Quantitative Aptitude PYQs

Calculation∶

The series follows following pattern

3 - 14 = -11

-11 + 28 = 17

17 - 56 = -39

-39 + 112 = 73

73 - 224 = -151

∴ The value of ? is -151

GIVEN:

?, 4000, 3500, 3250, 3125, 3062.5

Calculation:

The series follows the following pattern:

⇒ ? - 1000/1 = 4000

⇒ 4000 - 1000/2 = 3500

⇒ 3500 - 1000/4 = 3250

⇒ 3250 - 1000/8 = 3125

⇒ 3125 - 1000/16 = 3062.5

Value of ?:

⇒ ? - 1000/1 = 4000

⇒ ? = 4000 + 1000

⇒ ? = 5000

∴ The required value of "?" is 5000.

 

∴ The required value of "?" is 5000.

Given:

Series is 2, 5, 11, 23, 44, 77, ?

Calculation:

Pattern of the given series can be explained as,

∴ 125 will come in the place of "?"

The correct answer is: 5

Given:

 110, 121, 143, 176, ? , 275, 341

Calculation:

The given series follows the following pattern:

 ⇒ 121 - 110 = 11

 ⇒ 143 - 121 = 22

 ⇒ 176 - 143 = 33

 ⇒ 220 - 176  = 44

 ⇒ 275 - 220 = 55

 ⇒ 341 - 275 = 66

 Hence, 220 will come in place of '?'.

Calculation:

The pattern of the given series is:

⇒ 111.5 - (1 × 6.5) = 105

⇒ 105 + (2 × 6.5) = 118

⇒ 118 - (1 × 6.5) = 111.5

⇒ 111.5 + (2 × 6.5) = 124.5

⇒ 124.5 - (1 × 6.5) = ? = 118

∴ the missing number in the series is 118.

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college A and B = (192 + 168) = 360

Total number of students studying science in all the colleges = (2000 - 1200) = 800

Required percentage = 360/800 ×  100 = 45%.

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college D = 336

Number of students studying arts in college E = 264

Number of students studying arts in college F = (336 + 264)/2 = 300 + 20

Number of students studying science in college D = 114

Number of students studying science in college E = 236

Number of students studying science in college F = (350)/2 = 175 + 25

Required ratio = (320 : 200) = 8: 5

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts in college B = 168

If 25% of students studying arts in college B is increased = 168 ×  (125/100) = 210

If y numbers of students studying in college B studying science stream is increased by y = (110 + y)

Then the ratio becomes 7: 4.

To find the value of y

210/(110 + y) = 7/4

840 = 770 + 7y

70 = 7y

y = 10

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying arts from college C = 240

Number of students studying arts from college C attending seminar = 240 ×  (75/100) = 180

Number of students studying arts from college C does not attend seminar = (240 - 180) = 60

Number of students studying science from college C attending seminar = 110 × 4/11 = 40

Number of students studying Science from college C does not attend seminar = (110 - 40) = 70

Required sum = (60 + 70) = 130

General Solution:

 

College A:

Total number of students studying (Arts + Science) = 2000 ×  (20/100) = 400

Number of students studying Arts = 1200 ×  (16/100) = 192

Number of students studying Science = (400 - 192) = 208

 

College B:

Total number of students studying (Arts + Science) = 2000 ×  (15/100) = 300

Number of students studying Arts = 1200 ×  (14/100) = 168

Number of students studying Science = (300 - 168) = 132

 

College C:

Total number of students studying (Arts + Science) = 2000 ×  (17.5/100) = 350

Number of students studying Arts = 1200 ×  (20/100) = 240

Number of students studying Science = (350 - 240) = 110

 

College D:

Total number of students studying (Arts + Science) = 2000 ×  (22.5/100) = 450

Number of students studying Arts = 1200 ×  (28/100) = 336

Number of students studying Science = (450 - 336) = 114

 

College E:

Total number of students studying (Arts + Science) = 2000 ×  (25/100) = 500

Number of students studying Arts = 1200 ×  (22/100) = 264

Number of students studying Science = (500 - 264) = 236

 

Solution:

Number of students studying Arts in college A = 192

Number of boys  studying arts in college A = 192/3 = 64

Number of boys studying arts in college A having two wheelers = 64 ×  (25/100) = 16

Number of students studying science in college A = 208 

Number of boys studying science in college A = 208 ×  3/8 = 78

Number of boys studying science in college A having two wheelers = 78 ×  (50/100) = 39

Required sum = (39 + 16) = 55

Shortcut Trick

Breadth of rectangle = 750 ÷ 30 = 25 m.

Perimeter of rectangle = 2 × (30 + 25) = 110 m.

Ratio 11 units = 110 m ⇒ 1 unit = 10 m.

Perimeter of square = 8 units = 8 × 10 = 80 m.

Fencing cost = 80 × 20 = ₹1600.

∴ The correct answer is ₹1600.

