SSC CGL Mock – Tier I Mock Test 12 – Section C · Quantitative Aptitude
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1.2² = 1.44 → increase of 44%.
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SSC CGL Mock – Tier I Mock Test 12 – 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.
C paid ₹ 2,640 for a table that B had bought from A. A made a 10% profit on it and B a 20% profit. What had A paid for the table?
Correct Answer: B [₹ 2,000]
Explanation:
2,640 ÷ (1.1 × 1.2) = 2,640 ÷ 1.32 = 2,000.
2.
The marked price of a cooler is ₹ 1,500. Selling it at a 12% discount gives a 10% profit. What is the cost price?
Correct Answer: A [₹ 1,200]
Explanation:
SP = 1,500 × 0.88 = 1,320 → cost = 1,320 ÷ 1.1 = 1,200.
3.
A 600 km journey is made partly by train at 80 km/h and the rest by car at 60 km/h. The whole journey takes 8 hours 30 minutes. How far is travelled by car?
Correct Answer: C [240 km]
Explanation:
x/80 + (600 − x)/60 = 8.5 → x = 360 km by train → 240 km by car.
4.
Alloy P has copper and zinc in the ratio 5 : 3, and alloy Q has them in the ratio 3 : 1. If 2 kg of P is melted with 1 kg of Q, what is the ratio of copper to zinc in the new alloy?
Correct Answer: D [2 : 1]
Explanation:
Copper = 2 × 5/8 + 3/4 = 2 kg; zinc = 1 kg → 2 : 1.
5.
If sin θ + sin² θ = 1, what is the value of cos¹² θ + 3 cos¹⁰ θ + 3 cos⁸ θ + cos⁶ θ − 1?
Correct Answer: A [0]
Explanation:
sin θ = cos² θ, so cos⁴ θ + cos² θ = sin² θ + sin θ = 1; the expression is (cos⁴ θ + cos² θ)³ − 1 = 1 − 1 = 0.
6.
Find the least value that 4 sec² θ + 9 cos² θ can take.
Correct Answer: B [12]
Explanation:
AM ≥ GM: 4 sec² θ + 9 cos² θ ≥ 2√(4 × 9) = 12, reached when cos² θ = 2/3.
7.
A loan is repaid in two equal annual instalments of ₹ 4,410 each, interest being 5% per annum compounded annually. What was the loan?
Correct Answer: B [₹ 8,200]
Explanation:
4,410/1.05 + 4,410/1.05² = 4,200 + 4,000 = 8,200.
8.
Among all the divisors of 2,520, how many are odd numbers?
Correct Answer: D [12]
Explanation:
2,520 = 2³ × 3² × 5 × 7; odd divisors use only 3² × 5 × 7 → 3 × 2 × 2 = 12.
9.
Find the value of √(10 + 2√21) − √(10 − 2√21).
Correct Answer: A [2√3]
Explanation:
10 ± 2√21 = (√7 ± √3)² → (√7 + √3) − (√7 − √3) = 2√3.
10.
A alone needs 12 days and B alone 18 days for a contract. With C's help all three finish it in 6 days and receive ₹ 7,200 in total. If payment is in proportion to work done, how much does C get?
Correct Answer: C [₹ 1,200]
Explanation:
In 6 days A does 1/2 and B 1/3 → C does 1/6 → 1/6 × 7,200 = 1,200.
11.
A 60-litre solution contains 25% alcohol. How much pure alcohol must be added to make the alcohol content 40%?
Correct Answer: D [15 litres]
Explanation:
15 + x = 0.4(60 + x) → 0.6x = 9 → x = 15 litres.
12.
Arun's average monthly spending is ₹ 8,500 for the first 3 months, ₹ 9,200 for the next 4 months and ₹ 10,400 for the last 5 months of a year. He saves ₹ 29,700 in the year. What is his average monthly income?
Correct Answer: B [₹ 12,000]
Explanation:
Spending = 25,500 + 36,800 + 52,000 = 1,14,300; income = 1,14,300 + 29,700 = 1,44,000 → ÷ 12 = 12,000.
