Which of the following statement(s) is/are true? I. There are 12 multiples of 9 from 7 to 109. II. There are 9 multiples of 13 from 19 to 119.
Which of the following statement(s) is/are true?
I. There are 12 multiples of 9 from 7 to 109.
II. There are 9 multiples of 13 from 19 to 119.1). Only I
2). Only II
3). Both I and II
4). Neither I nor II
1 answers
Considering each statement one by one:
Statement I:
Multiples of 9 between 7 and 109 are 9, 18, 27, …., 108
⇒ The above series is an AP with first term = 9 and common difference = 9 and last term = 108
In an AP, An = a + (n - 1) × d
$(\Rightarrow 108 = 9 + \left( {n - 1} \right)9 = 9 + 9n - 9)$
⇒ 108 = 9n
⇒ n = 108/9 = 12
∴ Statement I is correct.
Statement II:
Multiples of 13 from 19 to 119 are 26, 39, …., 117
The above series is an AP with first term = 26 and common difference = 13 and last term = 117
In an AP, An = a + (n - 1) × d
⇒ $(117 = 26 + \left( {n - 1} \right)13 = 26 + 13n - 13)$
⇒ 117 - 13 = 13n
⇒ 13n = 104
⇒ n = 104/13 = 8
∴ Statement II is incorrect.Other Questions
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