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# If t is a positive integer, can t^2 + 1 be evenly divided by 10?

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Manager
Joined: 17 Oct 2016
Posts: 81

Kudos [?]: 33 [0], given: 17

Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GPA: 3.05
WE: Pharmaceuticals (Health Care)
If t is a positive integer, can t^2 + 1 be evenly divided by 10? [#permalink]

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12 Aug 2017, 03:30
00:00

Difficulty:

65% (hard)

Question Stats:

53% (00:48) correct 47% (01:06) wrong based on 19 sessions

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If t is a positive integer, can t^2 + 1 be evenly divided by 10?

(1) 91^6 × t leaves a remainder of 1 when divided by 2

(2) 91^6 × t leaves a remainder of 2 when divided by 5
[Reveal] Spoiler: OA

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Dr. Pratik

Kudos [?]: 33 [0], given: 17

Senior Manager
Joined: 06 Jul 2016
Posts: 412

Kudos [?]: 116 [0], given: 99

Location: Singapore
Concentration: Strategy, Finance
Re: If t is a positive integer, can t^2 + 1 be evenly divided by 10? [#permalink]

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12 Aug 2017, 04:22
fitzpratik wrote:
If t is a positive integer, can t^2 + 1 be evenly divided by 10?

t>0
$$t^2$$ + 1 = 10m ?

Quote:
(1) 91^6 × t leaves a remainder of 1 when divided by 2
(2) 91^6 × t leaves a remainder of 2 when divided by 5

1) $$91^6$$*t = 2Q + 1
=> t = odd
=> t = 1, 3, 5, 7, 9
Insufficient.

2) $$91^6$$*t = 5P + 2
=> t = 2 or 7
Insufficient.

1+2)
t = 7
=> $$t^2$$ + 1 = 50 = 10*5
=> Sufficient.

C is the answer.
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Kudos [?]: 116 [0], given: 99

Re: If t is a positive integer, can t^2 + 1 be evenly divided by 10?   [#permalink] 12 Aug 2017, 04:22
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# If t is a positive integer, can t^2 + 1 be evenly divided by 10?

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