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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If t is a positive integer and r is the remainder when t^2+5 [#permalink]
23 Feb 2012, 14:50

6

This post received KUDOS

Expert's post

7

This post was BOOKMARKED

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.

[1] If a quotient is squared, the remainder also gets squared and we need to adjust the new remainder based on no. we get on squaring.

Here quotient = t, r = 6. So, t^2 will have r' = 36 (7*5 + 1). Therefore r' =1

[2] If a quotient is multiplied by an integer k , the remainder also gets multiplied and we need to adjust the new remainder based on no. we get on multiplication.

Here quotient = t, r = 6. So, 5t will have r'' = 30 (7*4 + 2). Therefore r'' = 2

We get [A] using [1] and [2].

Clearly Stmt (2) can have multiple possibilities i.e. if t= 1 (t^2 =1) and t =6 (t^2 = 36) both give remainder 1, so no unique answer and hence rejected.

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 yield different remainder upon division by 7. Not sufficient.

Answer: A.

Hope it's clear.

Sorry Bunuel but this part highlighted is not completely clear: on the left side of = we have the two roots of our equation; on the right (t+2) ----> is 7q+6+2 ---> 7q+8 (same reasoning for 7q+9) BUT why we equal this two part ?? Can you explain me please ??

Thank you

We are asked to find the remainder when \(t^2+5t+6\) is divided by 7 or as \(t^2+5t+6=(t+2)(t+3)\), the remainder when \((t+2)(t+3)\) is divided by 7.

Now, from (1) we have that \(t=7q+6\). Substitute \(t\) with \(7q+6\) in \((t+2)(t+3)\) to get \((7q+8)(7q+9)\). So, finally we have that we need to find the remainder when \((7q+8)(7q+9)\) is divided by 7 (\(t^2+5t+6=(t+2)(t+3)=(7q+8)(7q+9)\)).

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 yield different remainder upon division by 7. Not sufficient.

Answer: A.

Hope it's clear.

Sorry Bunuel but this part highlighted is not completely clear: on the left side of = we have the two roots of our equation; on the right (t+2) ----> is 7q+6+2 ---> 7q+8 (same reasoning for 7q+9) BUT why we equal this two part ?? Can you explain me please ??

If t is a positive integer and r is the remainder when t^2+5 [#permalink]
25 Aug 2014, 11:51

1

This post was BOOKMARKED

(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.

Bunuel could you please explain why statement 2 is not sufficient and how the values for 't' could be either 1 or 6?

Re: If t is a positive integer and r is the remainder when t^2+5 [#permalink]
06 Sep 2014, 04:17

Shehryar Khan wrote:

(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.

Bunuel could you please explain why statement 2 is not sufficient and how the values for 't' could be either 1 or 6?

Hii Shehryar khan, let me try to explain..

t^2/7=1----------given

as u can see,we have 2 values of 2..1^2/7=remainder 1 and 6^2/7=36/7=remainder 1.. when we substitute 1 in (t+2)(t+3)/7 ,we get remainder as 5.. when we substitute 6 in (t+2)(t+3)/7, we get remainder as 2..

So,since the results are inconsistent,we cant have one definite remainder,which we are required to find,as per the stem..so,not sufficient..

Please consider KUDOS if my post helped _________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

gmatclubot

Re: If t is a positive integer and r is the remainder when t^2+5
[#permalink]
06 Sep 2014, 04:17

The Importance of Financial Regulation : Before immersing in the technical details of valuing stocks, bonds, derivatives and companies, I always told my students that the financial system is...

One question I get a lot from prospective students is what to do in the summer before the MBA program. Like a lot of folks from non traditional backgrounds...