SSC CGL Previous Year Question Paper 18th August Shift 3 | QA | Quantitative Ability questions | CGL Past Year Papers

1. SSC CGL 18th August Shift 3 - QA | Tables & Graphs - SSC

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

Number of students studying commerce in institute D is what percent of the total number of students of the 5 institutes?

A.
5.5
B.
5.3
C.
27.7
D.
20.1

2. SSC CGL 18th August Shift 3 - QA | Triangles - SSC

In △ABC,AB and AC produced to points D and E respectively. If the bisectors of angle CBD and angle BCE meet at point O, such that ∠BOC = 63°, then ∠A = ?

A.
36°
B.
27°
C.
54°
D.
63°

3. SSC CGL 18th August Shift 3 - QA | Simplification - SSC

Simplify the expression

441 ÷ [270 ÷ $\frac{3}{7}$ + (17 ÷ $\frac{1}{3}$ ) - (8 $\frac{1}{2}$ - $\frac{5}{2}$ )]

A.
$\frac{39}{75}$
B.
$\frac{29}{75}$
C.
$\frac{19}{75}$
D.
$\frac{49}{75}$

4. SSC CGL 18th August Shift 3 - QA | Circles - SSC

Points A and B are on a circle with centre O. Point C is on the major are AB. If ∠OAC=35° and ∠OBC=45°, then what is the measure (in degrees) of the angle subtended by the minor are AB at the centre?

A.
70
B.
160
C.
80
D.
100

5. SSC CGL 18th August Shift 3 - QA | Tables & Graphs - SSC

then what is the measure (in degrees) of the angle subtended by the minor are AB at the centre?

Expenditure on food is what percent more than expenditure on rent?

A.
$\frac{200}{3}$ %
B.
$\frac{100}{3}$ %
C.
50%
D.
$\frac{50}{3}$ %

6. SSC CGL 18th August Shift 3 - QA | Time & Work - SSC

Five men can complete a work in 20 days. Ten women can complete the same work in 15 days. Two men and six women started working together. After 5 days, three women left the work and a new man joined the work. The group continued working togethertill the end of the work. In how many days will they be able to do the remaining work?

A.
16 $\frac{2}{3}$
B.
14
C.
18 $\frac{1}{3}$
D.
19

7. SSC CGL 18th August Shift 3 - QA | Percentage, Profit & Loss - SSC

A T.V. is sold at 8%gain. Hadit been sold for ₹2553 less; there would have beenloss of 15%. To gain 18%, the selling price (in ₹) of T.V. would be:

A.
13098
B.
15000
C.
9102
D.
11100

8. SSC CGL 18th August Shift 3 - QA | Time, Speed & Distance - SSC

If a train runs with the speed of 72 km/h, it reaches its destination late by 15 minutes. However,if its speed is 90 km/h, it is late by only 5 minutes. The correct time to cover its journey in minutes is:

A.
45
B.
40
C.
35
D.
32

9. SSC CGL 18th August Shift 3 - QA | Triangles - SSC

What is the length (in cm) of the smallest altitude of the triangle whose sides are 5 cm, 12 cm and 13 cm? (correct to one decimal place)

A.
12.0
B.
5.1
C.
2.6
D.
4.6

10. SSC CGL 18th August Shift 3 - QA | Triangles - SSC

In a right angled triangle ABC, the lengths ofthe sides containing the right angle are 5 cm and 12 cm respectively. A circle is inscribed in the triangle ABC. Whatis the radius ofthe circle (in cm)?

A.
2
B.
2.8
C.
2.5
D.
3

11. SSC CGL 18th August Shift 3 - QA | Average, Mixture & Alligation - SSC

In a right angled triangle ABC, the lengths ofthe sides containing the right angle are 5 cm and 12 cm respectively. A circle is inscribed in the triangle ABC. Whatis the radius ofthe circle (in cm)?