Alternate Method

Given: Length (L) = 30 m, Area = 750 m², Rate = ₹20/m, Ratio P_s:P_r = 8:11

Formula: Area = L × B | Perimeter = 2(L + B)

⇒ Breadth of rectangle (B) = Area ÷ L = 750 ÷ 30 = 25 m

⇒ Perimeter of rectangle (P_r) = 2(30 + 25) = 2 × 55 = 110 m

⇒ According to ratio, 11 units = 110 m

⇒ 1 unit = 10 m

⇒ Perimeter of square (P_s) = 8 units = 8 × 10 = 80 m

⇒ Total Cost of fencing = Perimeter × Rate = 80 × 20 = ₹1600

∴ The correct answer is ₹1600.

Additional Information

Square Properties

Perimeter = 4 × side, Area = side². The diagonal of a square is side × √2.

Rectangle Properties

Perimeter = 2(length + breadth), Area = length × breadth. Diagonal = √(L² + B²).

Fencing Cost

Fencing is always done along the boundary, so total cost = Perimeter × Rate per unit length.

Shortcut Trick

Total distance (Train + Platform) = 180 + 1.25 × 180 = 180 + 225 = 405 m

Initial speed = 405 ÷ 32.4 = 12.5 m/s

New speed = 12.5 × (4/3) = 50/3 m/s (since 33.33% increase → 4/3 factor)

New distance (Train + Tunnel) = 180 + 200 = 380 m

Required time = 380 ÷ (50/3) = (380 × 3) ÷ 50 = 22.8 seconds

∴ The correct answer is 22.8 sec.

Alternate Method

Given:

Length of Train (L₁) = 180 m

Length of Platform (L₂) = 180 + 25% of 180 = 180 + 45 = 225 m

Length of Tunnel (L₃) = 200 m

Formula Used:

Speed = Total Distance ÷ Total Time

Calculations:

⇒ Total Distance₁ = L₁ + L₂ = 180 + 225 = 405 m

⇒ Initial Speed (S₁) = 405 ÷ 32.4 = 12.5 m/s

⇒ New Speed (S₂) = 12.5 + (33.33% of 12.5) = 12.5 + (1/3 × 12.5) = 12.5 × (4/3) = 50/3 m/s

⇒ Total Distance₂ = L₁ + L₃ = 180 + 200 = 380 m

⇒ Required Time = 380 ÷ (50/3) = (380 × 3) ÷ 50

⇒ Required Time = 1140 ÷ 50 = 22.8 seconds

∴ The correct answer is 22.8 sec.

Additional Information

Train Crossing Stationary Object with Length

When a train crosses a platform, bridge, or tunnel, the total distance covered is the sum of the length of the train and the object.

Fractional Equivalent of Percentages

Memorizing 33.33% = 1/3 and 25% = 1/4 helps in faster calculation. An increase of 33.33% means multiplying by (1 + 1/3) = 4/3.

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Given:

(27.02)% of 300.08 + 19% of 120 + 29.8% of 500

Concept:

We have to follow the BODMAS rule

Calculation:

Taking the approximate values

27% of 300 + 19% of 120 + 30% of 500 = ?

⇒ 81 + 22.8 + 150 = ?

⇒ 253.8 = ?

⇒ ? ≈ 254

∴ The value of ? is 254.

Given:

(43.12 × 6 ÷ 2 – 63) – {6.2 of 8 + 48.89 – (11)² + 25}

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking the approximate values

(43 × 6 ÷ 2 – 63) – {6 of 8 + 49 – (11)² + 25} = ?

⇒ (43 × 3 – 63) – {48 + 49 – 121 + 25} = ?

⇒ (129 – 63) – {122 – 121} = ?

⇒ 66 – 1 = 65

⇒ ? = 65

∴ The value of ? is 65.

Given:

{(86.01)² + (120.03)² + (150.02) × 143}/300

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking approximate values

{(86)² + (120)² + 150 × 143}/300

⇒ {7396 + 14400 + 21450}/300

⇒ 43246/300 = 144.15 ≈ 144

∴ The value of ? is 144.

Concept:

Calculation:

Giving expression is,

38.73 × 15.11 - 27.88 × 10.23 = ( 20 + ?) × 2 + 11.1 - 9.8

Taking approximate values as,

⇒ 39 × 15 - 28 × 10 = (20 + ?) × 2 + 11 - 10

⇒ 585 - 280 = 40 + 2? + 1

⇒ 305 = 41 + 2?

⇒ 264 = 2?

⇒ ? = 132

∴ Correct answer is 132

Given:

12.12 – 8.11 + 2.99 × (14.28%) of 1190.1 ÷ 16.99 = ?

Concept used:

We have to follow the BODMAS rule

Calculation:

Taking approximate values

12.12 – 8.11 + 2.99 × (14.28%) of 1190.1 ÷ 16.99 = ?

⇒ 12 – 8 + 3 × (1/7) of 1190 ÷ 17 = ?

⇒ 12 – 8 + 3 × (1/7) of 1190 ÷ 17 = ?

⇒ 12 – 8 + 3 × 170 ÷ 17 = ?

⇒ 12 – 8 + 3 × 10 = ?

