SSC CGL CGL Quant PYQ (2019–21) Questions & Solutions

A sample of real SSC CGL CGL Quant PYQ (2019–21) past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 74 CGL Quant PYQ (2019–21) questions in all — sign up free to practise them timed.

1. Q1.SSC 2019

   The length, breadth and height of a cuboidal box are in the ratio of 7:5:3 and its whole surface area is 27,832 cm². Its volume is -

   • 288120 cm³

   • 265390 cm³

   • 207505 cm³

   • 329000 cm³

   Show solution

   Total surface area of a cuboid = 2(lb+bh+lh) Here, l = Length ; b= breadth ; h= height Let, Length= 7P ; Breadth= 5P ; Height=3P According to question, 2(lb+bh+lh)=27832 =>2(7P×5P+5P×3P+7P×3P)=27832 =>35P²+15P²+21P² = 27832/2 =>71P²=13916 =>P²=13916/71 =>P =√196 => P=14 :.Volume of the cuboid= lbh =7×14×5×14×3×14 cm³ = 288120 cm³
2. Q2.SSC 2019

   Find the value of 1800÷20×{(12-6)+(24-12)}

   • 1530

   • 1620

   • 1390

   • 1800

   Show solution

   1800÷20×{(12-6)+(24-12)} =1800÷20×(6+12) =1800÷20×18 =90×18 =1620
3. Q3.SSC 2019

   If 6tanθ - 5√3secθ + 12cotθ = 0, (0°< θ < 90°),then find the value of ( cosecθ + secθ).

   • 2/3( 3+√3)

   • 1/3( 2+√3)

   • 2/5( 3+√5)

   • 1/5( 2+√3)

   Show solution

   Let, θ=60° Using value putting method, 6tanθ - 5√3secθ + 12cotθ = 6tan60° -5√3sec60° + 12cot60° = 6√3 - 5√3 ×2 + 12 × 1/√3 = 6√3 -10√3 +4√3 = 0 L.H.S = R.H.S (satisfied) Now, ( cosec θ + sec θ) =cosec 60°+sec 60° = 2/√3 + 2 = (2+2√3)/√3 = 2/3(3+√3)
4. Q4.SSC 2019

   If A+B=12 and AB=17, what is the value of A³+B³?

   • 996

   • 1116

   • 1326

   • 1556

   Show solution

   A³ + B³ = (A + B)(A² + B² - AB) = (A + B){(A + B)² - 2AB - AB} = 12 × { (12)² - 3 × 17} = 12 × (144 - 51) = 12 × 93 = 1116
5. Q5.SSC 2019

   (3a - 4b)³ is equal to-

   • 27a³ - 64b³

   • 9a² - 24ab + 16b²

   • 27a³ - 64b³ - 108a²b + 144ab²

   • 9a² - 16b²

   Show solution

   (3a - 4b)³ = (3a)³ - 3 × (3a)² × 4b + 3 × 3a × (4b)² - (4b)³ = 27a³ - 108a²b + 144ab² - 64b³ = 27a³ - 64b³ - 108a²b + 144ab² Comment
6. Q6.SSC 2020

   If 4x⁴ - 37x² + 9 = 0, x>√(3/2), then what is the value of 8x³ - 27/x³ .

   • -215

   • 215

   • 35

   • -35

   Show solution

   Let, x² = p 4p² - 37p + 9 = 0 => 4p² - 36p - p + 9 = 0 => (4p - 1)(p - 9) = 0 :. p = 1/4 , 9 Here p=x²=1/4 is not acceptable because in question given x²=3/2 . So, x² = 9 =>x = 3 Now, 8x³ - 27/x³ = 8×3³ - 27/3³ = 215 :. The required value is = 215
7. Q7.SSC 2020

   If 2sin(3x-15)°=1, 0°<(3x-15)°<90°, then find the value of cos²(2x+15)°+cot²(x+15)°.