A.
55 $\frac{5}{9}$ %
B.
33 $\frac{4}{9}$ %
C.
44 $\frac{4}{9}$ %
D.
66 $\frac{4}{9}$ %

12. SSC CGL 18th August Shift 3 - QA | Ratio, Proportion & Variation - SSC

Keshav, Surjeet and Thomasstarted a business with investments in the ratio 2 : 3 : 4. The ratio of their period of investments is 5 : 6 : 9. Twenty percentof the profit was spent on rent and maintenanceof the office. Remaining profit was distributed among themselves.If the difference in the shares of profit of Keshav and Surjeet is ₹7264, then how muchis the total profit (in ₹)?

A.
72640
B.
46490
C.
51060
D.
58112

13. SSC CGL 18th August Shift 3 - QA | Simplification - SSC

If a + b + c = 0, then what is the value of $\frac{{(b + c)}^{2}}{b c}$ + $\frac{{(c + a)}^{2}}{c a}$ + $\frac{{(a + b)}^{2}}{a b}$ ?

A.
1
B.
-3
C.
-1
D.
3

14. SSC CGL 18th August Shift 3 - QA | Simplification - SSC

If x - $\frac{1}{x}$ = $\sqrt{77}$ , then one of the values of x³ + $\frac{1}{x^{3}}$ is:

A.
80 $\sqrt{77}$
B.
-702
C.
77 $\sqrt{77}$
D.
3 $\sqrt{77}$

Answer: Option B

Explanation :

x - $\frac{1}{x}$ = $\sqrt{77}$

${(x - \frac{1}{x})}^{2}$ = $\sqrt{77}$

x² + $\frac{1}{x^{2}}$ = 79

x² + $\frac{1}{x^{2}}$ + 2 = 81

${(x + \frac{1}{x})}^{2}$ = 81

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

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

x³ + $\frac{1}{x^{3}}$ + 3.x. $\frac{1}{x}$ $(x + \frac{1}{x})$ = -729

x³ + $\frac{1}{x^{3}}$ + 3(-9) = -729

x³ + $\frac{1}{x^{3}}$ - 27 = -729

x³ + $\frac{1}{x^{3}}$ = -702

Hence, the correct answer is Option B

15. SSC CGL 18th August Shift 3 - QA | Average, Mixture & Alligation - SSC

The average daily production of toys in a factory in the month of December is 512. If the average production during first 20 days is 515 and that of the last 13 days is 510, then what is the average of production on 19 and 20 December?

A.
1058
B.
513
C.
529
D.
512

Answer: Option C

Explanation :

The average daily production of toys in a factory in the month of December is 512.

Total production of toys in the month of December = 512 x 31 = 15872........(1)

The average production during first 20 days is 515.

Total production during first 20 days = 515 x 20 = 10300

Production during first 18 days + 19 December + 20 December = 10300........(2)

The average production during last 13 days is 510.

Total production during last 13 days = 510 x 13 = 6630

19 December + 20 December + Production during last 11 days = 6630........(3)

Solving (2) + (3) - (1), we get

19 December + 20 December = 10300 + 6630 - 15872

19 December + 20 December = 1058

Total production on 19 and 20 December = 1058

Average of production on 19 and 20 December = $\frac{1058}{2}$ = 529

Hence, the correct answer is Option C

16. SSC CGL 18th August Shift 3 - QA | Simple & Compound Interest - SSC

A sum of money was lentin two parts in the ratio 4 : 5 for 4 years and 5 years respectively, both at the rate of 8% per annum simple interest. If the difference between the interests earned from the twoparts is ₹ 4680, then what was the total sum lent(in ₹)?

A.
538500
B.
42120
C.
46800
D.
65000

17. SSC CGL 18th August Shift 3 - QA | Percentage, Profit & Loss - SSC

A shopkeeper bought a machine for ₹4600 and spent ₹500 on its repairs and transport. He marked the machine at 8% above the over all cost price. If he sold the machine for ₹4681.80 after giving x% discount, then the value of x is:

A.
15
B.
20
C.
12
D.
18

Answer: Option A

Explanation :

Total cost price = 4600 + 500 = ₹5100

Marked price = $\frac{108}{100}$ × 5100 = ₹5508

Discount = x%

Selling price = ₹4681.80

100 - x = $\frac{468180}{5508}$

100 - x = 85

x = 15

Hence, the correct answer is Option A

18. SSC CGL 18th August Shift 3 - QA | Circles - SSC

In a circle with centre O, AB and CD are parallel chords on the opposite sides of a diameter. If AB = 12 cm, CD = 18 cm and the distance between the chords AB and CD is 15 cm, then find the radius of the circle (in cm).