⇒ ? = 34

∴ The value of ? is 34.

Shortcut Trick

Net discount = 25 + 20 − (25 × 20) ÷ 100 = 40%.

SP = MP × (100 − 40) ÷ 100 = 0.6 MP.

Since loss is 10%, SP = 0.9 CP ⇒ 0.6 MP = 0.9 CP ⇒ MP = 1.5 CP.

Given MP − CP = 900 ⇒ 0.5 CP = 900 ⇒ CP = 1800, MP = 2700.

To get Profit 360, new SP = 1800 + 360 = 2160. New MP × 0.6 = 2160 ⇒ New MP = 3600.

Increase in MP = (3600 − 2700) ÷ 2700 × 100 = 100 ÷ 3%.

∴ The correct answer is (100/3)%.

Alternate Method

Formulas: SP = CP × (100 − L%) ÷ 100 | MP = SP ÷ (1 − Total Discount) | Profit = SP − CP

⇒ Let Cost Price (CP) be x. Marked Price (MP) = x + 900.
⇒ Successive discounts of 25% and 20% ⇒ Single discount = 25 + 20 − (25 × 20)/100 = 40%.
⇒ Selling Price (SP) = (x + 900) × 0.6.
⇒ Loss of 10% means SP = 0.9x.
⇒ Equating SP: 0.6(x + 900) = 0.9x ⇒ 0.6x + 540 = 0.9x ⇒ 0.3x = 540 ⇒ x = 1800.
⇒ Initial MP = 1800 + 900 = 2700.
⇒ To earn Profit of Rs. 360, new SP = 1800 + 360 = 2160.
⇒ New MP = 2160 ÷ 0.6 = 3600.
⇒ % increase in MP = [(3600 − 2700) ÷ 2700] × 100 = (900 ÷ 2700) × 100 = 100/3 %.

∴ The correct answer is (100/3)%.

Additional Information

Successive Discounts

When two discounts a% and b% are given, the equivalent single discount is (a + b − ab/100)%.

Marked Price and Selling Price

SP is the price after applying the discount on MP. SP = MP × (100 − D%)/100.

Shortcut Trick

Apply Alligation: Boys (38) and Girls (39) with Mixture Average (38.49).

Ratio of Boys to Girls = (39 − 38.49) : (38.49 − 38) = 0.51 : 0.49 = 51 : 49.

Difference in ratio parts = 51 − 49 = 2 units. Given difference (x − (x − 2)) = 2 students.

Total students = (51 + 49) units = 100 students.

∴ The correct answer is 100 students.

Alternate Method

Given: Boys = x, Girls = x − 2, Avg Boys = 38, Avg Girls = 39, Avg Class = 38.49.

Formula: Total Score = Average × Number of Students

⇒ 38x + 39(x − 2) = 38.49(x + x − 2)

⇒ 38x + 39x − 78 = 38.49(2x − 2)

⇒ 77x − 78 = 76.98x − 76.98

⇒ 77x − 76.98x = 78 − 76.98

⇒ 0.02x = 1.02

⇒ x = 102 ÷ 2 = 51

⇒ Total Students = x + (x − 2) = 51 + 49 = 100

∴ The correct answer is 100 students.

Additional Information

Alligation Rule

Quantity₁ : Quantity₂ = (Value₂ − Mean) : (Mean − Value₁). It is the fastest way to find ratios in mixtures.

Weighted Average

The average of a whole group is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Deviation Method

Total sum of deviations from the mean is always zero. This can be used to find missing values in a dataset.

Shortcut Trick

Let Son's age = 100 units → Man's age = 250 units → Ratio Man : Son = 5 : 2.

Total age = 30 × 3 = 90 years.

Substitute options: Check for ratio 5 : 2 (or 20 : 8) between Man and Son.

Only Option (1) 20 : 17 : 8 satisfies Man : Son = 20 : 8 = 5 : 2 and total sum 20+17+8=45 units, where 45 units = 90 years.

∴ The correct answer is 20 : 17 : 8.

Alternate Method

Given: Average age = 30, Man = 250% of Son, Wife = Man − 6.

Formula: Total Age = Average × Number of members

⇒ Let Son's age = x

⇒ Man's age = 2.5x

⇒ Wife's age = 2.5x − 6

⇒ Total Age = x + 2.5x + (2.5x − 6) = 30 × 3

⇒ 6x − 6 = 90

⇒ 6x = 96 → x = 16

⇒ Son = 16, Man = 2.5 × 16 = 40, Wife = 40 − 6 = 34

⇒ Ratio = 40 : 34 : 16 = 20 : 17 : 8

∴ The correct answer is 20 : 17 : 8.

Additional Information

Average Age Concept

The sum of ages of n members is Average × n. If each person's age increases by k years, the average also increases by k.

Ratio and Proportion

To find the ratio of three quantities A:B:C, ensure all values are in the same unit and simplify by dividing by their HCF.

Percentage to Ratio Conversion

250% can be written as 250/100 or 5/2. Thus, if the base is 2 parts, the resultant is 5 parts.