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Senior Manager  P
Joined: 10 Apr 2018
Posts: 277
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34 GPA: 3.3
If t is a positive integer, can t2 + 1 be completely divided by 10? (  [#permalink]

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2 00:00

Difficulty:   75% (hard)

Question Stats: 29% (01:46) correct 71% (02:42) wrong based on 24 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.
Math Expert V
Joined: 02 Aug 2009
Posts: 8157
Re: If t is a positive integer, can t2 + 1 be completely divided by 10? (  [#permalink]

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iamsiddharthkapoor 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.

For a number to be a multiple of 10, the unit digit should be 10, so $$t^2+1$$ should have a 0 as units digit. So, $$t^2$$ should have a 9 as units digit, meaning that t has to end in 3 or 7.

(1) $$91^2$$ × t leaves a remainder of 1 when divided by 2.
t could be any odd number as 91^2*t is ODD.
If ending in 3 or 7 yes, otherwise no.
Insuff

(2) $$91^2$$ × t = 5q+2, where q is a non-negative integer.
Now, RHS 5q+2 can end in two ways.
When q is even = 5*even+2=0+2=2, so it will end in 2 and $$91^2*t$$ would also end in t, meaning that t has a units digit of 2, and then answer is NO.
When q is odd = 5*odd+2=5+2=7, so it will end in 7 and $$91^2*t$$ would also end in t, meaning that t has a units digit of 7, and then answer is YES.
Insuff

Combined..
t is odd from I, so t cannot be ending in 2. t ends in 7 and so our answer is YES.

C
_________________ Re: If t is a positive integer, can t2 + 1 be completely divided by 10? (   [#permalink] 13 Oct 2019, 22:40
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# If t is a positive integer, can t2 + 1 be completely divided by 10? (  