Quantitative Aptitude PYQs

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,

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.

(12 × 5)² ÷ 60 + 8²

⇒ 60² ÷ 60 + 8²

⇒ 60 + 64

∴ Value is 124

⇒ {2/3 × 5/6 + 8/9 – 9/5}

⇒ {5/9 + 8/9 – 9/5}

⇒ 13/9 – 9/5}

⇒ - 16/45

Solve the given question, using following laws of indices,

Laws of Indices:

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

3√3 × 9³ ÷ 3⁵ = 3^{? + 2}

⇒ 3 × 3^1/2 × (3²)⁵ ÷ 3³ = 3^{? + 2}

⇒ 3^{1 + 1/2 + 10} ÷ 3³ = 3^{? + 2}

⇒ 3^11.5-3 = 3^{? + 2}

⇒ 11.5 - 3 = ? + 2

⇒ ? = 11.5 - 3 - 2 = 6.5

Given:

5/3 + 2/8 - ? × 8/2 = 4/5

Calculation:

⇒ ? × 8/2 = 5/3 + 2/8 - 4/5

⇒ ? × 4 = (5 × 8)/(3 × 8) + (2 × 3)/(8 × 3) - 4/5

⇒ ? × 4 = (40 + 6)/24 - 4/5

⇒ ? × 4 = (46 × 5)/(24 × 5) - (4 × 24)/(5 × 24)

⇒ ? × 4 = (230 - 96)/120

⇒ ? = 134/120 × ¼

∴ ? = 134/480 = 67/240

Concept used:

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

Calculation:

⇒ (2772 ÷ 42) + 184 = 28 × 34 + 184 - ?

⇒ 66 + 184 = 28 × 34 + 184 - ?

⇒ 66 + 184 = 952 + 184 - ?

⇒ 250 = 1136 - ?

⇒ ? = 1136 - 250

⇒ ? = 886

∴ The value of ? is 886

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,

914 + 772 - 386 = 2 × ? + 600

⇒ 1686 - 386 = 2 × ? + 600

⇒ 1300 = 2 × ? + 600

⇒ 2 × ? = 700

⇒ ? = 350

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,

60% of 80 ÷ 16 × 30% of 70 = ?

⇒ 48 ÷​ 16 ×​ 21 = ?

⇒ 3 ×​ 21 = ?​

∴ ? = 63

By using the law of indices∶

Laws of Indices∶-

1-∶ am × an = a{m + n}

2-∶ am ÷ an = a{m – n}

3-∶ [(am)n] = amn

4-∶ (a)(1/m) = m√a

5-∶ (a)(-m) = 1/am

6-∶ (a)(m/n) = n√am

7-∶ (a)0 = 1

Given expression is,

√324​ – √225​ + √289 = ? + √100

⇒ 18 – 15 + 17 = ? + 10

⇒ 20 = ? + 10

∴ ? = 10

√6889 ÷ 20.75 × 8 = ? ÷ 5 × 2.5

⇒ 83 ÷ 20.75 × 8 = ? ÷ 5 × 2.5

Applying BODMAS Rule;

⇒ 4 × 8 = ? ÷ 5 × 2.5

⇒ 32 = ? ÷ 5 × 2.5

⇒ 12.8 = ?/5

∴ ? = 64

Given 

28 + 5 × (?) ÷ 3 = 73

⇒ 5 × (?) ÷ 3 = 45

⇒ ? = 45 × 3/5

∴ ? = 27.

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 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.

⇒ 27⁸ × 3⁶ ÷ 27^3.4 × 27^2.4 = 3^?

⇒ 27⁸ × (3³)² ÷ 27^3.4 × 27^2.4 = 3^?

⇒ 27⁸ × (27)^-1.4 × 27^2.4 = 3^?

⇒ 27⁸ × (27)¹ = 3^?

⇒ 27⁹ = 3^?

⇒ (3³)⁹ = 3^?

⇒ 3²⁷ = 3^?

∴ ? = 27

Calculation:

81.25 ÷ 1.3 ÷ 2\(\frac{1}{2}\) × 103 = 2.5 × ?

⇒ 62.5 ÷ \(\frac{5}{2}\) × 1000 = 2.5 × ?

⇒ 62.5 × 2/5 × 1000 = 2.5 × ?

⇒ 25000 = 2.5 × ?

⇒ ? = 10000

∴ The correct answer is option (3).

(?)² = 805 – 625 – 36

⇒ (?)² = 144

⇒ ? = 12

224/7 + 132 - 30% of 560 = ? × 7

\(\Rightarrow 32 + 169 - \frac{{30}}{{100}} \times 560 = 7x\)

⇒ 32 + 169 - 168 = 7x

⇒ 201 - 168 = 7x

⇒ 33 = 7x

\(\Rightarrow x = \frac{{33}}{7}\)

\(\therefore x = 4\frac{5}{7}\)

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ (74 × 4 – 66) ÷ 5 = 89 + 37 - ?

⇒ (296 – 66) ÷ 5 = 89 + 37 – ?

⇒ 230 ÷ 5 = 126 – ?

⇒ ? = 126 – 46

⇒ ? = 80

∴ The value of ? is 80

Given:

Sum of three consecutive numbers = 105

Calculations:

If numbers are (n − 1), n, (n + 1)

Sum = 3n

Average of highest and second highest = (n + (n + 1)) ÷ 2

⇒ 3n = 105

⇒ n = 105 ÷ 3

⇒ n = 35

Numbers are: 34, 35, 36

⇒ Average of 35 and 36 = (35 + 36) ÷ 2

⇒ 71 ÷ 2 = 35.5

∴ Required average = 35.5.

Given:

A invests = 8000

B invests = 6000

B withdraws after 8 months

B’s profit share = 4200

Formula used:

Profit share ∝ Capital × Time

Calculations:

B’s ratio = 6000 × 8

A’s ratio = 8000 × 12

⇒ A’s value = 8000 × 12 = 96000

⇒ B’s value = 6000 × 8 = 48000

⇒ Ratio A : B = 96000 : 48000

⇒ = 2 : 1

If B’s share = 4200

⇒ 1 part = 4200

⇒ A’s share = 2 × 4200

⇒ = 8400

∴ A’s share of profit = Rs. 8400.

Given:

Total mixture = 44 litres

Milk is 6 litres more than water

Calculations:

Let water = x

Milk = x + 6

x + (x + 6) = 44

To make milk : water = 1 : 1 → Milk = New water

⇒ 2x + 6 = 44

⇒ 2x = 38

⇒ x = 19

⇒ Water = 19 L

⇒ Milk = 25 L

To make ratio 1 : 1 ⇒ Water must become 25 L

⇒ Extra water needed = 25 − 19

⇒ = 6 L

∴ Amount of water to be added = 6 litres.

Calculation

Male in A = 44.

If ratio = 4k : 5k and 4k = 44 → k = 11.

Females = 5k = 55.

Calculation

(60 + F) / 2 = 39 → 60 + F = 78 → F = 18.