SSC CGL Mock – Tier I Mock Test 05 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 05 – Section C · Quantitative Aptitude – 25 questions, subject: Full Mock Tests. 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.  
Working together, A and B complete a task in 12 days. A works twice as fast as B. How many days would A need working alone?

Correct Answer: A [18 days]

Explanation:

Rates 2 : 1 → work = 12 × 3 = 36 units → A alone = 36/2 = 18 days.

2.  
What is the sum 1 + 3 + 5 + … + 49 (all odd numbers from 1 to 49)?

Correct Answer: D [625]

Explanation:

There are 25 odd numbers; their sum is 25² = 625.

3.  
Find the value of 18 ÷ 3 × 2 + 4 × 5 − 6 ÷ 2.

Correct Answer: B [29]

Explanation:

Division and multiplication left to right: 6 × 2 = 12, 4 × 5 = 20, 6 ÷ 2 = 3; 12 + 20 − 3 = 29.

4.  
A grocer charges only the cost price, but his 'kilogram' weight actually weighs 900 g. Find his percentage gain.

Correct Answer: B [11 1/9%]

Explanation:

Gain 100 g on 900 g → 11 1/9%.

5.  
Bananas are bought at the rate of 4 for ₹ 3 and sold at the rate of 3 for ₹ 4. Find the percentage profit.

Correct Answer: D [77 7/9%]

Explanation:

Cost of one = ₹ 3/4, selling price of one = ₹ 4/3 → (4/3)/(3/4) = 16/9 → profit 77 7/9%.

6.  
The average weight of A, B and C is 60 kg. The average of A and B is 56 kg and that of B and C is 62 kg. What is B's weight?

Correct Answer: C [56 kg]

Explanation:

(A + B) + (B + C) − (A + B + C) = 112 + 124 − 180 = 56 kg.

7.  
Find x if 2 raised to the power (x + 1) equals 64.

Correct Answer: A [5]

Explanation:

Answer: 5. 64 = 2⁶ → x + 1 = 6 → x = 5.

8.  
Given p − 1/p = 5 (p ≠ 0), the value of p² + 1/p² is:

Correct Answer: B [27]

Explanation:

(p − 1/p)² = p² + 1/p² − 2 → 25 + 2 = 27.

9.  
Which expression is identical to the sum (a + b)² + (a − b)²?

Correct Answer: A [2(a² + b²)]

Explanation:

a² + 2ab + b² + a² − 2ab + b² = 2(a² + b²).

10.  
Towns M and N are 360 km apart. A car leaves M for N at 50 km/h and at the same moment another leaves N for M at 70 km/h. How soon do the two cars meet?

Correct Answer: D [3 hours]

Explanation:

Closing speed 120 km/h → 360/120 = 3 hours.

11.  
How many kg of sugar costing ₹ 42 per kg must be mixed with 30 kg of sugar costing ₹ 36 per kg so that the mixture costs ₹ 38 per kg?

Correct Answer: C [15 kg]

Explanation:

Ratio (₹ 42 kind : ₹ 36 kind) = (38 − 36) : (42 − 38) = 1 : 2 → 15 kg.

12.  
If sin (2θ − 10°) = cos (θ + 40°), where both angles are acute, what is θ?

Correct Answer: A [20°]

Explanation:

(2θ − 10°) + (θ + 40°) = 90° → 3θ = 60° → θ = 20°.

13.  
A tower casts a shadow 30 m long when the sun's altitude is 30°. How long will its shadow be when the sun's altitude is 60°?

Correct Answer: B [10 m]

Explanation:

Height = 30 tan 30° = 10√3 m; new shadow = 10√3/tan 60° = 10 m.

14.  
The pass mark in a test is 36% of the maximum. Rekha got 123 marks and missed passing by 21 marks. Find the maximum marks of the test.

Correct Answer: D [400]

Explanation:

Pass mark = 123 + 21 = 144 = 36% of maximum → maximum = 144 × 100/36 = 400.

15.  
A 2.5 m wide gravel path runs around the outside of a rectangular garden measuring 30 m by 20 m. Find the area of the path.

Correct Answer: C [275 m²]

Explanation:

(35 × 25) − (30 × 20) = 875 − 600 = 275 m².

16.  
A conical cap has base radius 7 cm and height 24 cm. What area of material covers its sloping surface? (Take π = 22/7)

Correct Answer: B [550 cm²]

Explanation:

Slant height = √(49 + 576) = 25 cm → πrl = 22/7 × 7 × 25 = 550 cm².

17.  
The simple interest on a sum for 3 years at 6% per annum is ₹ 2,160. What is the sum?

Correct Answer: D [₹ 12,000]

Explanation:

P = 2,160 × 100/(6 × 3) = 12,000.

18.  
What is the fourth proportional to 6, 15 and 22?

Correct Answer: C [55]

Explanation:

6 : 15 = 22 : x → x = 15 × 22/6 = 55.

19.  
The vertex angle of an isosceles triangle is 40°. What is each base angle?

Correct Answer: A [70°]

Explanation:

Answer: 70°. (180° − 40°)/2 = 70°.

20.  
The sides that form the right angle of a triangle measure 20 cm and 21 cm. Find the side opposite the right angle.

Correct Answer: B [29 cm]

Explanation:

Answer: 29 cm. √(400 + 441) = √841 = 29 cm.

21.  
ABCD is a quadrilateral inscribed in a circle, and angle A is three times angle C. Find angle A.

Correct Answer: C [135°]

Explanation:

∠A + ∠C = 180° and ∠A = 3∠C → ∠C = 45°, ∠A = 135°.

22.  

Directions (Q 72–75): The table gives the marks (out of 100) of five students in four subjects (fictional data).

Student Maths Science English Social Science
Asha 78 85 66 90
Bilal 82 70 75 85
Chitra 65 92 80 71
Dev 90 60 88 74
Esha 70 78 72 96
Data tableWhich student has the highest total marks?

Correct Answer: D [Asha]

Explanation:

Totals: Asha 319, Bilal 312, Chitra 308, Dev 312, Esha 316.

23.  
(Use the directions above – Q 72–75)
Data tableWhat is the average Science mark of the five students?

Correct Answer: A [77]

Explanation:

(85 + 70 + 92 + 60 + 78)/5 = 77.

24.  
(Use the directions above – Q 72–75)
Data tableWhat is Dev's overall percentage in the four subjects?

Correct Answer: C [78%]

Explanation:

Answer: 78%. 312/400 × 100 = 78%.

25.  
(Use the directions above – Q 72–75)
Data tableHow many students scored more than 75 in English?

Correct Answer: D [2]

Explanation:

Chitra (80) and Dev (88); Bilal's 75 is not more than 75 → 2.

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