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

 It is currently 16 Jan 2019, 09:23

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

Events & Promotions

Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If a and b are positive integers, what is the remainder when 9^2a+b

Author Message
TAGS:

Hide Tags

Manager
Joined: 17 Jan 2017
Posts: 61
If a and b are positive integers, what is the remainder when 9^2a+b  [#permalink]

Show Tags

05 Apr 2018, 05:32
2
1
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:09) correct 42% (01:33) wrong based on 62 sessions

HideShow timer Statistics

If a and b are positive integers, what is the remainder when $$9^{2a+b}$$ is divided by 20?

(1) a = 3
(2) b = 5

Source: ExpertsGlobal
Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: If a and b are positive integers, what is the remainder when 9^2a+b  [#permalink]

Show Tags

05 Apr 2018, 10:04
1
1
benejo wrote:
if a and b are positive integers, what is the remainder when $$9^{2a+b}$$ is divided by 20?

(1) a = 3
(2) b = 5

Source: ExpertsGlobal

$$9^{2a+b}$$ to know the remainder of this number when it is divided by 20 we need to know the last two digits of this number, i.e. we need to know the units and tens digit of this number.

The cyclicity of $$9$$ is as follows -

$$9^1=9; 9^2=81; 9^3=729; 9^4=6561; 9^5=59049$$

So units digit of the number will be either $$1$$ or $$9$$ and tens digit will always be an even number. Hence the remainder of $$9^{2a+b}$$ when divided by $$20$$ will depend on the UNITS digit of this number.

Now $$2a$$ is always EVEN irrespective of the value of $$a$$. Hence $$9^{{Even}+b}$$. So we only need to know the value of $$b$$ to get the units digit.

Statement 1: Nothing mentioned about $$b$$. Insufficient

Statement 2: $$b$$ is odd so $$9^{2a+b}=9^{{Even}+Odd}=9^{Odd}$$. Hence the remainder will be $$9$$. Sufficient

Option B
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If a and b are positive integers, what is the remainder when 9^2a+b  [#permalink]

Show Tags

05 Apr 2018, 10:50
benejo wrote:
if a and b are positive integers, what is the remainder when $$9^{2a+b}$$ is divided by 20?

(1) a = 3
(2) b = 5

Source: ExpertsGlobal

Similar questions to practice:
https://gmatclub.com/forum/if-a-and-b-a ... 28194.html
https://gmatclub.com/forum/if-a-and-b-a ... 36733.html
_________________
Intern
Joined: 07 Feb 2018
Posts: 3
Re: If a and b are positive integers, what is the remainder when 9^2a+b  [#permalink]

Show Tags

12 Apr 2018, 21:13
Please explain to me why we can make sure that 9^odd (I know that the unit digit of which is always 9) when divided by 20 doesn't leave a remainder of 19 instead of 9? Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: If a and b are positive integers, what is the remainder when 9^2a+b  [#permalink]

Show Tags

12 Apr 2018, 23:00
1
vap311096 wrote:
If a and b are positive integers, what is the remainder when $$9^{2a+b}$$ is divided by 20?

(1) a = 3
(2) b = 5

Please explain to me why we can make sure that 9^odd (I know that the unit digit of which is always 9) when divided by 20 doesn't leave a remainder of 19 instead of 9? Thanks!

When x9 is divided by 20, the remainder could be either 9 or 19.

If x is odd, then x9 is 19, 39, 59, ..., all of which give the remainder of 19 upon division by 20.
If x is even, then x9 is 09, 29, 49, ..., all of which give the remainder of 9 upon division by 20.

Now, 9^odd, not only results in the units digit of 9 but also in the even tens digit: 9^1 = 09, 9^3 = 729, 9^5 = 59,049, ... Thus, 9^odd = ...(even)(9), which as we saw above will always give the remainder of 9 upon division by 20.

Hope it's clear.
_________________
Re: If a and b are positive integers, what is the remainder when 9^2a+b &nbs [#permalink] 12 Apr 2018, 23:00
Display posts from previous: Sort by