   • 1

   • -7/2

   • 7/2

   • 5/2

   Show solution

   2sin(3x-15)° = 1 => Sin(3x-15)° = 1/2 = sin30° => 3x - 15 = 30 => x = 45/3 = 15° Now, Cos²(2x+15)° + cot²(x+15)° =cos²(30+15)° + cot²(15+15)° = cos²45° + cot²30° = (1/√2)² + (√3)² = 1/2 + 3 = 7/2 :. The required value = 7/2
8. Q8.SSC 2020

   If the nine digit number 7p5964q28 is completely divisible by 88, what is the value of (p² - q) for the largest value of q, where p & q are natural numbers ?

   • 9

   • 81

   • 5

   • 72

   Show solution

   Number divisible by 88 means it should be divisible by 8 and 11 both. Largest possible value of q should be 9 [ number divisible by 8 when it's last 3 digits divisible by 8] For q = 9, number should be divisible by 11 ( 7+5+6+9+8) - ( p+9+4+2) = (20 - p) (20 - p) should be divisible by 11 if p = 9. Now, p² - q = 9² - 9 = 72 :. The required value is 72.
9. Q9.SSC 2021

   The average weight of a boy and his three friends is 55 kg. If the boy is 4 kg more than the average weight of his three friends, what is the weight of the boy ( in kg)?

   • 54 kg

   • 60 kg

   • 58 kg

   • 62 kg

   Show solution

   Total weight of the boy and his three friends =55× 4 = 220 kg Let, the average weight of three friends = x kg Total weight of three friends = 3x kg The boy's weight = ( x + 4) kg According to question, (x + 4) + 3x = 220 => x = 216/4 = 54 kg ∴ The weight of the boy = (54 + 4) = 58 kg.
10. Q10.SSC 2021

    Some students(only boys and girls) from different schools appeared for an Olympiad examination. 20% of the boys and 15% of the girls failed in the examination. The number of boys who passed the examination was 70 more than that of the girls who passed the examination. A total of 90 students failed. Find the number of students that appeared for the examination.

    • 350

    • 420

    • 400

    • 500

    Show solution

    The percentage of boys passed = 100-20 = 80% The percentage of girls passed=100-15 = 85% Let, Number of total boys appeared in exam= P Number of total girls appeared in exam = Q According to question, P×(80/100) - Q×(85/100) = 70 => 16P - 17Q = 1400 ---------(1) Again from the question, P×(20/100) + Q×(15/100) = 90 => 4P + 3Q = 1800.............(2) On multiplying the eq 2 by 4 we get, => 16P + 12Q = 7200 ------(3) Now, subtracting equation (1) from equation (3), 16P + 12Q - 16P + 17Q = 7200 - 1400 => 29Q = 5800 ∴ Q = 200 Putting the value of Q in equation (3),we get 16P + 12 ×200 = 7200 => 16P = 7200 - 2400 => P = 4800/16 ∴ P = 300 ∴ Total students appeared in the examination =(300 + 200) = 500
11. Q11.SSC 2021

    The following bar graph shows exports of cars of type A and B (in Rs. millions) from 2014 to 2018. What is the ratio of the total exports of cars of type A in 2014 and 2017 to the total exports of cars of type B in 2015 and 2016?

    • 5 : 6

    • 11 : 10

    • 6 : 7

    • 7 : 9

    Show solution

    The total exports of cars of type A in 2014 and 2017 = ( 200 +175) = 375 The total exports of cars of type B in 2015 and 2016 = 250 + 200 = 450 Required ratio = 375 : 450 = 5 : 6 ∴ The ratio of the total exports of cars of type A in 2014 and 2017 to the total exports of cars of type B in 2015 and 2016 is = 5 : 6
12. Q12.SSC 2021

    A solid cube of side 8 cm dropped into a rectangular container of length 16 cm ,breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level is -

    • 6 cm

    • 4 cm

    • 2.5 cm

    • 5.5 cm

    Show solution

    The water level increased means its height increased. Let, the water level increase = h cm According to the question, The volume of cube = volume of the water displaced (because the cube is completely submerged) 8³ = 16 × 8 × h => h = (8×8×8)/(16×8) => h = 4 ∴ The water level increased by 4 cm. Directions (Q20-21). The number of cars passing the road near a colony from 6 am to 12 noon has been shown in the following histogram.

SSC CGL CGL Quant PYQ (2019–21) previous year questions with solutions — AthenaPrep