SSC CGL Mock – Tier I Mock Test 08 – Section C · Quantitative Aptitude
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Upstream 4 km/h, downstream 10 km/h → still water = (4 + 10)/2 = 7 km/h.
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SSC CGL Mock – Tier I Mock Test 08 – 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.
In a school, 45% of the students are girls. 30% of the girls and 40% of the boys learn music. If 1,032 students do not learn music, how many students are there in the school?
Correct Answer: D [1,600]
Explanation:
Non-music share = 0.45 × 0.70 + 0.55 × 0.60 = 0.645 → 1,032 ÷ 0.645 = 1,600.
2.
D and E are the midpoints of sides AB and AC of triangle ABC. What is the ratio of the area of triangle ADE to the area of quadrilateral DBCE?
Correct Answer: B [1 : 3]
Explanation:
ΔADE ~ ΔABC with ratio 1/2 → areas 1 : 4 → ADE : DBCE = 1 : 3.
3.
A regular polygon has 20 diagonals. How many sides does it have?
Correct Answer: C [8]
Explanation:
Answer: 8. n(n − 3)/2 = 20 → n = 8.
4.
Diagram-basedChords AB and CD of the circle shown cross at P, with AP = 6 cm, PB = 4 cm and CP = 3 cm. What is the length of PD?
Correct Answer: A [8 cm]
Explanation:
AP × PB = CP × PD → 24 = 3 × PD → PD = 8 cm.
5.
₹ 20,000 is invested for one year at 10% per annum, with interest added every six months. How much interest does it earn?
Correct Answer: D [₹ 2,050]
Explanation:
5% per half-year for 2 half-years: 20,000 × 1.05² − 20,000 = 2,050.
6.
Pipes A and B can fill a tank in 12 minutes and 16 minutes respectively. Both are opened together. After how many minutes should B be closed so that the tank is full in exactly 9 minutes?
Correct Answer: B [4 minutes]
Explanation:
A works all 9 minutes: 9/12 = 3/4; B fills the remaining 1/4 in 16/4 = 4 minutes.
7.
Real numbers a, b, c satisfy a² + b² + c² − ab − bc − ca = 0. If a = 7, find a + b + c.
Correct Answer: A [21]
Explanation:
2(a² + b² + c² − ab − bc − ca) = (a − b)² + (b − c)² + (c − a)² = 0 → a = b = c = 7 → 21.
8.
The positive square root of 7 − 4√3 is:
Correct Answer: C [2 − √3]
Explanation:
7 − 4√3 = 4 + 3 − 2 × 2 × √3 = (2 − √3)², and 2 − √3 > 0.
9.
Two-quantity comparison
Quantity I: x, where 32x − 1 = 243
Quantity II: y, where 2y + 2 = 32
Quantity I: x, where 32x − 1 = 243
Quantity II: y, where 2y + 2 = 32
Correct Answer: C [Quantity I = Quantity II]
Explanation:
243 = 3⁵ → 2x − 1 = 5 → x = 3; 32 = 2⁵ → y + 2 = 5 → y = 3.
10.
A rhombus has diagonals of 16 cm and 30 cm. Find the sum of the lengths of its four sides.
Correct Answer: D [68 cm]
Explanation:
Side = √(8² + 15²) = 17 cm → perimeter = 68 cm.
11.
A right prism has a triangular base with sides 3 cm, 4 cm and 5 cm and a height of 10 cm. What is its total surface area?
Correct Answer: C [132 cm²]
Explanation:
Lateral = 12 × 10 = 120; two right-triangle bases = 2 × 6 = 12 → 132 cm².
12.
A number divided by 391 leaves remainder 57. Find the remainder when the same number is divided by 17.
Correct Answer: B [6]
Explanation:
391 = 17 × 23, so the remainder is 57 mod 17 = 6.
13.
When 125! is written out in full, how many zeros does it end with?
