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

 It is currently 18 Jun 2019, 20:13

### 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 and r is the remainder when t^2+5

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Oct 2017
Posts: 32
Location: India
Schools: ISB '20 (WA), IIM (A)
GMAT 1: 640 Q47 V32
GMAT 2: 710 Q49 V38
If t is a positive integer and r is the remainder when t^2+5  [#permalink]

### Show Tags

30 Sep 2018, 23:28
dpark wrote:
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

(1) When t is divided by 7, the remainder is 6.
(2) When t^2 is divided by 7, the remainder is 1.

Statement (1) Says that when t is divided by 7, the reminder is 6.

Say : t = 7A + 6
t^2 = 47A^2 + 84A + 36
Hence, when t^2 is divided by 7, the remainder is 1.

5t = 35A + 30
Hence, when 5t is divided by 7, the remainder is 2.

Hence, the remainder of t^2+5t+6 is divided by 7 would be (1+2+6)/7 = 2

So, statement 1 is sufficient.

From statement 2, we cant derive what would be the value of t as t^2 can be 1 , 36, 64 ... so on. Hence, not sufficient.
Intern
Joined: 05 Oct 2017
Posts: 46
Concentration: Accounting, Social Entrepreneurship
Re: If t is a positive integer and r is the remainder when t^2+5  [#permalink]

### Show Tags

01 Nov 2018, 20:58
1
Bunuel wrote:
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

First of all factor $$t^2+5t+6$$ --> $$t^2+5t+6=(t+2)(t+3)$$.

(1) When t is divided by 7, the remainder is 6 --> $$t=7q+6$$ --> $$(t+2)(t+3)=(7q+8)(7q+9)$$. Now, no need to expand and multiply all the terms, just notice that when we expand all terms but the last one, which will be 8*9=72, will have 7 as a factor and 72 yields the remainder of 2 upon division by 7. Sufficient.

(2) When t^2 is divided by 7, the remainder is 1 --> different values of t possible: for example t=1 or t=6, which when substituted in $$(t+2)(t+3)$$ will give different remainder upon division by 7. Not sufficient.

Hope it's clear.

Hi, I think in statement (2), t can not be equal to 1.
If we rephrase the statement, we get: t^2=7q+1, and t and q must be integer.
Here (7q+1) has to be a perfect square. So if t=1, the quantity (7q+1) becomes 8. We know 8 can not be equal to t^2 because t has to be an integer.
Correct me if I am wrong.

Posted from my mobile device
_________________
Manager
Joined: 29 Nov 2016
Posts: 116
Re: If t is a positive integer and r is the remainder when t^2+5  [#permalink]

### Show Tags

20 Feb 2019, 14:19
Let me give an algebric approach to solve second part.

You need to get the value of remainder when t^2+5t+6 is divided by 7.

Since, t^2 leaves a remainder 1 on division with 7. t^2+6 will leave a remainder of 0.
Or
t^2+6 will be completely divisible by 7.
Now what you need to find is remainder when 5t is divided by 7.

When t^2 is divided by 7, the remainder is 1.

We can say that here t^2-1 will be divisible by 7. Or to say (t-1)*(t+1) will be divisible by 7.

Please note that t-1,t,t+1 would be consecutive numbers. hence if (t-1)*(t+1) is divided by 7 then either t-1 OR t+1 will be completely divisible by 7.

( Both can not be completely divisible as the gap between them has to be atleast 7 to be completely divisible).

In either case that is if t-1 is completely divisible the remainder on dividing t by 7 would be 1.

OR if t+1 is divisible by 7, the remainder on dividing t with 7 would be 6.

Hence we can have 2 remaindes for t i.e 1 OR 6.

5t on dividing with 7 will leave either 5 or (30/7=2) as remainder . Hence the possible values for remainder is 2 or 5.

This is clearly insufficient .

This thought process is long but illustrates why 2 and 5 are logical values for remainder once we substitute.

Posted from my mobile device
Re: If t is a positive integer and r is the remainder when t^2+5   [#permalink] 20 Feb 2019, 14:19

Go to page   Previous    1   2   [ 23 posts ]

Display posts from previous: Sort by