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24 Jun 2022, 09:55
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Difficulty:
35%
(medium)
Question Stats:
70% (02:11) correct
30%
(02:14)
wrong
based on 93
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When \(n\) is divided by 9 the remainder is 2. If \(n\) is a positive integer, then what is the value of \(n\)?
(I) When \(n\) is divided by 11 the remainder is 3.
(II) \(n\) is a two-digit integer.
(I) When \(n\) is divided by 11 the remainder is 3.
(II) \(n\) is a two-digit integer.
n is of the form 9k+2, where k is an integer, by putting k as 1,2,3,...n can take values as 11,20,29,38,47,56,65,74,83,92,101,110,119,128,137,146..
From statement 1, n is also of the form 11m+3
n=11m+3 n can take values 14,25,36,47,58,69,80,91,102,113,124,135,146...
From above 2 we have common terms as 47,146...so Statement I alone is not sufficient.
Using Statement II, n is a two digit number and can take many values such as 11,20,29,38....
Statement II alone is also Not sufficient.
On combining statement I and II, we get 47 which is a two digit number and takes the form of 11m+3 and 9k+2.
Thus Option C.
From statement 1, n is also of the form 11m+3
n=11m+3 n can take values 14,25,36,47,58,69,80,91,102,113,124,135,146...
From above 2 we have common terms as 47,146...so Statement I alone is not sufficient.
Using Statement II, n is a two digit number and can take many values such as 11,20,29,38....
Statement II alone is also Not sufficient.
On combining statement I and II, we get 47 which is a two digit number and takes the form of 11m+3 and 9k+2.
Thus Option C.
10 Jul 2022, 03:17
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Catman
but 47 is also common between both the values
