SSC CGL Previous Year Question Paper 20th August Shift 1 | QA | Quantitative Ability questions | CGL Past Year Papers

1. SSC CGL 20th August Shift 1 - QA | Circles - SSC

In circle with centre O and radius 13 cm, a chord AB is drawn. Tangentsat A and B intersect at P such that ∠APB = 60°. If Distance of AB from the centre O is 5 cm, then what is the length (in cm) of AP?

A.
12
B.
11
C.
22
D.
24

2. SSC CGL 20th August Shift 1 - QA | Tables & Graphs - SSC

The table shows the daily income of 50 persons.
Study the table and answer the question.

What is the ratio of the number of persons earning less than ₹200 to the number of persons earning ₹300 or more?

A.
6 : 5
B.
3 : 4
C.
3 : 10
D.
6 : 17

3. SSC CGL 20th August Shift 1 - QA | Circles - SSC

In a circle, chords AB and CD intersect internally, at E. If CD = 16 cm, DE = 6 cm, AE = 12 cm, and BE = X cm then the value of x is:

A.
6
B.
17
C.
5
D.
9

4. SSC CGL 20th August Shift 1 - QA | Ratio, Proportion & Variation - SSC

The ratio of two numbers A and B is 5 : 8. If 5 is added to each of A and B, then the ratio becomes 2 : 3. The difference in A and B is:

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

Answer: Option A

Explanation :

The ratio of two numbers A and B is 5 : 8.

Let the two numbers are 5p and 8p respectively.

According to the problem,

$\frac{5 p + 5}{8 p + 5}$ = $\frac{2}{3}$

15p + 15 = 16p + 10

p = 5

Difference in A and B = 8p - 5p

= 3p

= 3 x 5

= 15

Hence, the correct answer is Option A

5. SSC CGL 20th August Shift 1 - QA | Trigonometry - SSC

If sec(5α - 15°) = cosec (15° - 2α), then the value of cos α + sin 2α + tan (1.5α) is:

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

6. SSC CGL 20th August Shift 1 - QA | Trigonometry - SSC

If sin(20 + x)° = cos 60°, 0 ≤ (20 + x) ≤ 90, then find the value of 2 sin² (3x + 15)° - cosec² (2x + 10)°.

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

Answer: Option B

Explanation :

sin (20 + x)° = cos 60°

sin (20 + x)° = sin 30°

20 + x = 30

x = 10

2sin² (3x + 15)° - cosec² (2x + 10)° = 2 sin² 45° - cosec² 30°

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

= 2 $(\frac{1}{2})$ - 4

= 1 - 4

= -3

Hence, the correct answer is Option B

7. SSC CGL 20th August Shift 1 - QA | Percentage, Profit & Loss - SSC

Weight of A is 20% more than weight of B, whose weight is 30% more than weight of C. By how much percent weight of A is more than weight of C?

A.
44
B.
56
C.
69
D.
35.89

Answer: Option B

Explanation :

Weight of B is 30% more than weight of C.

B = $\frac{130}{100}$ × C

Weight of A is 20% more than weight of B.

A = $\frac{120}{100}$ × B = $\frac{120}{100}$ × $\frac{130}{100}$ × C = $\frac{156}{100}$ C

Required percentage = $\frac{\frac{156}{100} C - C}{C}$ × 100

= $\frac{56}{100}$ × 100

= 56%

Hence, the correct answer is Option B

8. SSC CGL 20th August Shift 1 - QA | Time, Speed & Distance - SSC

A takes 2 hours more than B to cover a distance of 40 km. If A doubles his speed, he takes 1 $\frac{1}{2}$ hour more than B to cover 80 km. To cover a distance of 120 km, how much time(in hours) will B take travelling at his same speed?

A.
1 $\frac{2}{3}$
B.
1 $\frac{1}{4}$
C.
1 $\frac{1}{3}$
D.
1 $\frac{1}{2}$

9. SSC CGL 20th August Shift 1 - QA | Simplification - SSC

If $(2 a + \frac{3}{a} - 1)$ = 11, what is the value of $(4 a^{2} + \frac{9}{a^{2}})$ ?