A.
9 $\sqrt{13}$
B.
9
C.
3 $\sqrt{13}$
D.
12

Answer: Option C

Explanation :

From triangle AJO,

r² = 6² + (15 - x)²

r² = 36 + (15 - x)² ...(1)

From triangle CKO,

r² = 9² + x²

r² = 81 + x² ...(2)

From (1) and (2),

36 + (15 - x)² = 81 + x²

225 + x² - 30x = 45 + x²

30x = 180

x = 6

From (2),

r² = 81 + x²

r² = 81 + 6²

r² = 81 + 36

r² = 137

r = 3 $\sqrt{13}$

Hence, the correct answer is Option C

19. SSC CGL 18th August Shift 3 - QA | Trigonometry - SSC

If sin(A + B) = 1 and cos(A - B) = $\frac{\sqrt{3}}{2}$ , A + B ≤ 90° and A > B, then the value of $\frac{5 \sin^{2} B + 4 \tan^{2} A}{2 \sin B \cos A}$ is:

A.
16 $\frac{1}{2}$
B.
18
C.
20
D.
26 $\frac{1}{2}$

20. SSC CGL 18th August Shift 3 - QA | Trigonometry - SSC

If sin⁶ θ + cos⁶ θ = $\frac{1}{3}$ , 0° < θ < 90°, then what is the value of sin θ cos θ?

A.
$\frac{\sqrt{2}}{3}$
B.
$\frac{\sqrt{6}}{6}$
C.
$\frac{\sqrt{2}}{\sqrt{3}}$
D.
$\frac{2}{9}$

Answer: Option A

Explanation :

sin⁶ θ + cos⁶ θ = $\frac{1}{3}$

(sin² θ)³ + (cos² θ)³ = $\frac{1}{3}$

(sin² θ + cos² θ) (sin⁴ θ - sin² θ cos² θ + cos⁴ θ) = $\frac{1}{3}$

(1) (sin⁴ θ + cos⁴ θ + 2 sin² θ cos² θ - 3 sin² θ cos² θ) = $\frac{1}{3}$

(sin² θ + cos² θ)² - 3 sin² θ cos² θ = $\frac{1}{3}$

1 - 3 sin² θ cos² θ = $\frac{1}{3}$

3 sin² θ cos² θ = $\frac{2}{3}$

sin² θ cos² θ = $\frac{2}{9}$

sin θ cos θ = $\frac{\sqrt{2}}{3}$

Hence, the correct answer is Option A

21. SSC CGL 18th August Shift 3 - QA | Simplification - SSC

If a³ - b³ = 2349 and (a - b) = 9, then (a + b)² - ab is equal to:

A.
280
B.
244
C.
261
D.
229

22. SSC CGL 18th August Shift 3 - QA | Number Theory - SSC

If a number P is divisible by 2 and another number Q is divisible by 3, then which of the following is true?

A.
P + Q is divisible by 6
B.
P + Q is divisible by 5
C.
P × Q is divisible by 6
D.
P × Q is divisible by 5

23. SSC CGL 18th August Shift 3 - QA | Tables & Graphs - SSC

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

How many persons earn ₹250 or more but less than ₹350 daily?

A.
18
B.
24
C.
28
D.
14

24. SSC CGL 18th August Shift 3 - QA | Trigonometry - SSC

(sec θ + tan θ)² + $\frac{1 + \cos e c θ}{1 - \cos e c θ}$ , 0° < θ < 90° is:

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

25. SSC CGL 18th August Shift 3 - QA | Tables & Graphs - SSC

The following table shows the daily seats occupancy in different classes of a train. Numbers in bracket represent the total seats available for a particular class.

What is the ratio of number of seats that remained vacant in all the Non-AC classes on Wednesday and Thursday taken together to number of seats remained vacant in AC classes on Monday, Tuesday and Friday?

A.
62 : 35
B.
39 : 62
C.
62 : 39
D.
35 : 62

SSC CGL 18th August Shift 3 - QA

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