SSC CGL Quant – Mock Test M3 – Tier II Mathematical Abilities – Mock M3 · Tier II · Mathematical Abilities

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SSC CGL Quant – Mock Test M3 – Tier II Mathematical Abilities – Mock M3 · Tier II · Mathematical Abilities – 30 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.  
The mean of 40 observations is 50. The mean of the first 25 of them is 46. The mean of the remaining 15 observations is:

Correct Answer: D [56⅔]

Explanation:

Total 2,000 − 1,150 = 850; 850 ÷ 15 = 56⅔.

2.  
In a moderately skewed distribution the median is 36 and the mode is 30. Using Mode = 3 Median − 2 Mean, the mean is:

Correct Answer: C [39]

Explanation:

30 = 108 − 2 Mean → Mean = 39.

3.  
The variance of the 11 numbers 2, 4, 6, …, 22 is:

Correct Answer: B [40]

Explanation:

1, 2, …, 11 has variance (11² − 1)/12 = 10; doubling every value multiplies the variance by 2² = 4 → 40.

4.  
A data set has mean 6 and variance 4. Every value is multiplied by 3 and then 2 is added. The new variance is:

Correct Answer: A [36]

Explanation:

Adding 2 changes nothing; multiplying by 3 multiplies the variance by 9 → 36.

5.  
Two dice are thrown. The probability that the product of the two numbers is a perfect square is:

Correct Answer: A [2/9]

Explanation:

Six doubles plus (1, 4) and (4, 1) → 8 of 36 outcomes = 2/9.

6.  
A card is drawn from a well-shuffled pack of 52. The probability that it is a king or a heart is:

Correct Answer: C [4/13]

Explanation:

4 + 13 − 1 = 16 cards → 16/52 = 4/13.

7.  
A bag has 5 red and 7 blue balls. Two balls are drawn at random together. The probability that they are of different colours is:

Correct Answer: D [35/66]

Explanation:

5 × 7 = 35 mixed pairs out of ¹²C₂ = 66 → 35/66 (5/33 is both red, 7/22 both blue).

8.  
How many factors of 2,160 are perfect squares?

Correct Answer: B [6]

Explanation:

2,160 = 2⁴ × 3³ × 5; even powers only: 2 (0, 2, 4) × 3 (0, 2) × 5 (0) → 3 × 2 × 1 = 6.

9.  
The remainder when 5⁹⁹ is divided by 13 is:

Correct Answer: D [8]

Explanation:

5⁴ = 625 = 13 × 48 + 1; 99 = 4 × 24 + 3 → 5³ = 125 = 13 × 9 + 8 → 8.

10.  
If x² − 3x + 1 = 0, then x⁴ + 1/x⁴ = ?

Correct Answer: C [47]

Explanation:

Divide by x: x + 1/x = 3 → x² + 1/x² = 7 → x⁴ + 1/x⁴ = 49 − 2 = 47.

11.  
If 2x + 3y = 12 and 3x − 2y = 5, then x² + y² = ?

Correct Answer: A [13]

Explanation:

x = 3, y = 2 → 9 + 4 = 13.

12.  
With a 10% discount a trader gains 26%. If he gives a 20% discount instead, his gain is:

Correct Answer: B [12%]

Explanation:

MP/CP = 126/90 = 1.4; 0.8 × 1.4 = 1.12 → 12%.

13.  
A loan of ₹ 10,500 at 10% per annum compound interest is repaid in two equal annual instalments. Each instalment is:

Correct Answer: C [₹ 6,050]

Explanation:

x/1.1 + x/1.21 = 10,500 → x × 210/121 = 10,500 → x = ₹ 6,050 (check: 5,500 + 5,000 = 10,500).

14.  
The difference between the compound interest and the simple interest on ₹ 16,000 for 3 years at 5% per annum is:

Correct Answer: A [₹ 122]

Explanation:

CI = 16,000 × (1.157625 − 1) = 2,522; SI = 2,400 → ₹ 122.

15.  
Two trains 120 m and 180 m long run in opposite directions at 54 km/h and 36 km/h. They cross each other in:

Correct Answer: D [12 seconds]

Explanation:

Relative speed 90 km/h = 25 m/s; 300/25 = 12 s.

