GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Nov 2019, 12:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
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]

### Show Tags

13 Oct 2019, 22:22
2
00:00

Difficulty:

75% (hard)

Question Stats:

29% (01:46) correct 71% (02:42) wrong based on 24 sessions

### HideShow timer Statistics

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
Joined: 02 Aug 2009
Posts: 8157
Re: If t is a positive integer, can t2 + 1 be completely divided by 10? (  [#permalink]

### Show Tags

13 Oct 2019, 22:40
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
Display posts from previous: Sort by