A.
121
B.
148
C.
132
D.
110

Answer: Option C

Explanation :

$(2 a + \frac{3}{a} - 1)$ = 11

2a + $\frac{3}{a}$ = 12

4a² + $\frac{9}{a^{2}}$ + 2.2a $\frac{3}{a}$ = 144

4a² + $\frac{9}{a^{2}}$ + 12 = 144

4a² + $\frac{9}{a^{2}}$ = 132

Hence, the correct answer is Option C

10. SSC CGL 20th August Shift 1 - QA | Simplification - SSC

If a² + b² + c² + 216 = 12(a + b - 2c), then $\sqrt{a b - b c - c a}$ is:

A.
3 $\sqrt{5}$
B.
8 $\sqrt{5}$
C.
6 $\sqrt{5}$
D.
4 $\sqrt{5}$

11. SSC CGL 20th August Shift 1 - QA | Time & Work - SSC

Fourteen persons can do a work in 18 days. After 5 days of work, 6 workers left the work, and joined back onthe last day of the work. In how many days the work got completed?

A.
27
B.
24
C.
12
D.
21

12. SSC CGL 20th August Shift 1 - QA | Trigonometry - SSC

Find the value of tan35° cot40° tan45° cot50° tan55°.

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

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

What is the value of k such that number 72k460k is divisible by 6?

A.
4
B.
7
C.
9
D.
8

14. SSC CGL 20th August Shift 1 - QA | Triangles - SSC

In △ABC,D is a point on side AB such that BD = 3 cm and DA = 4 cm. E is a point on BC such that DE || AC. Then Area of △BDE : Area of trapezium ACED =

A.
40 : 9
B.
33 : 16
C.
16 : 33
D.
9 : 40

15. SSC CGL 20th August Shift 1 - QA | Average, Mixture & Alligation - SSC

The average of squares of five consecutive odd natural numbers is 233. Whatis the average of the largest number and the smallest number?

A.
15
B.
17
C.
11
D.
13

16. SSC CGL 20th August Shift 1 - QA | Simplification - SSC

Simplify (x - y + z)² - (x - y - z)².

A.
4xz - 4yz
B.
2xz + 2yz
C.
4yz - 4xz
D.
4xz + 4yz

17. SSC CGL 20th August Shift 1 - QA | Simplification - SSC

Simplify the following expression:

3 × 8 ÷ 9 of 6 − 2 ÷ 3 × (5 − 2) × 2 + 18 ÷ 3 of 3

A.
-1 $\frac{5}{9}$
B.
2 $\frac{12}{13}$
C.
-4
D.
2 $\frac{1}{3}$

Answer: Option A

Explanation :

3 × 8 ÷ 9 of 6 − 2 ÷ 3 × (5 − 2) × 2 + 18 ÷ 3 of 3

= 3 × 8 ÷ 54 − 2 ÷ 3 × 3 × 2 + 18 ÷ 9

= 3 × $\frac{8}{54}$ - $\frac{2}{3}$ × 3 × 2 + $\frac{18}{9}$

= $\frac{4}{9}$ - 4 + 2

= $\frac{4 - 36 + 8}{9}$

= $\frac{- 14}{9}$

= -1 $\frac{5}{9}$

Hence, the correct answer is Option A

18. SSC CGL 20th August Shift 1 - QA | Simple & Compound Interest - SSC

Acertain sum amounts to ₹81840 in 3 years and to ₹92400 in 5 years at x% p.a under simpleinterest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?

A.
8
B.
10
C.
20
D.
12 $\frac{1}{2}$

19. SSC CGL 20th August Shift 1 - QA | Tables & Graphs - SSC

In factory there are 39 workers who have been categorized into five groups (A, B, C, D, E) on the basis of the range of their daily wages (in multiples of ₹100). The distribution is presented through a Histogram shown below:

What is the ratio of the number of employees whose daily wages are ₹200 or more but less than ₹400 to that of the number of employees whose daily wages are ₹400 or more but less than ₹600?

A.
41 : 23
B.
23 : 41
C.
14 : 23
D.
23 : 14

20. SSC CGL 20th August Shift 1 - QA | Tables & Graphs - SSC

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

Number of students studying Computer Science in the institutes A and C taken together is what percent of the number of students studying Arts in the institutes B and D taken together?

A.
108
B.
200
C.
120
D.
83.3

Answer: Option C

Explanation :

Number of students studying Computer Science in the institutes A and C taken together = 57 + 51 = 108

Number of students studying Arts in the institutes B and D taken together = 45 + 45 = 90

Required percentage = $\frac{108}{90}$ × 100 = 120%

Hence, the correct answer is Option C

21. SSC CGL 20th August Shift 1 - QA | Tables & Graphs - SSC

Bar graph shows the number of males and females in five organizations A, B, C, D and E.

For which organisation, difference between the number of males and the average number of females of all the organisations is minimum?

