Quantitative Aptitude PYQs

GIVEN:

Ages are consecutive odd numbers.

Youngest : Oldest (5 years ago) = 4 : 5

EXPLANATION:

Let the ages be x, x + 2, x + 4

A.T.Q

(x - 5)/(x + 4 - 5) = 4/5

⇒ 5x - 25 = 4x - 4

⇒ x = 21 years

Required age = 21 + 2 + 2 = 25 years

∴ The answer is 25 years.

Given:

One side of the square is 4 cm = Breadth of the rectangle

The area of the rectangle is thrice the area of the square

Formula used:

Area of a square = side²

Area of a rectangle = (Length × Breadth)

Calculation:

So, the area of the square = 4² cm² = 16 cm²

According to the question, the area of the rectangle = (16 × 3) cm² = 48 cm²

As per the question, the breadth of the rectangle is 4 cm

So, the length = (48/4) cm = 12 cm

∴ The length of the rectangle is 12 cm.

Given:

Time is taken by boat in still water to cover 48 km = 3 hours

Speed of the current = 4 km/hr

Formula used:

Speed = Distance/Time taken

Upstream speed = Speed of boat in still water - Speed of current

Calculation:

Speed of boat in still water = 48/3 km/hr

⇒ 16 km/hr

Upstream speed = (16 – 4) km/hr

⇒ 12 km/hr

Time is taken to cover the distance upstream = 48/12 hours

⇒ 4 hours

Difference in time = (4 – 3) hour

⇒ 1 hour

∴ The difference in time taken is 1 hour

Let A and B take x and (x + 6) hours respectively. Then,

\(\Rightarrow \frac{1}{x} + \frac{1}{{x + 6}} = \frac{1}{4}\)

\(\Rightarrow \frac{{x + 6 + x}}{{x\left( {x + 6} \right)}} = \frac{1}{4}\)

⇒ 8x + 24 = x (x + 6)

⇒ x² – 2x – 24 = 0

⇒ x = 6

Hence, time taken by A = 6 hours.

The number series looks like a difference series by first look.

Series:         67        82     98       118      147     192

Differences:        15      16       20       29        45

Double Diff:               1        4          9       16

Hence, 192 is correct.

Follow BODMAS rule to solve this question, as per the order given below,

Step -1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step -2- Any mathematical 'Of' or 'Exponent' must be solved next,

Step -3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step -4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

⇒ 32000 × 3/4 × ? × 1/2 = 4800

⇒ 8000 × 3 × ? × 1/2 = 4800

⇒ 4000 × 3 × ? = 4800

⇒ 12000 × ? = 4800

⇒ ? = 4800/12000

∴ ? = 4/10 = 2/5

Concept used:

Follow BODMAS rule to solve this question, as per the order given below:

Given expression is,

(3584 ÷ 32) – 11 = √?

⇒ 112 – 11 = √?

⇒ 101 = √?

⇒ ? = 101 × 101

∴ ? = 10201

121 ÷ (7/5 × 3/8 × 4/5) = ?

⇒ ? = 121 ÷ (21/50)

⇒ ? = 121 × 50/21

⇒ ? = 6050/21

∴ ? = 288.09 ≈ 288

Using laws of Indices:

(a)^m × (a)ⁿ = a^{(m + n)}

1. (a)^m ÷ (a)ⁿ = a^{(m - n)}
2. (a^m)ⁿ = (a)^mn
3. (a)^(-m) = 1/a^m
4. (a)⁰ = 1
5. (a)^1/m = ^m√a

Given expression is,

62² – 32² + ?² = 3144

⇒ 3844 – 1024 + ?² = 3144

⇒ 2820 + ?² = 3144

⇒ ?² = 3144 – 2820

⇒ ?² = 324

∴ ? = 18

Follow BODMAS rule to solve this question, as per the order given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated

4 + 1/13 of {2600 ÷ (118 – 108)} = ?

⇒ 4 + 1/13 of {2600 ÷ 10} = ?

⇒ 4 + 1/13 of 260 = ?

⇒ 4 + 20 = ?

