SSC CGL Quant – Speed Rounds – Level 2 · Speed Round 2 · Tier I Sprint

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SSC CGL Quant – Speed Rounds – Level 2 · Speed Round 2 · Tier I Sprint – 24 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
What is the value of 0.15 × 0.06?

Correct Answer: B [0.009]

Explanation:

Decimals – 15 × 6 = 90 with 4 decimal places → 0.0090 = 0.009.

2.  
What is the square root of 1764?

Correct Answer: C [42]

Explanation:

Square root – ends in 4 → root ends in 2 or 8; 40² = 1600, so 42.

3.  
What is the least perfect square that is divisible by 9, 10 and 12?

Correct Answer: A [900]

Explanation:

Number system – LCM = 180 = 2² × 3² × 5; make every power even: 2² × 3² × 5² = 900.

4.  
What is the remainder when 2¹⁰ is divided by 7?

Correct Answer: A [2]

Explanation:

Remainder – 2³ = 8 ≡ 1 (mod 7); 2¹⁰ = (2³)³ × 2 → remainder 2.

5.  
A number is increased by 20% and the result is decreased by 20%. The final value is 768. What was the number?

Correct Answer: C [800]

Explanation:

Percentage – net multiplier 1.2 × 0.8 = 0.96; 768 ÷ 0.96 = 800.

6.  
₹ 9,900 is divided among A, B and C in the ratio 2 : 4 : 5. What is C's share?

Correct Answer: D [₹ 4,500]

Explanation:

Ratio – 9900 × 5/11 = 4500.

7.  
The average of 10 numbers is 24. If one number, 42, is removed, what is the average of the rest?

Correct Answer: B [22]

Explanation:

Average – (240 − 42)/9 = 198/9 = 22.

8.  
A vendor buys bananas at 6 for ₹ 5 and sells them at 5 for ₹ 6. What is his profit percentage?

Correct Answer: B [44%]

Explanation:

Profit – CP of 1 = 5/6, SP of 1 = 6/5; SP/CP = 36/25 = 1.44 → 44%.

9.  
Two successive discounts of 25% and 12% are equal to a single discount of:

Correct Answer: D [34%]

Explanation:

Discount – 25 + 12 − 25 × 12/100 = 34%.

10.  
What is the difference between compound interest and simple interest on ₹ 5,000 for 2 years at 8% per annum?

Correct Answer: A [₹ 32]

Explanation:

Interest – difference for 2 years = P(r/100)² = 5000 × 0.0064 = 32.

11.  
A pipe fills a tank in 10 hours. Because of a leak at the bottom it takes longer; the leak alone can empty the full tank in 15 hours. How long does the pipe take to fill the tank with the leak open?

Correct Answer: D [30 hours]

Explanation:

Pipes – LCM 30 units; +3 − 2 = 1 unit per hour → 30 hours.

12.  
A boat's speed in still water is 15 km/h and the stream flows at 3 km/h. How long will it take to go 36 km downstream?

Correct Answer: C [2 hours]

Explanation:

Boats – downstream speed 18 km/h; 36/18 = 2 hours.

13.  
Two trains, 150 m and 100 m long, run on parallel tracks in opposite directions at 50 km/h and 40 km/h. How many seconds do they take to cross each other?

Correct Answer: A [10]

Explanation:

Trains – relative speed 90 km/h = 25 m/s; (150 + 100)/25 = 10 s (90 s would be the same-direction answer).

14.  
Tea costing ₹ 240 per kg is blended with tea costing ₹ 330 per kg so that the blend costs ₹ 270 per kg. The two teas are taken in the ratio:

Correct Answer: B [2 : 1]

Explanation:

Alligation – (330 − 270) : (270 − 240) = 60 : 30 = 2 : 1.

15.  
If a + b = 9 and ab = 14, what is the value of a³ + b³?

Correct Answer: C [351]

Explanation:

Algebra – (a + b)³ − 3ab(a + b) = 729 − 378 = 351 (a, b = 2, 7).

16.  
If 4x + 3y = 25 and 3x + 4y = 24, what is the value of x + y?

Correct Answer: B [7]

Explanation:

Linear equations – add: 7x + 7y = 49 → x + y = 7 (subtracting gives x − y = 1).

17.  
What is the value of 999²?

Correct Answer: D [998001]

Explanation:

Squares – (1000 − 1)² = 1000000 − 2000 + 1 = 998001.

18.  
In triangle ABC, the median AD is 12 cm long and G is the centroid. What is the length of AG?

Correct Answer: A [8 cm]

Explanation:

Centroid – it divides each median in the ratio 2 : 1 from the vertex; AG = 2/3 × 12 = 8 cm.

19.  
A point is 13 cm from the centre of a circle of radius 5 cm. What is the length of the tangent from the point to the circle?

Correct Answer: D [12 cm]

Explanation:

Tangent – √(13² − 5²) = √144 = 12 cm.

20.  
A rectangle has area 192 m² and length 16 m. What is its perimeter?

Correct Answer: B [56 m]

Explanation:

Rectangle – breadth 192/16 = 12; perimeter 2(16 + 12) = 56 m.

21.  
What is the curved surface area of a cylinder with radius 7 cm and height 20 cm? (Take π = 22/7)

Correct Answer: A [880 cm²]

Explanation:

Cylinder – 2πrh = 2 × 22/7 × 7 × 20 = 880 cm² (1188 is the total surface area, 3080 the volume).

22.  
What is the value of sec 60° × cos 60° + sin² 45°?

Correct Answer: C [3/2]

Explanation:

Trigonometry – sec 60° × cos 60° = 1; sin² 45° = 1/2 → 3/2.

23.  
The angle of elevation of the top of a 25 m tower from a point on the ground is 45°. How far is the point from the foot of the tower?

Correct Answer: C [25 m]

Explanation:

Heights – tan 45° = 1, so the distance equals the height = 25 m.

24.  
In a pie chart of a total budget of ₹ 72,000, a sector has a central angle of 40°. What amount does it show?

Correct Answer: D [₹ 8,000]

Explanation:

Pie chart – 72000 × 40/360 = 8000.

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