SSC CGL Quant – Speed Rounds – Tier II Level · Speed Round 4 · Marathon

← Back

SSC CGL Quant – Speed Rounds – Tier II Level · Speed Round 4 · Marathon – 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.

Get daily current affairs & exam alerts – follow us YouTube WhatsApp Channel Telegram Channel Facebook Page Instagram
Share with friends & study groups
Link to this page from your website / blog (HTML code)
1.  
What is the remainder when 17²⁰⁰ is divided by 18?

Correct Answer: C [1]

Explanation:

Remainder – 17 ≡ −1 (mod 18); (−1)²⁰⁰ = 1.

2.  
How many zeros are there at the end of 160! (160 factorial)?

Correct Answer: C [39]

Explanation:

Factorial – count the 5s: 32 + 6 + 1 = 39.

3.  
What is the value of √(42 + √(42 + √(42 + …)))?

Correct Answer: A [7]

Explanation:

Surds – x² = 42 + x → x = 7 (the positive root).

4.  
What is the largest four-digit number exactly divisible by 16, 24 and 36?

Correct Answer: B [9936]

Explanation:

LCM – LCM = 144; 9999 = 144 × 69 + 63 → 9999 − 63 = 9936.

5.  
A is 25% more than B and B is 20% more than C. By what percentage is A more than C?

Correct Answer: D [50%]

Explanation:

Percentage – 1.25 × 1.2 = 1.5 → 50% more.

6.  
A invests ₹ 30,000 for 12 months and B invests ₹ 40,000 for 9 months in a business. Out of a profit of ₹ 14,000, what is A's share?

Correct Answer: A [₹ 7,000]

Explanation:

Partnership – 30000 × 12 = 360000 = 40000 × 9 → equal shares → 7000.

7.  
Thirteen readings have an average of 60. The first seven average 58 and the last seven average 63. What is the seventh reading?

Correct Answer: D [67]

Explanation:

Average – 7 × 58 + 7 × 63 − 13 × 60 = 406 + 441 − 780 = 67 (the 7th reading is counted twice).

8.  
A shopkeeper claims to sell at cost price but uses a 990 g weight in place of 1 kg. What is his gain percentage?

Correct Answer: C [1 1/99%]

Explanation:

Dishonest dealer – gain = 10/990 × 100 = 100/99 = 1 1/99%.

9.  
A sum at compound interest amounts to ₹ 8,820 in 2 years and ₹ 9,261 in 3 years. What is the sum?

Correct Answer: B [₹ 8,000]

Explanation:

Compound interest – rate = 441/8820 = 5%; sum = 8820 ÷ (1.05)² = 8000.

10.  
A and B can do a work in 18 days, B and C in 24 days, and C and A in 36 days. In how many days can A, B and C together do it?

Correct Answer: A [16]

Explanation:

Work – LCM 72: pairs give 4 + 3 + 2 = 9 units = twice (A + B + C) → 4.5 units per day → 16 days.

11.  
A train crosses a 180 m long platform in 20 seconds and a pole in 8 seconds. What is the length of the train?

Correct Answer: B [120 m]

Explanation:

Trains – the extra 12 s are for 180 m → 15 m/s; length = 15 × 8 = 120 m.

12.  
A boat goes 24 km upstream in 4 hours and 24 km downstream in 2 hours. What is the speed of the stream?

Correct Answer: D [3 km/h]

Explanation:

Boats – upstream 6, downstream 12 km/h; stream = (12 − 6)/2 = 3 km/h.

13.  
A container holds 64 litres of milk. 16 litres are taken out and replaced by water; this is done once more. How much milk is left?

Correct Answer: C [36 litres]

Explanation:

Replacement – 64 × (48/64)² = 64 × 9/16 = 36 L.

14.  
If x + 1/x = 8, what is the value of x³ + 1/x³?

Correct Answer: D [488]

Explanation:

Algebra – 8³ − 3 × 8 = 512 − 24 = 488.

15.  
If a + b + c = 0 (a, b, c non-zero), what is the value of (a³ + b³ + c³)/abc?

Correct Answer: C [3]

Explanation:

Algebra – a + b + c = 0 ⇒ a³ + b³ + c³ = 3abc.

16.  
What is the standard deviation of 6, 8, 10, 12, 14, 16, 18?

Correct Answer: A [4]

Explanation:

Statistics – mean 12; squared deviations 36, 16, 4, 0, 4, 16, 36 → 112/7 = 16 = variance; SD = 4.

17.  
What is the area of the triangle formed by the line 7x + 2y = 28 and the coordinate axes?

Correct Answer: B [28 sq units]

Explanation:

Coordinate geometry – intercepts 4 and 14; area = 1/2 × 4 × 14 = 28.

18.  
In triangle ABC, ∠B = 90°, AB = 9 cm and BC = 12 cm. What is the radius of its circumcircle?

Correct Answer: A [7.5 cm]

Explanation:

Triangle – hypotenuse 15 is a diameter → R = 7.5 cm (3 cm is the inradius).

19.  
I is the incentre of triangle ABC and ∠A = 52°. What is ∠BIC?

Correct Answer: D [116°]

Explanation:

Incentre – ∠BIC = 90° + A/2 = 116° (104° = 2A is for the circumcentre, 128° = 180° − A for the orthocentre).

20.  
Each interior angle of a regular polygon is 150°. How many sides does it have?

Correct Answer: C [12]

Explanation:

Polygon – exterior angle 30° → 360/30 = 12.

21.  
A regular right pyramid has a square base of side 12 cm and height 8 cm. What is its lateral surface area?

Correct Answer: B [240 cm²]

Explanation:

Pyramid – slant height √(8² + 6²) = 10; LSA = 4 × ½ × 12 × 10 = 240 cm² (384 includes the base).

22.  
The surface area of a sphere is 616 cm². What is its volume? (Take π = 22/7)

Correct Answer: A [1437⅓ cm³]

Explanation:

Sphere – 4πr² = 616 → r² = 49, r = 7; V = 4/3 × 22/7 × 343 = 4312/3 = 1437⅓ cm³.

23.  
If sec θ + tan θ = 2, what is the value of sec θ?

Correct Answer: C [5/4]

Explanation:

Trigonometry – sec² − tan² = 1 → sec θ − tan θ = 1/2; adding, 2 sec θ = 5/2 → sec θ = 5/4.

24.  
What is the maximum value of 7 sin θ + 24 cos θ?

Correct Answer: B [25]

Explanation:

Trigonometry – maximum of a sin θ + b cos θ is √(a² + b²) = √625 = 25.

25.  
Two cards are drawn one after the other without replacement from a well-shuffled pack of 52 cards. What is the probability that both are aces?

Correct Answer: D [1/221]

Explanation:

Probability – 4/52 × 3/51 = 12/2652 = 1/221 (1/169 would be with replacement).

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

📘 TNPSC திறனறிவும் மனக்கணக்கு நுண்ணறிவும் (Aptitude & Mental Ability) – முழுமையான பாடநூல்
Here you get the answer with a one-line explanation. TNPSC திறனறிவு & காரணவியல் சிலபஸ் முழுவதும் · 14 அத்தியாயங்கள் + 2 அலகு மாதிரித் தேர்வுகள் · 357 பயிற்சி வினாக்கள் படிப்படியான தீர்வுடன் · மாதிரித் தாள்கள் (50 வினாக்கள்) · 14 மனவரைபடங்கள் · சூத்திரச் சுருக்கம், கணக்கு அட்டவணைகள்
Get the book – ₹199 ₹399 →
Score: 0 Answered: 0 / 0