SSC CGL Previous Year Question Paper 20th August Shift 2 | QA | Quantitative Ability questions | CGL Past Year Papers

1. SSC CGL 20th August Shift 2 - QA | Number Theory - SSC

What is the sum of the digits of the largest five digit number which is divisible by 5, 35, 39 and 65?

A.
30
B.
33
C.
27
D.
35

2. SSC CGL 20th August Shift 2 - QA | Tables & Graphs - SSC

331

A.
324
B.
303
C.
328
D.

Answer: Option A

Explanation :

The total marks obtained by Anuj in all the five subjects = $\frac{80}{100}$ × 75 + $\frac{55}{100}$ × 80 + $\frac{68}{100}$ × 100 + $\frac{66}{100}$ × 50 + $\frac{84}{100}$ × 150

= 60 + 44 + 68 + 33 + 126

= 331

Hence, the correct answer is Option A

3. SSC CGL 20th August Shift 2 - QA | Triangles - SSC

Points P and Q are on the sides AB and BC respectively of a triangle ABC, right angled at B. If AQ = 11 cm, PC = 8 cm, and AC = 13 cm, then find the length (in cm) of PQ.

A.
$\sqrt{15}$
B.
4.5
C.
4
D.
4 $\sqrt{17}$

4. SSC CGL 20th August Shift 2 - QA | Percentage, Profit & Loss - SSC

A shopkeeper sold two items. The selling price of the first item equals the cost price of the second item. He sold the first item at a profit of 20% and the second item at a loss of 10%. What is his overall profit’ loss percent?

A.
Profit, 3 $\frac{7}{11}$ %
B.
Loss, 4 $\frac{6}{11}$ %
C.
Profit, 4 $\frac{7}{11}$ %
D.
Loss, 8 $\frac{1}{3}$ %

Answer: Option A

Explanation :

Let the cost price of first item = 100C

Profit on first item = 20%

Selling price of first item = $\frac{120}{100}$ × 100C = 120C

The selling price of the first item equals the cost price of the second item.

Cost price of the second item = 120C

Loss on second item = 10%

Selling price of second item = $\frac{90}{100}$ = 120C = 108C

Total cost price = 100C + 120C = 220C

Total selling price = 120C + 108C = 228C

Overall profit percentage = $\frac{228 C - 220 C}{220 C}$ × 100

= $\frac{8 C}{220 C}$ × 100

= $\frac{40}{11}$

= 3 $\frac{7}{11}$ %

Hence, the correct answer is Option A

5. SSC CGL 20th August Shift 2 - QA | Percentage, Profit & Loss - SSC

What price (in ₹) should Radha mark on a bag which costs ₹1680 so as to earn a profit of 25% after allowing a discount of 16% on the marked price?

A.
2800
B.
2000
C.
2100
D.
2500

Answer: Option D

Explanation :

Cost price of the bag = ₹1680

Profit = 25%

Selling price of the bag = $\frac{125}{100}$ × 1680

Let the marked price of the bag = M

Discount = 16%

Selling price of the bag = $\frac{84}{100}$ × M

⇒ $\frac{84}{100}$ × M = $\frac{125}{100}$ × 1680

⇒ M = 2500

Marked price of the bag = M = ₹2500

Hence, the correct answer is Option D

6. SSC CGL 20th August Shift 2 - QA | Simple Equation - SSC

If $\frac{x}{y}$ + $\frac{y}{x}$ = 2, (x, y ≠ 0), then the value of (x - y) is:

A.
1
B.
0
C.
2
D.
-2

Answer: Option B

Explanation :

$\frac{x}{y}$ + $\frac{y}{x}$ = 2

$\frac{x^{2} + y^{2}}{x y}$ = 2

x² + y² = 2xy

x² + y² - 2xy = 0

(x - y)² = 0

x - y = 0

Hence, the correct answer is Option B

7. SSC CGL 20th August Shift 2 - QA | Tables & Graphs - SSC

The data given in the table shows the number of students studying in 4 different disciplines in 5 institutes. Study the table and answer the question:

What is the ratio of number of students studying Science in institutes C and D taken together to the number of students studying Computer Science in institutes A and E taken together?

A.
41 : 56
B.
43 : 56
C.
42 : 55
D.
3 : 4

8. SSC CGL 20th August Shift 2 - QA | Lines & Angles - SSC

Points A, D, C, B and E are concyclic. If ∠AEC = 50° and ∠ABD = 30°, then what is the measure(in degrees) of ∠CBD?

