Question : Find the greatest number that will divide 49, 147, and 322 to leave the same remainder in each case.
Option 1: 9
Option 2: 5
Option 3: 7
Option 4: 8
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Correct Answer: 7
Solution : When two numbers are divided by another number and have the same remainder, their difference must produce a remainder of zero. Use this concept to solve the question. According to the question, The differences will be, ⇒ 147 – 49 = 98 ⇒ 322 – 147 = 175 ⇒ 322 – 49 = 273 The set of numbers {98, 175, 273} Now HCF of {98, 175, 273} ⇒ 98 = 7 × 7 × 2 ⇒ 175 = 5 × 5 × 7 ⇒ 273 = 13 × 7 × 3 The HCF of {98, 175, 273} is 7 Hence, the correct answer is 7.
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Question : Directions: By interchanging the given two signs and numbers which of the following equations will be correct? × and +, 9 and 6
Option 1: 7 × 6 ÷ 3 + 9 – 8 = 17
Option 2: 6 × 8 – 9 ÷ 3 + 5 = 50
Option 3: 7 + 6 × 4 ÷ 9 – 8 = 8
Option 4: 9 × 7 + 4 ÷ 1 – 6 = 7
Question : Find the greatest number that will divide 390, 495, and 300 without leaving a remainder.
Option 1: 5
Option 2: 15
Option 3: 25
Option 4: 35
Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 9 and 6
Option 1: 7 + 6 × 4 ÷ 9 – 8 = 5
Option 2: 6 × 8 – 9 ÷ 3 + 5 = 75
Option 3: 9 × 7 + 4 ÷ 1 – 6 = 38
Option 4: 7 × 6 ÷ 3 + 9 – 8 = 19
Question : Directions: By Interchanging the given two numbers which of the following equations will be correct? 5 and 9
Option 1: 9 – 5 × 4 + 6 ÷ 3 = 30
Option 2: 9 × 3 + 5 ÷ 1 – 6 = 20
Option 3: 7 × 9 + 5 – 8 ÷ 4 = 40
Option 4: 9 × 4 + 5 – 8 ÷ 2 = 25
Question : Directions: By Interchanging the given two numbers which of the following equations will be correct? 5 and 8
Option 1: 5 × 2 – 8 + 9 ÷ 1 = 20
Option 2: 8 + 5 × 4 – 9 ÷ 3 = 30
Option 3: 5 × 7 + 8 – 3 ÷ 1 = 55
Option 4: 8 – 5 × 2 + 6 ÷ 2 = –9
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