Number System
- The sum of three consecutive odd natural numbers each divisible by 3 is 72. What is the largest among them?
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Let the numbers be 3x, 3x + 3 and 3x + 6
∴ 3x + 3x + 3 + 3x + 6 = 72
⇒ 9x + 9 = 72
⇒ 9x = 72 – 9 = 63x = 63 = 7 9
∴ Largest number
= 3x + 6 = 3 × 7 + 6 = 27Correct Option: C
Let the numbers be 3x, 3x + 3 and 3x + 6
∴ 3x + 3x + 3 + 3x + 6 = 72
⇒ 9x + 9 = 72
⇒ 9x = 72 – 9 = 63x = 63 = 7 9
∴ Largest number
= 3x + 6 = 3 × 7 + 6 = 27
- Find three consecutive numbers such that twice the first, three times the second and four times the third together make 191.
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Numbers = x, x +1 and x + 2
∴ 2x + 3x + 3 + 4x + 8 = 191
⇒ 9x = 191 – 11 = 180
⇒ x = 20
∴ Numbers = 20, 21 and 22Correct Option: C
Numbers = x, x +1 and x + 2
∴ 2x + 3x + 3 + 4x + 8 = 191
⇒ 9x = 191 – 11 = 180
⇒ x = 20
∴ Numbers = 20, 21 and 22
- The sum of the squares of 3 consecutive positive numbers is 365. The sum of the numbers is
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102 + 112 + 122
= 100 + 121 + 144 = 365
∴ Required sum =10 + 11 + 12 = 33Correct Option: B
102 + 112 + 122
= 100 + 121 + 144 = 365
∴ Required sum =10 + 11 + 12 = 33
- The sum of all those prime numbers which are not greater than17 is
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Prime numbers upto 17
⇒ Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58Correct Option: B
Prime numbers upto 17
⇒ Required sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58
- If the sum of five consecutive integers is S, then the largest of
those integers in terms of’S is
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Sum of five consecutive integers = S
∴ Third integer = S 5 ∴ Largest integer = S + 2 5 = S + 10 5 Correct Option: D
Sum of five consecutive integers = S
∴ Third integer = S 5 ∴ Largest integer = S + 2 5 = S + 10 5
