SSC CGL Quant – Speed Rounds – Level 3 · Speed Round 3 · Tier I Challenge

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SSC CGL Quant – Speed Rounds – Level 3 · Speed Round 3 · Tier I Challenge – 25 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 3/8 of 2/5 of 560?

Correct Answer: A [84]

Explanation:

Fractions – 560 × 2/5 = 224; 224 × 3/8 = 84.

2.  
What is 125% of 64?

Correct Answer: B [80]

Explanation:

Percentage – 125% = 5/4; 64 × 5/4 = 80.

3.  
How many positive divisors does 180 have?

Correct Answer: A [18]

Explanation:

Factors – 180 = 2² × 3² × 5 → (2 + 1)(2 + 1)(1 + 1) = 18.

4.  
Which of these fractions is the greatest?

Correct Answer: C [2/3]

Explanation:

Fractions – as decimals: 0.6, 0.625, 0.636…, 0.667 → 2/3.

5.  
The price of sugar rises by 20%. By what percentage must a family cut its consumption so that its expenditure on sugar stays the same?

Correct Answer: D [16⅔%]

Explanation:

Percentage – cut = 20/120 × 100 = 16⅔%.

6.  
The present ages of A and B are in the ratio 5 : 7. Four years ago the sum of their ages was 40 years. What is A's present age?

Correct Answer: B [20 years]

Explanation:

Ages – present sum = 40 + 8 = 48; A = 48 × 5/12 = 20.

7.  
A car covers a distance at 36 km/h and returns over the same distance at 54 km/h. What is its average speed for the whole journey?

Correct Answer: B [43.2 km/h]

Explanation:

Average speed – 2 × 36 × 54/(36 + 54) = 3888/90 = 43.2 km/h.

8.  
The cost price of 18 pens equals the selling price of 15 pens. What is the profit percentage?

Correct Answer: D [20%]

Explanation:

Profit – SP/CP = 18/15 → 20% profit.

9.  
By selling a cupboard for ₹ 3,520 a dealer loses 12%. What was the cost price?

Correct Answer: C [₹ 4,000]

Explanation:

Loss – CP = 3520 × 100/88 = 4000.

10.  
What amount will ₹ 12,500 become in 2 years at 6% per annum compound interest (compounded annually)?

Correct Answer: A [₹ 14,045]

Explanation:

Compound interest – 12500 × 1.06² = 12500 × 1.1236 = 14045.

11.  
14 men can finish a job in 18 days. In how many days will 21 men finish the same job?

Correct Answer: D [12]

Explanation:

Work – 14 × 18 = 252 man-days; 252/21 = 12.

12.  
Two numbers are in the ratio 4 : 5 and their LCM is 180. What is the sum of the numbers?

Correct Answer: A [81]

Explanation:

Ratio and LCM – numbers 4k, 5k; LCM = 20k = 180 → k = 9; 36 + 45 = 81.

13.  
A runs 1 km in 4 minutes and B runs 1 km in 5 minutes. In a 1 km race, by how many metres does A beat B?

Correct Answer: C [200 m]

Explanation:

Races – when A finishes (4 min), B has run 4/5 km = 800 m → A wins by 200 m.

14.  
60 litres of a solution contain 20% alcohol. 15 litres of pure alcohol are added. What is the percentage of alcohol now?

Correct Answer: B [36%]

Explanation:

Mixture – alcohol 12 + 15 = 27 L in 75 L → 36%.

15.  
If x = 8 + √63, what is the value of x + 1/x?

Correct Answer: B [16]

Explanation:

Surds – 64 − 63 = 1, so 1/x = 8 − √63 and x + 1/x = 16 (254 is x² + 1/x²).

16.  
If a − b = 3 and a² + b² = 29, what is the value of ab?

Correct Answer: D [10]

Explanation:

Algebra – (a − b)² = a² + b² − 2ab → 9 = 29 − 2ab → ab = 10.

17.  
Solve for x: 5/x + 3 = 8

Correct Answer: A [1]

Explanation:

Equation – 5/x = 5 → x = 1.

18.  
What is the sum of the interior angles of a hexagon?

Correct Answer: C [720°]

Explanation:

Polygon – (6 − 2) × 180° = 720°.

19.  
A chord of length 30 cm is 8 cm away from the centre of a circle. What is the radius?

Correct Answer: B [17 cm]

Explanation:

Circle – half-chord 15; r = √(15² + 8²) = 17 cm.

20.  
Two tangents drawn from an external point to a circle meet at an angle of 70°. What angle do the two points of contact make at the centre?

Correct Answer: C [110°]

Explanation:

Circle – the quadrilateral has two right angles, so the centre angle = 180° − 70° = 110°.

21.  
The perimeter of an equilateral triangle is 42 cm. What is its area?

Correct Answer: A [49√3 cm²]

Explanation:

Triangle – side 14; area = √3/4 × 196 = 49√3 cm².

22.  
A right circular cone has radius 6 cm and height 8 cm. What is its curved surface area?

Correct Answer: D [60π cm²]

Explanation:

Cone – slant height 10 (6-8-10); CSA = π × 6 × 10 = 60π cm² (96π is the total surface area).

23.  
What is the value of sin² 25° + sin² 65° + tan² 45°?

Correct Answer: B [2]

Explanation:

Trigonometry – sin 65° = cos 25°, so the first two terms add to 1; 1 + 1 = 2.

24.  
If 2 sin θ = 1 and θ is acute, what is cos 2θ?

Correct Answer: D [1/2]

Explanation:

Trigonometry – θ = 30°, 2θ = 60°, cos 60° = 1/2.

25.  
A histogram has five classes with frequencies 6, 12, 18, 15 and 9. What percentage of all the observations lie in the two classes with the highest frequencies?

Correct Answer: A [55%]

Explanation:

Histogram – (18 + 15)/60 × 100 = 55%.

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