General Mathematics & Basic Arithmetic — Part 4 MCQs with Explanations

Let's denote the unknown n umber as 𝑥 According to the problem, the number is first multiplied by 7 and the n divided by 4, resulting in 14. This can be expressed as the equation: 7x/4 - 14 To solve for 𝑥 follow these steps: Multiply both sides of the equation by 4 to eliminate the fraction: 7x = 14 x 4 7x = 56 2. Divide both sides by 7 to solve for x: x = 56/7 x = 8 therefore, the number is 8

Increase = 75.50 − 65.50 = 10.00 Percentage increase = (10 ÷ 65.50) × 100 = 15.27% .

Total students = 345 + 255 = 600 Ratio = 345 : 600 Divide by 15 → 23 : 40 .

√64 = 8 8 + 3 = 11 .

Girls : Boys = 240 : 360 Divide by 120 = 2 : 3

Circumference = πd = 3.14 × 5.3 ≈ 16.64 cm. Depth = 6 m = 600 cm. Number of turns = 600 ÷ 16.64 ≈ 36 turns.

Pine is south of Tail . Tail is north of Sam → Sam is south of Tail. Jag is south of Sam. Therefore , Pine and Jag are both south, but their exact horizontal/vertical relationship is not determined from the given information.

Let marker = M and pen = P . Equation 1: 3M + P = 245 Equation 2: 3M + 3P = 345 Subtract Equation 1 from Equation 2: 3P − P = 345 − 245 2P = 100 P = 50 Now : 3M + 50 = 245 3M = 195 M = 65

Given: Train length = 90 m Tunnel length = 231 m Time = 11 seconds Distance covered = 90 + 231 = 321 m Speed = Distance ÷ Time = 321 ÷ 11 = 29.18 m/s Convert to km/h: 29.18 × 18/5 = 105.05 km/h

Current Ages: Let Zoya’s current age be x Then, Zaid’s current age is 6 x (since he is six times as old as Zoya). The sum of Ages in 7 Years: In 7 years, Zoya's age will be x + 7 x + 7 and Zaid's age will be 6x + 7 6 x + 7 . The sum of their ages in 7 years will be ( x + 7 ) + ( 6 x + 7 ) = 49 . Step 1: Formulate the Equation x + 7 + 6 x + 7 = 49 7 x + 14 = 49 Step 2: Solve for x Subtract 14 from both sides: 7 x = 35 Now divide by 7: x = 5 So, Zoya’s current age is 5 5 years and Zaid’s current age is: 6 x = 6 × 5 = 30 Step 3: Determine Zaid’s Age When Zoya Was Bor n When Zoya was born, Zaid would have been: 30 − 5 = 25

60% × 40 = 0.6 × 40 = 24

To convert a percentage into a decimal, divide by 100. 40% = 40/100 = 0.40 .

18 + 27 = 45

20% of 150 = (20/100) × 150 = 0.2 × 150 = 30

Given: a : b : c = 3 : 4 : 7 We need to find (a + b + c) : c Step 1: Add the ratios: 3 + 4 + 7 = 14 Step 2: The value of c = 7 Step 3: Form the ratio: 14: 7 Step 4: Simplify: 14 : 7 = 2 : 1

5 → 25, so multiplier = 25 ÷ 5 = 5 Second quantity = 8 × 5 = 40

Cost of 1 pen = 250 ÷ 5 = Rs. 50 Cost of 8 pens = 50 × 8 = Rs. 400

2 is the only even prime number. A prime number has exactly two factors: 1 and itself . The factors of 2 are 1 and 2.

LCM is the smallest number that both 4 and 12 divide evenly into. 12 is a multiple of both 4 and 12 , so it's the LCM .

60 = 2² × 3 × 5 65 = 5 × 13; 70 = 2 × 5 × 7 LCM = 2² × 3 × 5 × 7 × 13 = 5,460 .

14 × 35 = 490 . Therefore, 490 is a multiple of 14 and is less than 500 .

A point has zero dimensions . It has no length, width, or height. A point represents only a location or position in space. Additional information : Line = 1 dimension Plane = 2 dimensions Solid = 3 dimensions

a:b = 8:9 b:c = 4:6 To make b same, take LCM of 9 and 4 = 36 a:b = 8:9 = 32:36 b:c = 4:6 = 36:54 So a:b:c = 32:36:54 = 16:18:27

48 - x = 7x 48 = 7x + x 48 = 8x x = 48 / 8 x = 6

First, divide: 42 ÷ 2 = 21 Then: 21 + 45 − 22 = 44

3% = 3/100 (3 ÷ 100) × 800,000 = 24,000 .

Non-terminating repeating decimals can be expressed as fractions, so they are rational numbers . In contrast, irrational numbers have non-terminating, non-repeating decimal expansions.

An event is a subset of the sample space. The sample space contains all possible outcomes of an experiment . An event contains one or more possible outcomes.

Height is an example of continuous data . Continuous data can take any value within a range. Height can be measured as 170 cm, 170.5 cm, 170.55 cm, etc .

To convert a percentage to decimal, divide by 100: 40 ÷ 100 = 0.4 .

Given: 2/5, 1/3 For the LCM of fractions: LCM = LCM of numerators/ HFC of denominators LCM of 2 and 1 = 2 HCF of 5 and 3 = 1 Therefore: L CM =1/2 ​ = 2 ​

5- 23/9 - 12/7 LCM of 9 and 7 =63 5 = 315/63, 23/9 = 161/63, 12/7 = 108/63 =46/63

Given: Length (L) = 15 Width (W) = 4 Perimeter formula: P = 2(L+W) Put the values: P= 2(15 +4) P= 2 X19 P = 2 times 19 P = 38 ​

Given: 2x + 4 /x =9 Multiply both sides by x : x ( 2x + 4/x) = 9x Now multiply each term: 2x^2 + 4x/x =9x Since x/x =1 2 x^ 2 + 4 = 9 x ​

216 × 216 = 46,656

10, 14, 19, 28, 54, ? Find differences: 14 - 10 = 4 19 - 14 = 5 28 - 19 = 9 54 - 28 = 26 Differences: 4, 5, 9, 26 Look at the pattern in differences: 4 = 2^2 5 = 2^2 + 1 9 = 3^2 26 = 5^2 + 1 The next logical difference is 7^2 = 49 So next term = 54 + 49 = 103

Check the pattern: 66 to 64 = -2 64 to 70 = +6 70 to 68 = -2 68 to ? = +6 So it alternates: -2, +6, -2, +6... Next step after 68 should be +6 68 + 6 = 74

Average of numbers from 1 to 40 For consecutive numbers, average = (First + Last) / 2 = (1 + 40) / 2 = 41 / 2 = 20.5

Pattern: Multiply by 2 and add 2 . 3 × 2 + 2 = 8 8 × 2 + 2 = 18 18 × 2 + 2 = 38 38 × 2 + 2 = 78 78 × 2 + 2 = 158 Verified & Updated

The password must contain: 1 integer: 5 choices 1 letter: 3 choices 1 symbol: 2 choices First select one from each category: 5 × 3 × 2 = 30 Now, these 3 selected characters can be arranged in different orders: 3 ! = 3 × 2 × 1 = 6 Therefore: Answer 30 × 6 = 180