SSC CGL Mock – Tier I Mock Test 09 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 09 – 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.  
Alloy A contains copper and tin in the ratio 1 : 3, and alloy B contains them in the ratio 3 : 5. They are melted together so that the new alloy has copper and tin in the ratio 1 : 2. In what ratio were A and B taken?

Correct Answer: B [1 : 2]

Explanation:

Copper fractions 1/4 and 3/8, target 1/3 → (3/8 − 1/3) : (1/3 − 1/4) = 1/24 : 1/12 = 1 : 2.

2.  
The average age of a family of six is 28 years. The youngest member is 4 years old. What was the average age of the family just before the youngest member was born?

Correct Answer: C [28.8 years]

Explanation:

Others now: 168 − 4 = 164; 4 years ago: 164 − 5 × 4 = 144 → 144/5 = 28.8 years.

3.  
A trader allows a 10% discount and still makes a 17% profit. By what per cent above cost has he marked his goods?

Correct Answer: A [30%]

Explanation:

Marked = 1.17/0.9 = 1.3 of cost → 30% above cost.

4.  
A watch sold for ₹ 528 gives a loss of 12%. At what price must it be sold to gain 15%?

Correct Answer: B [₹ 690]

Explanation:

Cost = 528 ÷ 0.88 = 600 → 600 × 1.15 = 690.

5.  
Two-quantity comparison
Quantity I: the value of three-eighths of 480
Quantity II: the value obtained when 800 is multiplied by 0.225

Correct Answer: C [Quantity I = Quantity II]

Explanation:

I = 480 × 3/8 = 180; II = 800 × 9/40 = 180.

6.  
Pairs of workers finish a job as follows: A with B in 10 days, B with C in 15 days and C with A in 18 days. How long would all three take working together?

Correct Answer: D [9 days]

Explanation:

2(A + B + C) = 1/10 + 1/15 + 1/18 = 2/9 → A + B + C = 1/9 → 9 days.

7.  
At compound interest (compounded annually) a sum becomes ₹ 7,260 in 2 years and ₹ 7,986 in 3 years. What is the sum?

Correct Answer: C [₹ 6,000]

Explanation:

Growth in the 3rd year = 726/7,260 = 10% → sum = 7,260 ÷ 1.21 = 6,000.

8.  
The five-digit number 4x63y (x and y are digits) is divisible by 72. What is the value of x + y?

Correct Answer: B [5]

Explanation:

Divisible by 8: the last three digits 63y must be a multiple of 8 → 632 → y = 2; divisible by 9: 4 + x + 6 + 3 + 2 = 15 + x → x = 3; x + y = 5.

9.  
How many prime factors (counted with repetition) does 10⁸ × 14⁵ × 33⁴ have?

Correct Answer: C [34]

Explanation:

10⁸ = 2⁸5⁸ → 16; 14⁵ = 2⁵7⁵ → 10; 33⁴ = 3⁴11⁴ → 8; total 16 + 10 + 8 = 34.

10.  
For an acute angle θ, √[(1 − cos θ)/(1 + cos θ)] is equal to:

Correct Answer: A [cosec θ − cot θ]

Explanation:

Multiply inside by (1 − cos θ): √[(1 − cos θ)²/sin² θ] = (1 − cos θ)/sin θ = cosec θ − cot θ.

11.  
A man whose eyes are 1.6 m above the ground stands 20 m from a tree. The angle of elevation of the top of the tree from his eyes is 45°. How tall is the tree?

Correct Answer: D [21.6 m]

Explanation:

Height above eye level = 20 tan 45° = 20 m → tree = 20 + 1.6 = 21.6 m.

12.  
Diagram-basedIn the figure, ∠ABC = 90° and BD ⊥ AC. If AD = 4 cm and DC = 9 cm, find BD.

Correct Answer: C [6 cm]

Explanation:

BD² = AD × DC = 36 → BD = 6 cm.

13.  
Diagram-basedThe centres of two circles of radii 7 cm and 3 cm are 26 cm apart. How long is the transverse common tangent PQ in the figure?

Correct Answer: D [24 cm]

Explanation:

PQ = √(d² − (r₁ + r₂)²) = √(676 − 100) = √576 = 24 cm.

14.  
In triangle ABC, side BC is produced to D and ∠ACD = 115°. If ∠A : ∠B = 3 : 2, what is ∠A?

Correct Answer: A [69°]

Explanation:

∠A + ∠B = 115° (exterior angle) → ∠A = 115° × 3/5 = 69°.

15.  
What is the length of the arc of a sector of radius 35 cm and central angle 72°? (Take π = 22/7)

Correct Answer: B [44 cm]

Explanation:

2πr × 72/360 = 220 × 1/5 = 44 cm.

16.  
A metal ball of radius 9 cm is melted down and recast into small cones, each with base radius 3 cm and height 9 cm. How many cones can be made?

Correct Answer: A [36]

Explanation:

(4/3)π × 729 = 972π; each cone (1/3)π × 9 × 9 = 27π → 36 cones.

17.  
x is a root of the equation x² − 4x + 1 = 0. Find x³ + 1/x³.

Correct Answer: D [52]

Explanation:

Divide by x: x + 1/x = 4 → x³ + 1/x³ = 64 − 12 = 52.

18.  
The graph of y = 2x − 6 cuts off a triangle with the x-axis and the y-axis. Find the area of this triangle.

Correct Answer: B [9 sq units]

Explanation:

The line meets the axes at (3, 0) and (0, −6) → area = ½ × 3 × 6 = 9 sq units.

19.  
Which of the following is a factor of x² − 5x − 24?

Correct Answer: C [x − 8]

Explanation:

x² − 5x − 24 = (x − 8)(x + 3).

20.  
Two trains of lengths 150 m and 210 m approach each other on parallel tracks at 54 km/h and 36 km/h. From the moment their fronts meet, how long until they are completely clear of each other?

Correct Answer: C [14.4 seconds]

Explanation:

Relative speed 90 km/h = 25 m/s → 360/25 = 14.4 seconds.

21.  

Directions (Q 71–74): The line graph shows the monthly sales (units) of three products X, Y and Z of a shop from January to June (fictional data).

Line graphWhat were the total sales of the three products in April?

Correct Answer: B [115]

Explanation:

Answer: 115. 38 + 35 + 42 = 115.

22.  
(Use the directions above – Q 71–74)
Line graphIn which month did product X first sell more units than product Z?

Correct Answer: D [March]

Explanation:

Jan 30 < 40, Feb 35 < 38, Mar 40 > 36 → March.

23.  
(Use the directions above – Q 71–74)
Line graphWhat is the average monthly sale of product Y?

Correct Answer: A [33 1/3]

Explanation:

Answer: 33 1/3. 200/6 = 33 1/3.

24.  
(Use the directions above – Q 71–74)
Line graphBy what percentage did the sales of product X rise from January to June?

Correct Answer: C [66 2/3%]

Explanation:

Answer: 66 2/3%. (50 − 30)/30 × 100 = 66 2/3%.

25.  
Each month, A and B save ₹ 4,000 each. Their incomes are in the ratio 5 : 4 and their spending in the ratio 3 : 2. What is A's monthly income?

Correct Answer: B [₹ 10,000]

Explanation:

5x − 3y = 4,000 and 4x − 2y = 4,000 → x = 2,000 → A's income = 10,000.

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