A.
D
B.
C
C.
A
D.
B

Answer: Option D

Explanation :

The average number of females in all the organisations = $\frac{300 + 275 + 250 + 200 + 125}{5}$ = $\frac{1150}{5}$ = 230

For Organisation A, difference between the number of males and the average number of females of all the organisations = 250 - 230 = 20

For Organisation B, difference between the number of males and the average number of females of all the organisations = 230 - 225 = 5

For Organisation C, difference between the number of males and the average number of females of all the organisations = 325 - 230 = 95

For Organisation D, difference between the number of males and the average number of females of all the organisations = 275 - 230 = 45

∴ For Organisation B, difference between the number of males and the average number of females of all the organisations is minimum.

Hence, the correct answer is Option D

22. SSC CGL 20th August Shift 1 - QA | Triangles - SSC

Triangle ABC is an equilateral triangle. D and E are points on AB and AC respectively such that DE is parallel to BC and is equal to half the length of BC. If AD + CE + BC = 30 cm, then find the perimeter (in cm) of the quadrilateral BCED.

A.
37.5
B.
25
C.
45
D.
35

Answer: Option A

Explanation :

Triangle ABC is an equilateral triangle.

Let the length of BC = 2p

BC = AB = AC = 2p

DE is equal to half the length of BC.

Triangle ABC and triangle ADE are similar triangles.

⇒ $\frac{A D}{A B}$ = $\frac{D E}{B C}$

⇒ $\frac{A D}{A B}$ = $\frac{p}{2 p}$

⇒ AD = $\frac{1}{2}$ AB

⇒ AD = $\frac{1}{2}$ × 2p

⇒ AD = p

Similarly, AE = p

and EC = AC - AE = 2p - p = p

AD + CE + BC = 30 cm

p + p + 2p = 30

4p = 30

p = $\frac{15}{2}$ cm

Perimeter of the quadrilateral BCED = BD + DE + CE + BC

= p + p + p + 2p

= 5p

= 5 × $\frac{15}{2}$

= 37.5 cm

Hence, the correct answer is Option A

23. SSC CGL 20th August Shift 1 - QA | Percentage, Profit & Loss - SSC

An article is marked 27% above its cost price. If x % discount is allowed on the marked price and still there is a profit of 6.68%, then what is the value of x ?

A.
15
B.
20
C.
16
D.
12.5

Answer: Option C

Explanation :

Let the cost price of the article = 100C

Profit = 6.68%

Selling price of the article = 106.68C

Article is marked 27% above its cost price.

Marked price of the article = 127C

Discount = x%

Selling price of the article = $\frac{100 - x}{100}$ × 127C

⇒ $\frac{100 - x}{100}$ × 127C = 106.68C

⇒ 100 - x = $\frac{10668}{127}$

⇒ 100 - x = 84

⇒ x = 16

Hence, the correct answer is Option C

24. SSC CGL 20th August Shift 1 - QA | Coordinate Geometry - SSC

The area of a quadrant of a circle is $\frac{π}{9}$ m². Its radius (in metres) is equal to:

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

Answer: Option A

Explanation :

Let the radius of the circle = r

Area of the quadrant of the circle = $\frac{π}{9}$ m².

$\frac{1}{4}$ × πr² = $\frac{π}{9}$

r² = $\frac{4}{9}$

r = $\frac{2}{3}$

Radius of the circle = $\frac{2}{3}$ m

Hence, the correct answer is Option A

25. SSC CGL 20th August Shift 1 - QA | Percentage, Profit & Loss - SSC

A sold an article to B at a profit of 25%. B sold it to C at a profit of 15%. The profit made by B is ₹40 less than the profit made by A. What is the cost price (in ₹) of the article for A?

A.
240
B.
640
C.
546
D.
400

Answer: Option B

Explanation :

Let the cost price of A = 100C

Profit percentage of A = 25%

Profit of A = $\frac{25}{100}$ × 100C = 25C

Selling price of A = Cost price of B = 100C + 25C = 125C

Profit percentage of B = 15%

Profit of B = $\frac{15}{100}$ × 125C = $\frac{75}{4}$ C

The profit made by B is ₹40 less than the profit made by A.

$\frac{75}{4}$ C = 25C - 40

25C - $\frac{75}{4}$ C = 40

$\frac{25}{4}$ C = 40

C = $\frac{32}{5}$

Cost price of the article for A = 100C = 100 × $\frac{32}{5}$ = Rs. 640

Hence, the correct answer is Option B

SSC CGL 20th August Shift 1 - QA

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