SSC CGL Mock – Tier I Mock Test 11 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 11 – 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 invests three times as much as B, and B invests two-thirds of what C invests. Out of a profit of ₹ 1,10,000, what is B's share?

Correct Answer: D [₹ 20,000]

Explanation:

A : B : C = 3 : 1 : 3/2 = 6 : 2 : 3 → B = 2/11 × 1,10,000 = 20,000.

2.  
Diagram-basedIn the figure, AB is a diameter of the circle and ABCD is a cyclic quadrilateral with ∠ADC = 128°. Find ∠BAC.

Correct Answer: B [38°]

Explanation:

∠ABC = 180° − 128° = 52°; ∠ACB = 90° (semicircle) → ∠BAC = 90° − 52° = 38°.

3.  
In a triangle with sides 7 cm, 8 cm and 9 cm, a median is drawn from the vertex opposite the 8 cm side. Find its length.

Correct Answer: A [7 cm]

Explanation:

m² = (2 × 7² + 2 × 9² − 8²)/4 = 196/4 = 49 → m = 7 cm.

4.  
The incircle of triangle ABC touches the sides. If AB = 10 cm, BC = 12 cm and CA = 8 cm, what is the length of the tangent from B to the incircle?

Correct Answer: C [7 cm]

Explanation:

s = 15; tangent from B = s − CA = 15 − 8 = 7 cm.

5.  
A dealer sells a sofa at 18% profit. Had he bought it at 10% less and sold it for ₹ 54 less, he would have gained 30%. What is the cost price?

Correct Answer: C [₹ 5,400]

Explanation:

1.18C − 54 = 0.9C × 1.3 = 1.17C → 0.01C = 54 → C = 5,400.

6.  
A shopkeeper marks an article 50% above cost and allows two successive discounts, the first of 20%. If he still makes an 8% profit, what is the second discount?

Correct Answer: B [10%]

Explanation:

1.5 × 0.8 × (1 − d) = 1.08 → 1 − d = 0.9 → d = 10%.

7.  
A trapezium has parallel sides 18 cm and 30 cm, and each non-parallel side is 10 cm. What is its area?

Correct Answer: D [192 cm²]

Explanation:

Height = √(10² − 6²) = 8 → ½ × 48 × 8 = 192 cm².

8.  
A solid is a cylinder of radius 6 cm and height 10 cm with a hemisphere of the same radius on one end. What is its volume?

Correct Answer: A [504π cm³]

Explanation:

πr²h + (2/3)πr³ = 360π + 144π = 504π cm³.

9.  
At compound interest a sum becomes three times itself in 5 years. In how many years will it become 81 times itself?

Correct Answer: C [20 years]

Explanation:

81 = 3⁴ → four periods of 5 years = 20 years.

10.  
A's salary is 40% more than B's, and B's salary is 25% less than C's. If C earns ₹ 48,000 a month, what does A earn?

Correct Answer: D [₹ 50,400]

Explanation:

B = 0.75 × 48,000 = 36,000; A = 1.4 × 36,000 = 50,400.

11.  
In a class, the average weight of the boys is 50 kg and that of the girls is 45 kg. The class average is 48 kg. What is the ratio of boys to girls?

Correct Answer: B [3 : 2]

Explanation:

Alligation: boys : girls = (48 − 45) : (50 − 48) = 3 : 2.

12.  
A runs 1 km in 3 min 10 s and B runs it in 3 min 20 s. By how many metres does A beat B in a 1 km race?

Correct Answer: A [50 m]

Explanation:

In A's 190 s, B covers 1,000 × 190/200 = 950 m → A wins by 50 m.

13.  
A can finish a job in 18 days and B in 24 days. They work on alternate days, A working on the first day. In how many days will the job be finished?

Correct Answer: A [20 1/2 days]

Explanation:

Every 2 days 1/18 + 1/24 = 7/72; after 20 days 70/72 is done; A finishes the last 2/72 in half a day → 20 1/2 days.

14.  
The factorials of 1 to 100 are added: 1! + 2! + … + 100!. What remainder does this sum leave on division by 12?

Correct Answer: B [9]

Explanation:

From 4! onwards every term is a multiple of 12; 1 + 2 + 6 = 9 → remainder 9.

15.  
The HCF of two numbers is 28 and their LCM is 1,680. How many such pairs of numbers are possible?

Correct Answer: D [4]

Explanation:

Numbers 28a and 28b with a × b = 60 and a, b co-prime: (1, 60), (3, 20), (4, 15), (5, 12) → 4 pairs.

16.  
The average weight of 10 boys in a team rises by 1.5 kg when one of them, who weighs 58 kg, is replaced by a new boy. What is the weight of the new boy?

Correct Answer: C [73 kg]

Explanation:

New boy = 58 + 10 × 1.5 = 73 kg.

17.  

Directions (Q 67–70): The pie chart shows how 2,400 students are distributed among five colleges, and the table gives the percentage of girls in each college (fictional data).

College A B C D E
Girls (%) 40 48 50 35 60
Mixed DIHow many girls study in college D?

Correct Answer: C [252]

Explanation:

30% of 2,400 = 720; 35% of 720 = 252.

18.  
(Use the directions above – Q 67–70)
Mixed DIIn which college are boys the most numerous?

Correct Answer: B [College D]

Explanation:

Boys: A 288, B 312, C 180, D 468, E 96.

19.  
(Use the directions above – Q 67–70)
Mixed DIGirls form what percentage of all 2,400 students?

Correct Answer: A [44%]

Explanation:

Girls = 1,056 → 1,056/2,400 = 44%.

20.  
(Use the directions above – Q 67–70)
Mixed DIWhat is the ratio of boys in college B to girls in college C?

Correct Answer: D [26 : 15]

Explanation:

Answer: 26 : 15. 312 : 180 = 26 : 15.

21.  
If cos θ + sin θ = √2 cos θ (θ acute), what is the value of (cos θ − sin θ)/sin θ?

Correct Answer: A [√2]

Explanation:

sin θ = (√2 − 1)cos θ → cot θ = √2 + 1 → (cos θ − sin θ)/sin θ = cot θ − 1 = √2.

22.  
Two points on level ground, 2 m and 32 m from the foot of a tower and in line with it, see its top at complementary angles of elevation. How tall is the tower?

Correct Answer: B [8 m]

Explanation:

tan α × tan (90° − α) = 1 → (h/2)(h/32) = 1 → h² = 64 → h = 8 m.

23.  
Find the value of x² + 1/x² when x is the sum √3 + √2.

Correct Answer: C [10]

Explanation:

1/x = √3 − √2 → x + 1/x = 2√3 → x² + 1/x² = 12 − 2 = 10.

24.  
If a + b + c = 6, ab + bc + ca = 11 and abc = 6, what is a³ + b³ + c³?

Correct Answer: D [36]

Explanation:

a³ + b³ + c³ = (a + b + c)³ − 3(a + b + c)(ab + bc + ca) + 3abc = 216 − 198 + 18 = 36.

25.  
What is the least value of x² − 10x + 32, where x is real?

Correct Answer: A [7]

Explanation:

x² − 10x + 32 = (x − 5)² + 7 → least value 7 at x = 5.

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