SSC CGL Mock – Tier I Mock Test 13 – Section C · Quantitative Aptitude
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By 9:00 the first has gone 60 km; the remaining 270 km closes at 135 km/h in 2 h → 11:00 a.m.
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SSC CGL Mock – Tier I Mock Test 13 – 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.
A line parallel to BC cuts AB at D and AC at E, with AD : DB = 2 : 3. Find the ratio of the area of triangle ADE to the area of the trapezium DBCE.
Correct Answer: B [4 : 21]
Explanation:
ΔADE ~ ΔABC with ratio 2/5 → areas 4 : 25 → ADE : DBCE = 4 : 21.
2.
Diagram-basedIn the figure, TA and TB are tangents to the circle with centre O, and C is a point on the major arc AB with ∠ACB = 54°. Find ∠ATB.
Correct Answer: D [72°]
Explanation:
∠AOB = 2 × 54° = 108°; in quadrilateral OATB, ∠ATB = 180° − 108° = 72°.
3.
The interior angle of a regular polygon exceeds its exterior angle by 132°. How many sides does the polygon have?
Correct Answer: D [15]
Explanation:
I + E = 180° and I − E = 132° → E = 24° → n = 360/24 = 15.
4.
3²⁵⁰ is divided by 13. What is the remainder?
Correct Answer: B [3]
Explanation:
3³ = 27 = 2 × 13 + 1; 250 = 3 × 83 + 1, so 3²⁵⁰ leaves 3¹ = 3.
5.
What is the smallest five-digit number that is exactly divisible by 6, 7, 8 and 9?
Correct Answer: A [10,080]
Explanation:
LCM = 504; 10,000 ÷ 504 = 19 rem 424; next multiple = 504 × 20 = 10,080.
6.
The average of seven consecutive integers is n. If the next three consecutive integers are also included, what is the average of all ten?
Correct Answer: C [n + 1.5]
Explanation:
The ten integers run from n − 3 to n + 6 → average = (n − 3 + n + 6)/2 = n + 1.5.
7.
A shopkeeper claims to sell rice at 8% below cost price, but he gives only 800 g for every 1 kg. What is his actual result?
Correct Answer: D [15% profit]
Explanation:
He charges 0.92 of the cost of 1 kg for goods costing 0.8 → 0.92/0.8 = 1.15 → 15% profit.
8.
A discount of 15% on a fridge amounts to ₹ 255. If the fridge cost the shopkeeper ₹ 1,360, what is his profit per cent?
Correct Answer: A [6.25%]
Explanation:
Marked price = 255 ÷ 0.15 = 1,700; SP = 1,445; profit 85 on 1,360 = 6.25%.
9.
Vessel A has milk and water in the ratio 7 : 3 and vessel B in the ratio 1 : 3. In what ratio should A and B be mixed to get equal amounts of milk and water?
Correct Answer: B [5 : 4]
Explanation:
Milk fractions 7/10 and 1/4, target 1/2 → (1/2 − 1/4) : (7/10 − 1/2) = 1/4 : 1/5 = 5 : 4.
10.
Two numbers a and b satisfy a − b = 2 and a³ − b³ = 56. Find a² + b².
Correct Answer: C [20]
Explanation:
a² + ab + b² = 56/2 = 28 and a² + b² − 2ab = 4 → ab = 8, a² + b² = 20.
11.
What does x⁴ + 1/x⁴ equal for x = 2 + √3?
Correct Answer: B [194]
Explanation:
1/x = 2 − √3 → x + 1/x = 4 → x² + x⁻² = 14 → x⁴ + x⁻⁴ = 196 − 2 = 194.
12.
(x − 2) and (x − 3) are factors of x³ + px² + qx + 6. What is the third factor?
Correct Answer: C [x + 1]
Explanation:
Product of the roots = −6, so 2 × 3 × r = −6 → r = −1 → factor (x + 1) (p = -4, q = 1).
13.