∴ ? = 24

Follow BODMAS rule to solve this question, as per the order given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated

30% of 1200 + 50% of 720 = ? of 720

\(\Rightarrow \frac{{30}}{{100}} \times 1200; + \frac{{50}}{{100}} \times 720; = ;?; \times ;720\)

⇒ 360 + 360 = ? × 720

⇒ 720 = ? × 720

⇒ ? = 720/720 = 1

⇒ ? = 100%

Follow BODMAS rule to solve this question, as per the order given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated

\(\frac{70}{{4}} + \frac{90}{{4}} + \frac{110}{{4}} + \frac{60}{{4}} + \frac{70}{{4}} =: ?\)

Taking L.C.M

⇒ ? = (70 + 90 + 110 + 60 + 70)/4

⇒ ? = 400/4

∴ ? = 100

Follow BODMAS rules to solve the equation

Step -1: The part of the equation containing 'Brackets' must be solved first, and in the bracket,

Step -2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step -3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved

Step -4: At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

⇒ 2112 + 692 × 2 – 1111 × 5 + 7324 × 8 = ?

⇒ 2112 + 1384 – 5555 + 58592 = ?

⇒ ? = 62088 – 5555 = 56533

∴ ? = 56533.

Trick:

⇒ 444 × 13 – 48 × 17 + 1216 – 24 × 28 = ?

4 can be taken out as a common factor from each term, the answer will also contain a factor of 4 and will be divisible by 4.

⇒ 4[111 × 13 – 12 × 17 + 304 – 6 × 28]

To check divisibility by 4, last two digits of the number must be divisible by 4.

Only option 3 is divisible by 4

∴ 5500 is the answer.

Detailed Solution:

Solution:

We have to follow the BODMAS rule

Calculation:

⇒ 444 × 13 – 48 × 17 + 1216 – 24 × 28 = ?

⇒ 5772 – 816 + 1216 – 672 = ?

⇒ 5500 = ?

∴ ? = 5500.

Follow BODMAS rules to solve the equation

Step -1: The part of the equation containing 'Brackets' must be solved first, and in the bracket,

Step -2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step -3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved

Step -4: At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

⇒ (?)³ = (221 × 845) ÷ 85

⇒ (?)³ = (17 × 13 × 13 × 5 × 13) / (17 × 5)

⇒ (?)³ = 13 × 13 × 13

⇒ (?)³ = 2197

∴ ? = 13

Follow BODMAS rules to solve the equation

Step -1: The part of the equation containing 'Brackets' must be solved first, and in the bracket,

Step -2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step -3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved

Step -4: At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

⇒ 348 ÷ 29 × 45 + 468 = 3(?)³ + 360

⇒ 348/29 × 45 + 468 = 3(?)³ + 360

⇒ 12 × 45 + 468 = 3(?)³

⇒ 540 + 468 – 360 = 3(?)³

⇒ 1008 – 360 = 3(?)³

⇒ 648 = 3 × (?)³

⇒ 216 = (?)³

∴ ? = 6

Given expression:

Follow BODMAS rule to solve this question, as per the order is given below,

Step - 1 - Parts of an equation enclosed in 'Brackets' must be solved first,

Step - 2 - Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3 - Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4 - Last but not least, the parts of the equation that contains 'Addition' and 'Subtraction' should be calculated.

\(2\frac{1}{5} + 1\frac{1}{20} = ?\)

⇒ ? = 11/5 + 21/20

⇒ ? = (11 × 4 + 21)/20

⇒ ? = (44 + 21)/20

⇒ ? = 65/20

∴ ? = 13/4

Follow these BODMAS rules to solve the question

Step-1∶ The part of the equation containing 'Brackets' must be solved first and in the bracket,

Step-2∶ Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3∶ Next, the parts of the equation that contains 'Division' and 'Multiplication' is solved

Step-4∶ At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

Given expression is,

30% of 150 – 40% of 100 + 25% of 400 = ?

⇒ 3/10 × 150 - 4/10 × 100 + 25/100 × 400 = ?

⇒ 45 – 40 + 100 = ?

∴ ? = 105

15² + 12² – 11² = ? + 7²

⇒ 225 + 144 –​ 121 = ? + 49

⇒ 248 = ? + 49

∴ ? = 248 –​ 49 = 199

Follow BODMAS rule to solve this question, as per the order given below.

Step-1- Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket-

Step-2- Any mathematical 'Of' or 'Exponent' must be solved next.

Step-3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step-4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

432 + 88 × 230 ÷ ? = 652

Applying BODMAS Rule;

⇒ 88 × 230 ÷ ? = 652 – 432

⇒ 88 × 230 ÷ ? = 220

⇒ ? = (88 × 230) ÷ 220

⇒ ? = 4 × 23

∴ ? = 92