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Suppose n is an integer such that
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25 Jun 2021, 05:12
25 Jun 2021, 05:12
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Question Stats:
91% (01:03) correct
8% (02:45) wrong based on 12 sessions
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Suppose n is an integer such that \(2 < n^2 <100\). If the units digit of \(n^2\) is 6 and the units digit of \((n —1)^2\) is 5, what is the units digit of \((n +1)^2\)?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
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Suppose n is an integer such that
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25 Jun 2021, 05:44
25 Jun 2021, 05:44
1
Carcass wrote:
Suppose n is an integer such that \(2 < n^2 <100\). If the units digit of \(n^2\) is 6 and the units digit of \((n —1)^2\) is 5, what is the units digit of \((n +1)^2\)?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
We can solve this question by using the concept of CYCLICITY!
The Cyclicity (repeating pattern) of 6 is 0 i.e. any number with last digit as 6 when raised to any power - the last digit will always be 6
The Cyclicity (repeating pattern) of 5 is again 0 i.e. any number with last digit as 5 when raised to any power - the last digit will always be 5
Using this;
If \(n^2\) = _ 6, \(n\) must have units digit as 6
If \((n - 1)^2\) = _ 5, \(n\) must have units digit as 5
Therefore, In \((n + 1)^2\), \((n + 1)\) must have units digit as 7
(_\(7)^2\) = _9
Hence, option E
gmatclubot
Suppose n is an integer such that [#permalink]
25 Jun 2021, 05:44
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