For 3 years at 10% a year, the compound interest (compounded yearly) on a sum is ₹ 155 more than the simple interest. Find the sum.
Correct Answer: A [₹ 5,000]
Explanation:
Difference = P(0.331 − 0.300) = 0.031P = 155 → P = 5,000.
14.
If tan θ + sec θ = 4 (θ acute), what is cos θ?
Correct Answer: D [8/17]
Explanation:
sec θ − tan θ = 1/4 → sec θ = (4 + 1/4)/2 = 17/8 → cos θ = 8/17.
15.
Two vertical poles 20 m and 30 m high stand on level ground. The angle of elevation of the top of the taller pole from the top of the shorter one is 30°. How far apart are the poles?
Correct Answer: B [10√3 m]
Explanation:
Height difference 10 m = d tan 30° → d = 10√3 m.
16.
A pipe fills a cistern in 8 hours. Because of a leak at the bottom it takes 10 hours. How long will the leak take to empty the full cistern?
Correct Answer: A [40 hours]
Explanation:
Leak rate = 1/8 − 1/10 = 1/40 → 40 hours.
17.
A floor tile is a regular hexagon with each side 6 cm long. How much area does one tile cover?
Correct Answer: D [54√3 cm²]
Explanation:
Six equilateral triangles: 6 × (√3/4) × 36 = 54√3 cm².
18.
Water flows at 5 m/s through a pipe of internal diameter 7 cm. How many litres flow out in one minute? (Take π = 22/7)
Correct Answer: C [1,155 litres]
Explanation:
Area = 22/7 × 3.5² = 38.5 cm²; per second 38.5 × 500 = 19,250 cm³ → per minute 1,155 litres.
19.
Three quantities satisfy 2A = 3B and 4B = 5C. Express A : C in its simplest form.
Correct Answer: B [15 : 8]
Explanation:
A = 3B/2 and C = 4B/5 → A : C = 3/2 : 4/5 = 15 : 8.
20.
Of the candidates in an exam, 65% passed Mathematics, 58% passed English and 15% failed both subjects. If 1,368 candidates passed both, find the number who appeared.
Correct Answer: D [3,600]
Explanation:
Passed in at least one = 85%; both = 65 + 58 − 85 = 38% → 1,368 ÷ 0.38 = 3,600.
21. Bar chartHow many cars of the three models were sold in the third quarter?
Directions (Q 71–74): The bar chart shows the sales (in hundreds) of three car models P, Q and R in the four quarters of a year (fictional data).
Correct Answer: A [8,200]
Explanation:
(28 + 30 + 24) hundred = 8,200.
22.
(Use the directions above – Q 71–74)
Bar chartWhich model had the highest sales for the whole year?
Bar chartWhich model had the highest sales for the whole year?
Correct Answer: C [Model P]
Explanation:
P 118, Q 96, R 92 (hundreds) → P.
23.
(Use the directions above – Q 71–74)
Bar chartBy what percentage did model R's sales rise from the second quarter to the fourth quarter?
Bar chartBy what percentage did model R's sales rise from the second quarter to the fourth quarter?
Correct Answer: B [66 2/3%]
Explanation:
Answer: 66 2/3%. (30 − 18)/18 × 100 = 66 2/3%.
24.
(Use the directions above – Q 71–74)
Bar chartWhat is the ratio of model Q's annual sales to model R's annual sales?
Bar chartWhat is the ratio of model Q's annual sales to model R's annual sales?
Correct Answer: A [24 : 23]
Explanation:
Answer: 24 : 23. 96 : 92 = 24 : 23.
25.
Stations A and B are 330 km apart. A train leaves A for B at 8:00 a.m. at 60 km/h; another leaves B for A at 9:00 a.m. at 75 km/h. At what time do they meet?
Correct Answer: C [11:00 a.m.]
Explanation:
By 9:00 the first has gone 60 km; the remaining 270 km closes at 135 km/h in 2 h → 11:00 a.m.
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