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If t is a positive integer, can t2 + 1 be completely divided by 10?

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If t is a positive integer, can t2 + 1 be completely divided by 10?  [#permalink]

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New post 27 Oct 2018, 03:12
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If t is a positive integer, can \(t^2 + 1\)be completely divided by 10?
(1) \(91^2\)× t leaves a remainder of 1 when divided by 2
(2) \(91^2\) × t = 5q+2, where q is a non-negative integer.
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Re: If t is a positive integer, can t2 + 1 be completely divided by 10?  [#permalink]

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New post 27 Oct 2018, 18:53
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rencsee wrote:
If t is a positive integer, can \(t^2 + 1\)be completely divided by 10?
(1) \(91^2\)× t leaves a remainder of 1 when divided by 2
(2) \(91^2\) × t = 5q+2, where q is a non-negative integer.



\(t^2+1\) will be completely divisible by 10 when it's units digit is 10, so t^2 must have 9 as units digit, thus t can have 3 or 7 as units digit..

(1) \(91^2\)× t leaves a remainder of 1 when divided by 2
This will always happen when t is ODD..
Insufficient

(2) \(91^2\) × t = 5q+2, where q is a non-negative integer
\(91^2*t=5q+2\)....
a) if q is odd...\(91^2*t=5q+2\) means 5q will have 5+2 =7 as units digit then t will also have 7 as units digit.... YES then t^2+1 will be div by 10..
b) if q is even...\(91^2*t=5q+2\) means 5q will have 0+2 =2 as units digit then t will also have 2 as units digit.... NO, then t^2+1 will not be div by 10..
Insufficient

Combined..
statement I tells us t is odd
Statement gives two values 7 or 2..
Thus t has units digit of 7
Sufficient
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If t is a positive integer, can t2 + 1 be completely divided by 10? &nbs [#permalink] 27 Oct 2018, 18:53
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If t is a positive integer, can t2 + 1 be completely divided by 10?

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