16.  
A is twice as efficient as B, and B is three times as efficient as C. Working together they finish a job in 18 days. A alone would take:

Correct Answer: B [30 days]

Explanation:

Rates 6 : 3 : 1 → 10 units a day × 18 = 180 units; A alone 180 ÷ 6 = 30 days.

17.  
A drum holds 50 litres of pure milk. 5 litres are drawn out and replaced with water, and the step is repeated once. The milk now left is:

Correct Answer: C [40.5 litres]

Explanation:

50 × (45/50)² = 50 × 0.81 = 40.5 L.

18.  
Two parallel chords of lengths 48 cm and 14 cm lie on the same side of the centre of a circle of radius 25 cm. The distance between them is:

Correct Answer: D [17 cm]

Explanation:

Distances from the centre: √(625 − 576) = 7 and √(625 − 49) = 24; same side → 24 − 7 = 17 cm (31 cm for opposite sides).

19.  
The inradius of a triangle with sides 9 cm, 10 cm and 17 cm is:

Correct Answer: B [2 cm]

Explanation:

s = 18; area = √(18 × 9 × 8 × 1) = 36; r = area ÷ s = 2 cm.

20.  
The area of an equilateral triangle is 48√3 cm². Its inradius is:

Correct Answer: A [4 cm]

Explanation:

√3/4 × a² = 48√3 → a² = 192, a = 8√3; inradius = a/(2√3) = 4 cm (8 cm is the circumradius).

21.  
A solid sphere of radius 6 cm is melted and recast into cones of base radius 3 cm and height 4 cm. The number of cones is:

Correct Answer: C [24]

Explanation:

(4/3)π × 216 = 288π; each cone (1/3)π × 9 × 4 = 12π → 24.

22.  
A cylinder and a cone have equal base radii and equal heights. Their curved surface areas are in the ratio 8 : 5. The ratio of the radius to the height is:

Correct Answer: D [3 : 4]

Explanation:

2πrh : πrl = 2h : l = 8 : 5 → l = 5h/4 → r = √(l² − h²) = 3h/4 → r : h = 3 : 4.

23.  
If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ = ?

Correct Answer: B [1]

Explanation:

sin θ = 1 − sin² θ = cos² θ, so cos² θ + cos⁴ θ = sin θ + sin² θ = 1.

24.  
If sin θ + cos θ = √2 cos θ (θ acute), then cot θ = ?

Correct Answer: A [√2 + 1]

Explanation:

sin θ = (√2 − 1) cos θ → tan θ = √2 − 1 → cot θ = 1/(√2 − 1) = √2 + 1.

25.  
From the top of a 60 m building, the angles of depression of the top and the foot of a tower are 45° and 60°. The height of the tower is:

Correct Answer: D [20(3 − √3) m]

Explanation:

Distance = 60/tan 60° = 20√3 m; drop to the tower's top = 20√3 × tan 45° = 20√3 m → tower = 60 − 20√3 = 20(3 − √3) m.

26.  
How far apart are the points A(−4, 7) and B(8, 2)?

Correct Answer: A [13]

Explanation:

√(12² + 5²) = √169 = 13.

27.  
The area of the quadrilateral with vertices (0, 0), (6, 0), (8, 5) and (2, 7), taken in order, is:

Correct Answer: C [38 sq units]

Explanation:

Shoelace: ½ ∣0 + 30 + 46 + 0∣ = 38 (or split along a diagonal into two triangles).

28.  
The average weight of 30 students is 50 kg. When the teacher's weight is included, the average rises by 0.5 kg. The teacher weighs:

Correct Answer: B [65.5 kg]

Explanation:

Newcomer = 50 + 31 × 0.5 = 65.5 kg.

29.  
Two-quantity comparison
Quantity I: the probability of a sum of 7 with two dice
Quantity II: the probability of a head and a six when a coin and a die are tossed

Correct Answer: A [Quantity I > Quantity II]

Explanation:

I = 6/36 = 1/6; II = 1/2 × 1/6 = 1/12 → I > II.

30.  
Assertion–Reason
A: The mean and the median of the first 10 natural numbers are equal.
R: For numbers in arithmetic progression the mean equals the median.

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

Mean = 5.5 and median = (5 + 6)/2 = 5.5; an AP is symmetric about its middle.

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

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