A.
20
B.
10
C.
15
D.
30

9. SSC CGL 20th August Shift 2 - QA | Trigonometry - SSC

If 2 cos² θ - 5 cos θ + 2 = 0, 0° < θ < 90°, then the value of (sec θ + tan θ) is:

A.
2 + $\sqrt{3}$
B.
1 - $\sqrt{3}$
C.
1 + $\sqrt{3}$
D.
2 - $\sqrt{3}$

Answer: Option A

Explanation :

2 cos² θ - 5 cos θ + 2 = 0

2 cos² θ - 4 cos θ - cos θ + 2 = 0

2 cos θ (cos θ - 2) - 1 (cos θ - 2) = 0

(cos θ - 2) (2 cos θ - 1) = 0

cos θ = 2 or cos θ = $\frac{1}{2}$

cos θ = 2 is not possible.

So, cos θ = $\frac{1}{2}$

sec θ = 2

tan θ = $\sqrt{s e c^{2} θ - 1}$ = $\sqrt{4 - 1}$ = $\sqrt{3}$

∴ (sec θ + tan θ) = 2 + $\sqrt{3}$

Hence, the correct answer is Option A

10. SSC CGL 20th August Shift 2 - QA | Simplification - SSC

If (56 $\sqrt{7}$ $x^{3}$ - 2 $\sqrt{2}$ $y^{3}$ ) ÷ (2 $\sqrt{7}$ x - $\sqrt{2}$ y) = Ax² + By² - Cxy, then find the value of A + B - $\sqrt{14}$ C.

A.
38
B.
10
C.
19
D.
58

Answer: Option D

Explanation :

(56 $\sqrt{7}$ $x^{3}$ - 2 $\sqrt{2}$ $y^{3}$ ) ÷ (2 $\sqrt{7}$ x - $\sqrt{2}$ y) = Ax² + By² - Cxy

$\frac{(2 \sqrt{7} x - \sqrt{2} y) (28 x^{2} + 2 \sqrt{14} x y + 2 y^{2})}{(2 \sqrt{7} x - \sqrt{2} y)}$ = Ax² + By² - Cxy

28x²+ 2 $\sqrt{14}$ xy + 2y²= Ax²+ By²- Cxy

Comparing both sides,

A = 28, B = 2, C = -2 $\sqrt{14}$

A + B - $\sqrt{14}$ C = 28 + 2 - $\sqrt{14}$ (-2 $\sqrt{14}$ )

= 30 + 28

= 58

Hence, the correct answer is Option D

11. SSC CGL 20th August Shift 2 - QA | Coordinate Geometry - SSC

The volume of a wall whose height is 10 times its width and whose length is 8 times its height is 51.2 m³. What is the cost(in ₹) of painting the wall on one side at the rate of ₹100/m²?

A.
12800
B.
12750
C.
12250
D.
12500

Answer: Option A

Explanation :

Let the width of the wall = b

Height of the wall = 10b

Length of the wall = 8 x Height = 8 x 10b = 80b

Volume of the wall = 51.2 m³

length x width x height = 51.2

80b x b x 10b = 51.2

8000b³ = 512

b = $\frac{8}{20}$

b = $\frac{2}{5}$ m

Area of one side of the wall = length x height = 80b x 10b = 800b³ = 800 × $\frac{4}{25}$ = 128 m²

The cost of painting the wall on one side at the rate of ₹100/m² = 128 × 100 = ₹12800

Hence, the correct answer is Option A

12. SSC CGL 20th August Shift 2 - QA | Ratio, Proportion & Variation - SSC

The ratio of monthly incomes of A and B is 4 : 5 and that of their monthly expenditures is 3 : 8. If the income of A is equal to the expenditure of B, then what is the ratio of savings of A and B?

A.
3 : 8
B.
2 : 5
C.
8 : 3
D.
5 : 2

Answer: Option D

Explanation :

The ratio of monthly incomes of A and B is 4 : 5.

Let the monthly incomes of A and B are 4p and 5p respectively.

The income of A is equal to the expenditure of B.

Monthly expenditure of B = 4p

The ratio of monthly expenditures of A and B is 3 : 8.

Monthly expenditure of A = $\frac{3}{8}$ × 4p = $\frac{3}{2}$ p

The ratio of savings of A and B = (4p - $\frac{3}{2}$ p) : (5p - 4p)

= $\frac{5}{2}$ p : p

= 5 : 2

Hence, the correct answer is Option D

13. SSC CGL 20th August Shift 2 - QA | Time & Work - SSC

Two pipes A and can fill an empty tank in 10 hours and 16 hours respectively. They are opened alternately for 1 hour each, opening pipe first. In how many hours, will the empty tank be filled?

A.
14 $\frac{2}{5}$
B.
16 $\frac{2}{5}$
C.
10 $\frac{2}{5}$
D.
12 $\frac{2}{5}$

14. SSC CGL 20th August Shift 2 - QA | Trigonometry - SSC

If cot θ = $\frac{15}{8}$ , θ is an acute angle, then find the value of $\frac{(1 - \cos θ) (2 + 2 \cos θ)}{(2 - 2 \sin θ) (1 + \sin θ)}$ .

