- 4. 10%
Solution:
Selling Price (SP):
\[ SP = \text{Marked Price} - \text{Discount} = 500 - (20\% \times 500) = ₹400 \]
Profit:
\[ \text{Profit} = SP - CP = 400 - 350 = ₹50 \]
Profit Percentage:
\[ \text{Profit \%} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{50}{350} \times 100 = 14.29\% \approx 15\% \]
Question 5: If the ratio of the ages of two people is 5:7, and the sum of their ages is 48, find their ages.
- 1. 20 and 28
- 2. 30 and 18
- 3. 24 and 16
- 4. 21 and 27
Solution:
Let their ages be \(5x\) and \(7x\).
\[ 5x + 7x = 48 \implies 12x = 48 \implies x = 4 \]
Thus, their ages are:
\[ 5x = 20,\ 7x = 28 \]
Question 6: A can complete a task in 12 days, and B can complete the same task in 8 days. How long will it take for A and B together to complete the task?
- 1. 4.8 days
- 2. 5 days
- 3. 6 days
- 4. 7 days
Solution:
The work rates are:
\[ \text{A's rate} = \frac{1}{12},\ \text{B's rate} = \frac{1}{8} \]
Combined rate:
\[ \text{Combined rate} = \frac{1}{12} + \frac{1}{8} = \frac{2}{24} + \frac{3}{24} = \frac{5}{24} \]
Total time:
\[ \text{Time} = \frac{1}{\text{Combined Rate}} = \frac{1}{\frac{5}{24}} = \frac{24}{5} = 4.8\ \text{days} \]
Question 7: A tower is 50 meters tall. From a point on the ground, the angle of elevation to the top of the tower is \(60^\circ\). Find the distance of the point from the base of the tower.
- 1. \(25\sqrt{3}\) m
- 2. \(30\sqrt{3}\) m
- 3. \(50\sqrt{3}\) m
- 4. \(100\) m
Solution:
Using \(\tan \theta = \frac{\text{Height}}{\text{Base}}\):
\[ \tan 60^\circ = \sqrt{3} = \frac{50}{\text{Base}} \]
\[ \text{Base} = \frac{50}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{50\sqrt{3}}{3} \]
Question 8: Find the missing number in the following matrix:
2 4 6
3 6 ?
4 8 12
- 1. 8
- 2. 9
- 3. 12
- 4. 10
Solution:
For each element in the row, multiply row and column:
\[ \text{Element at (2,3)} = 2 \times 3 \times 2 = 12 \]
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Frequently asked questions
What topic do Questions 1-10 of SNAP 2024 Slot 1 Quant cover?
This range includes Interest-based questions, such as finding the difference between compound interest and simple interest on the same principal and rate.
What's an example interest question in this set?
One asks for the difference between CI (compounded annually) and SI on ₹12,000 at 10% per annum for 2 years.
Why does this question type matter for SNAP prep?
CI-SI difference questions are a recurring SNAP pattern, and knowing the shortcut formula (difference = P×(R/100)²) saves significant time over calculating both values separately.