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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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27 Oct 2018, 04:12
5
00:00

Difficulty:

95% (hard)

Question Stats:

28% (02:39) correct 72% (02:14) wrong based on 32 sessions

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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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Joined: 02 Aug 2009
Posts: 7685
Re: If t is a positive integer, can t2 + 1 be completely divided by 10?  [#permalink]

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27 Oct 2018, 19:53
1
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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Re: If t is a positive integer, can t2 + 1 be completely divided by 10?   [#permalink] 27 Oct 2018, 19:53
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