A.
$\frac{225}{64}$
B.
$\frac{64}{225}$
C.
$\frac{16}{15}$
D.
$\frac{8}{15}$

Answer: Option B

Explanation :

cot θ = $\frac{15}{8}$

tan θ = $\frac{8}{15}$

sec θ = $\sqrt{1 + \tan^{2} θ}$ = $\sqrt{1 + {(\frac{8}{15})}^{2}}$ = $\sqrt{\frac{289}{225}}$ = $\frac{17}{15}$

cos θ = $\frac{15}{17}$

sin θ = $\sqrt{1 - \cos^{2} θ}$ = $\sqrt{1 - {(\frac{15}{17})}^{2}}$ = $\sqrt{1 - \frac{225}{289}}$ = $\frac{64}{289}$ = $\frac{8}{17}$

$\frac{(1 - \cos θ) (2 + 2 \cos θ)}{(2 - 2 \sin θ) (1 + \sin θ)}$ = $\frac{(1 - \frac{15}{17}) [2 + 2 (\frac{15}{17})]}{[2 - 2 (\frac{8}{17})] (1 + \frac{8}{17})}$

= $\frac{(\frac{2}{17}) [\frac{64}{17}]}{[\frac{18}{17}] (\frac{25}{17})}$

= $\frac{2 \times 64}{18 \times 25}$

= $\frac{64}{225}$

Hence, the correct answer is Option B

15. SSC CGL 20th August Shift 2 - QA | Average, Mixture & Alligation - SSC

The present population of a village is 15280. If the number of males increases by 25% and the number of females increases by 15%, then the population will become 18428. The difference between present population of males and females in the village is:

A.
1840
B.
920
C.
2760
D.
1380

Answer: Option A

Explanation :

The present population of a village is 15280.

Let the number of males and females of the village are M and F respectively.

M + F = 15280............(1)

If the number of males increases by 25% and the number of females increases by 15%, then the population will become 18428.

$\frac{125}{100}$ M + $\frac{115}{100}$ F = 18428

25M + 115F = 18428 x 100

25M + 23F = 368560.........(2)

Solving 25 x (1) - (2), we get

25F - 23F = 382000 - 368560

2F = 13440

F = 6720

Substituting F = 6720 in equation (1),

M + 6720 = 15280

M = 8560

The difference between present population of males and females in the village = 8560 - 6720 = 1840

Hence, the correct answer is Option A

16. SSC CGL 20th August Shift 2 - QA | Tables & Graphs - SSC

Study the following table and answer the question:
Percentage of marks obtained by six students in five subjects A, B, C, D & E.

The total marks obtained by Amit in subjects A, B and C is what percent less than the total marks obtained by Vikram in subjects B, C, D and E?

A.
42
B.
35
C.
40
D.
38

Answer: Option C

Explanation :

Total marks obtained by Amit in subjects A, B and C = $\frac{64}{100}$ × 75 + $100$ × 80 + $\frac{80}{100}$ × 100 = 48 + 52 + 80 = 180

Total marks obtained by Vikram in subjects B, C, D and E = $\frac{70}{100}$ × 80 + $\frac{73}{100}$ × 100 + $\frac{84}{100}$ × 50 + $\frac{86}{100}$ × 150 = 56 + 73 + 42 + 129 = 300

Required percentage = $\frac{300 - 180}{300}$ × 100 = 40%

Hence, the correct answer is Option C

17. SSC CGL 20th August Shift 2 - QA | Simplification - SSC

Simplify the following expression:

15 ÷ 3 of 2 × 4 + 9 ÷ 18 of 2 × 3 − 4 ÷ 8 × 2

A.
12 $\frac{3}{4}$
B.
39 $\frac{3}{4}$
C.
42 $\frac{3}{4}$
D.
9 $\frac{3}{4}$

Answer: Option D

Explanation :

15 ÷ 3 of 2 × 4 + 9 ÷ 18 of 2 × 3 − 4 ÷ 8 × 2

= 15 ÷ 6 × 4 + 9 ÷ 36 × 3 − 4 ÷ 8 × 2

= $\frac{15}{6}$ × 4 + $\frac{9}{36}$ × 3 - $\frac{4}{8}$ × 2

= 10 + $\frac{3}{4}$ - 1

= 9 $\frac{3}{4}$

Hence, the correct answer is Option D

18. SSC CGL 20th August Shift 2 - QA | Tables & Graphs - SSC

The table shows the daily income (in ₹) of 50 persons.
Study the table and answer the question:

What is the percentage of persons earning ₹250 or more?