13.
The sides of a triangle are 13 cm, 14 cm and 15 cm. What is the length of the altitude on the 14 cm side?
Correct Answer: A [12 cm]
Explanation:
Area (Heron) = √(21 × 8 × 7 × 6) = 84 → altitude = 2 × 84/14 = 12 cm.
14.
Diagram-basedCircles with radii 13 cm and 20 cm cut each other at P and Q, and their centres lie 21 cm apart (see figure). How long is the common chord PQ?
Correct Answer: C [24 cm]
Explanation:
If the chord is x from the first centre: 169 − x² = 400 − (21 − x)² → x = 5 → half-chord = 12 → PQ = 24 cm.
15.
In triangle ABC, ∠A = 72°. The bisectors of the exterior angles at B and C meet at E. Find ∠BEC.
Correct Answer: D [54°]
Explanation:
∠BEC = 90° − ∠A/2 = 90° − 36° = 54°.
16.
A non-zero number x satisfies x − x⁻¹ = 4. Find the value of the fourth-power sum x⁴ + x⁻⁴.
Correct Answer: A [322]
Explanation:
x² + x⁻² = 16 + 2 = 18 → x⁴ + x⁻⁴ = 18² − 2 = 322.
17.
Given 2x + 1/(3x) = 5 (x ≠ 0), evaluate 9x² + 1/(4x²).
Correct Answer: B [213/4]
Explanation:
Multiply by 3/2: 3x + 1/(2x) = 15/2; square: 9x² + 1/(4x²) + 3 = 225/4 → 213/4.
18.
Which line passes through (−2, 5) and is perpendicular to 3x − y = 4?
Correct Answer: C [x + 3y = 13]
Explanation:
Given slope 3 → required slope −1/3; y − 5 = −(x + 2)/3 → x + 3y = 13.
19.
Data tableWhich village has the largest number of literate people?
Directions (Q 69–72): The table gives the population (in thousands) and the literacy rate of five villages (fictional data).
| Village | Population ('000) | Literacy rate (%) |
|---|---|---|
| V1 | 12 | 75 |
| V2 | 18 | 60 |
| V3 | 15 | 80 |
| V4 | 25 | 52 |
| V5 | 10 | 82 |
Correct Answer: D [V4]
Explanation:
Literates ('000): 9, 10.8, 12, 13, 8.2 → V4.
20.
(Use the directions above – Q 69–72)
Data tableWhat is the literacy rate of the five villages taken together?
Data tableWhat is the literacy rate of the five villages taken together?
Correct Answer: A [66.25%]
Explanation:
53 thousand literate out of 80 thousand → 66.25%.
21.
(Use the directions above – Q 69–72)
Data tableHow many people in village V2 are not literate?
Data tableHow many people in village V2 are not literate?
Correct Answer: C [7,200]
Explanation:
Answer: 7,200. 40% of 18,000 = 7,200.
22.
(Use the directions above – Q 69–72)
Data tableWhat is the ratio of illiterate people in V1 to illiterate people in V5?
Data tableWhat is the ratio of illiterate people in V1 to illiterate people in V5?
Correct Answer: B [5 : 3]
Explanation:
Answer: 5 : 3. V1: 3,000; V5: 1,800 → 5 : 3.
23.
Meena's salary was raised by 10%, then by 20%, and later cut by 25%. She now earns ₹ 29,700. What was her original salary?
Correct Answer: B [₹ 30,000]
Explanation:
Factor = 1.1 × 1.2 × 0.75 = 0.99 → original = 29,700 ÷ 0.99 = 30,000.
24.
The largest possible circle is cut from a square sheet of side 14 cm. What area of the sheet is left? (Take π = 22/7)
Correct Answer: C [42 cm²]
Explanation:
196 − 22/7 × 49 = 196 − 154 = 42 cm².
25.
Every edge of a cube is made 20% longer. Find the percentage increase in the total surface area.
Correct Answer: D [44%]
Explanation:
1.2² = 1.44 → increase of 44%.
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