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09 May 2023, 09:30
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Difficulty:
35%
(medium)
Question Stats:
65% (01:13) correct
35%
(01:11)
wrong
based on 55
sessions
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If \(n\) is positive integer, is 21 a factor of \(n\)?
(1) 21 is a factor of \(3n\)
(2) 21 is a factor of \(n^2\)
(1) 21 is a factor of \(3n\)
(2) 21 is a factor of \(n^2\)
11 May 2023, 09:57
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Given that n is positive integer, and we need to find is 21 a factor of n?
STAT 1: 21 is a factor of 3n
21 = 3*7
Now, there are multiple cases possible for which 21 is a factor of 3n
Ex1 : n = 7
=> 3n = 3*7 = 21, making 21 a factor of 21
=> But 21 is NOT a factor of n (which is 7)
Ex2 : n = 21
=> 3n = 3*21 = 63, making 63 a factor of 21
=> And 21 is NOT a factor of n (which is 21)
So, in some cases 21 is a factor of n and in some it is not
=> NOT SUFFICIENT
STAT 2: 21 is a factor of \(n^2\)
Given that n is an integer and 21 = 3*7 which is having only 1 power of 3 and 7
=> If 21 is a factor of \(n^2\) then 21 will also be a factor of n
=> SUFFICIENT
Let's understand when this would not be true
if instead of 21 we had any number which is a multiple of greater than 1 power of any number
Ex: 4 is a factor of \(n^2\), then it is NOT NECESSARY that 4 will be a factor of n also
case 1: n = 4, definitely 4 is a factor of n (which is 4)
case 2: n = 2, making \(n^2\) = 4 and 4 becomes a factor of \(n^2\), but 4 is NOT a factor of n (which is 2)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
STAT 1: 21 is a factor of 3n
21 = 3*7
Now, there are multiple cases possible for which 21 is a factor of 3n
Ex1 : n = 7
=> 3n = 3*7 = 21, making 21 a factor of 21
=> But 21 is NOT a factor of n (which is 7)
Ex2 : n = 21
=> 3n = 3*21 = 63, making 63 a factor of 21
=> And 21 is NOT a factor of n (which is 21)
So, in some cases 21 is a factor of n and in some it is not
=> NOT SUFFICIENT
STAT 2: 21 is a factor of \(n^2\)
Given that n is an integer and 21 = 3*7 which is having only 1 power of 3 and 7
=> If 21 is a factor of \(n^2\) then 21 will also be a factor of n
=> SUFFICIENT
Let's understand when this would not be true
if instead of 21 we had any number which is a multiple of greater than 1 power of any number
Ex: 4 is a factor of \(n^2\), then it is NOT NECESSARY that 4 will be a factor of n also
case 1: n = 4, definitely 4 is a factor of n (which is 4)
case 2: n = 2, making \(n^2\) = 4 and 4 becomes a factor of \(n^2\), but 4 is NOT a factor of n (which is 2)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Factors and Multiples
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