A.
52
B.
68
C.
32
D.
48

Answer: Option D

Explanation :

Number of persons earning less than ₹200 = 12

Number of persons earning between ₹200 and ₹250 = 26 - 12 = 14

Number of persons earning between ₹250 and ₹300 = 34 - 26 = 8

Number of persons earning between ₹300 and ₹350 = 40 - 34 = 6

Number of persons earning between ₹350 and ₹400 = 50 - 40 = 10

Percentage of persons earning ₹250 or more = $\frac{8 + 6 + 10}{50}$ × 100 = 48%

Hence, the correct answer is Option D

19. SSC CGL 20th August Shift 2 - QA | Simple Equation - SSC

If $\sqrt{x}$ - $\frac{1}{\sqrt{x}}$ = $\sqrt{7}$ , then the value of x² + $\frac{1}{x^{2}}$ is:

A.
81
B.
60
C.
79
D.
75

Answer: Option C

Explanation :

$\sqrt{x}$ - $\frac{1}{\sqrt{x}}$ = $\sqrt{7}$

${(\sqrt{x} - \frac{1}{\sqrt{x}})}^{2}$ = ${(\sqrt{7})}^{2}$

x + $\frac{1}{x}$ - 2 = 7

x + $\frac{1}{x}$ = 9

${(x + \frac{1}{x})}^{2}$ = 9²

x² + $\frac{1}{x^{2}}$ + 2 = 81

x² + $\frac{1}{x^{2}}$ = 79

Hence, the correct answer is Option C

20. SSC CGL 20th August Shift 2 - QA | Trigonometry - SSC

If cos(2θ + 54°) = sin θ, 0° < (2θ + 54°) < 90°, then what is the value of $\frac{1}{c o t 5 θ + s e c \frac{5 θ}{2}}$ ?

A.
$\frac{\sqrt{3}}{2}$
B.
$\frac{2 \sqrt{3}}{3}$
C.
$\frac{\sqrt{3}}{3}$
D.
$\frac{1}{3}$

21. SSC CGL 20th August Shift 2 - QA | Triangles - SSC

The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is 50° less than that of the largest angle, then find the largest angle (in degrees).

A.
90
B.
85
C.
80
D.
75

22. SSC CGL 20th August Shift 2 - QA | Average, Mixture & Alligation - SSC

The average monthly salary of 60 employees of a factory is ₹29900. If two officers are getting ₹90000 each and the average salary of 8 supervisors is ₹65000, then what is the average salary (in ₹) of the remaining employees?

A.
22680
B.
29080
C.
21080
D.
21880

Answer: Option D

Explanation :

The average monthly salary of 60 employees of the factory is ₹29900.

Total monthly salary of 60 employees of the factory = 29900 x 60 = ₹1794000

Two officers are getting ₹90000 each.

Sum of the salary of two officers = 2 x 90000 = ₹180000

The average salary of 8 supervisors is ₹65000.

Total salary of 8 supervisors = 65000 x 8 = ₹520000

Total salary of remaining 50 employees of the factory = 1794000 - 180000 - 520000 = ₹1094000

Average of remaining 50 employees of the factory = $\frac{1094000}{50}$ = ₹21880

Hence, the correct answer is Option D

23. SSC CGL 20th August Shift 2 - QA | Circles - SSC

Two circles of radii 18 cm and 16 cm intersect each other and the length of their common chord is 20 cm. What is the distance (in cm) between their centres?

A.
4 $\sqrt{2}$ - 2 $\sqrt{39}$
B.
4 $\sqrt{10}$ - 2 $\sqrt{39}$
C.
4 $\sqrt{10}$ + 2 $\sqrt{39}$
D.
4 $\sqrt{14}$ + 2 $\sqrt{39}$

Answer: Option D

Explanation :

From triangle AGH,

AH² + GH² = AG²

AH² + 10² = 16²

AH² + 100 = 256

AH² = 156

AH = 2 $\sqrt{39}$

From triangle CGH,

CH² + GH² = CG²

CH² + 10² = 18²

CH² + 100 - 324

CH² = 224

CH = 4 $\sqrt{14}$

Distance between centres of circles = AC = AH + CH = 2 $\sqrt{39}$ + 4 $\sqrt{14}$

Hence, the correct answer is Option D

24. SSC CGL 20th August Shift 2 - QA | Simple & Compound Interest - SSC

The interest (in ₹) to be paid on a sum of ₹30000 at 15% p.a. after 2 $\frac{2}{3}$ years, if interest compounded yearly, is:

A.
14362.50
B.
12364.50
C.
16342.50
D.
13642.50

25. SSC CGL 20th August Shift 2 - QA | Time, Speed & Distance - SSC

A boat can go 5 km upstream and 7 $\frac{1}{2}$ km downstream in 45 minutes.It can also go 5 km downstream and 2.5 km upstream in 25 minutes. How muchtime(in minutes) will it take to go 6 km downstream?

A.
10
B.
12
C.
15
D.
20

SSC CGL 20th August Shift 2 - QA

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