Correct Answer: A [31]
Explanation:
⌊125/5⌋ + ⌊125/25⌋ + ⌊125/125⌋ = 25 + 5 + 1 = 31.
14.
Under a 'Buy 5, get 1 free' offer, what percentage discount does a customer effectively get?
Correct Answer: A [16 2/3%]
Explanation:
Answer: 16 2/3%. 1 free in 6 → 1/6 = 16 2/3%.
15.
The cost prices of two articles are in the ratio 3 : 5. The first is sold at 20% profit and the second at 10% loss. What is the overall result?
Correct Answer: B [1.25% profit]
Explanation:
Take costs 3 and 5: sales 3.6 + 4.5 = 8.1 on cost 8 → profit 0.1/8 = 1.25%.
16.
The average of five consecutive odd numbers is 47. What is the product of the smallest and the largest of them?
Correct Answer: D [2,193]
Explanation:
The numbers are 43, 45, 47, 49, 51 → 43 × 51 = 2,193.
17.
A milkman buys milk at ₹ 60 per litre. He adds water and sells the mixture at ₹ 60 per litre, making a profit of 25%. What is the ratio of water to milk in the mixture?
Correct Answer: C [1 : 4]
Explanation:
Cost of a litre of mixture = 60/1.25 = ₹ 48 → milk 48/60 = 4/5 → water : milk = 1 : 4.
18.
A bag has ₹ 1, ₹ 2 and ₹ 5 coins in the ratio 5 : 3 : 2 (by number). The total value is ₹ 420. How many ₹ 2 coins are there?
Correct Answer: C [60]
Explanation:
One group (5 + 3 + 2 coins) is worth 5 + 6 + 10 = ₹ 21 → 20 groups → ₹ 2 coins = 3 × 20 = 60.
19.
Data tableWhich company earned the highest profit percentage?
Directions (Q 69–72): The table shows the income and expenditure (in ₹ lakh) of five companies in a year. Profit = Income − Expenditure and profit % = Profit/Expenditure × 100 (fictional data).
| Company | Income | Expenditure |
|---|---|---|
| A | 66 | 55 |
| B | 75 | 60 |
| C | 54 | 45 |
| D | 96 | 80 |
| E | 52 | 40 |
Correct Answer: B [E]
Explanation:
Profit %: A 20, B 25, C 20, D 20, E 30 → E.
20.
(Use the directions above – Q 69–72)
Data tableWhat is the total income of the five companies?
Data tableWhat is the total income of the five companies?
Correct Answer: D [₹ 343 lakh]
Explanation:
Answer: ₹ 343 lakh. 66 + 75 + 54 + 96 + 52 = 343.
21.
(Use the directions above – Q 69–72)
Data tableWhat is the profit of company D?
Data tableWhat is the profit of company D?
Correct Answer: A [₹ 16 lakh]
Explanation:
Answer: ₹ 16 lakh. 96 − 80 = 16.
22.
(Use the directions above – Q 69–72)
Data tableWhat is the ratio of the expenditure of company B to that of company D?
Data tableWhat is the ratio of the expenditure of company B to that of company D?
Correct Answer: C [3 : 4]
Explanation:
Answer: 3 : 4. 60 : 80 = 3 : 4.
23.
Find the value of sin² 10° + sin² 20° + sin² 30° + … + sin² 80°.
Correct Answer: B [4]
Explanation:
Pair sin² θ + sin² (90° − θ) = 1: four pairs → 4.
24.
The sum sec θ + tan θ equals 3. Use the identity sec² θ − tan² θ = 1 to find tan θ.
Correct Answer: A [4/3]
Explanation:
sec θ − tan θ = 1/3 → tan θ = (3 − 1/3)/2 = 4/3.
25.
Rowing against the current, a boat covers 24 km in 6 hours; with the current it covers 20 km in 2 hours. Find the boat's speed in still water.
Correct Answer: D [7 km/h]
Explanation:
Upstream 4 km/h, downstream 10 km/h → still water = (4 + 10)/2 = 7 km/h.
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