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

It is currently 18 Jan 2019, 03:50

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • 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.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
S
Joined: 07 Jun 2018
Posts: 42
If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s  [#permalink]

Show Tags

New post 04 Nov 2018, 08:33
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:56) correct 48% (01:56) wrong based on 21 sessions

HideShow timer Statistics

If r and s are non negative integers, \(p=1.9*10^r\) and \(q = 1.9*10^s\), what is the units digit of 10(p+q)?

(1) r is divisible by 2

(2) s is not divisible by 2
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 868
Re: If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s  [#permalink]

Show Tags

New post 04 Nov 2018, 09:33
depending on the values of s and r, p and q each have a units digit of either 1 (if r or s are 0, making the value 1.9), 9 (if r/s are 1, making the value 19), or 0 (if r/s >1, for which the value will be 190, 1900...etc)
Clearly, both statements on their own are insufficient, since each only gives information on one of r and s, and not on the other.
Combined: from 1), p's units digit is 0 (r=2 ==> 19, r = 4 ==> 19,00, etc). from 2), q's units digit can either 1 (s=0), 9 (s=1), or 0 (s>2). specifically, if s=0, then P+q will have a decimal digit of 9 (x.9), and 10(p+q) will have a units digit of 9. Since we don't if this is the case or not, this is insufficient.
_________________

Image
Sign up for 7-day free trial
Image

Director
Director
User avatar
P
Joined: 18 Jul 2018
Posts: 570
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s  [#permalink]

Show Tags

New post 04 Nov 2018, 09:33
Question : Unit digit of 10(p+q) = \(10(1.9*10^r+1.9*10^s)\) = \(19(10^r+10^s)\)

From statement 1:

r is divisible by 2.
Then r could be 0,2,4,6...
If r is 0 then 10^0 = 1.
If r is 2 then 10^1 = 10.
But no info about s.
Insufficient.

From statement 2:

s is not divisible by 2.
Then s could be 1,3,5...
Again r is unknown.
Insufficient.

Combining both:
Let r = 0. s = 1.
10^0 = 1 and 10^1 = 10. then 19(11) = last digit is 9.
If r = 2. and s= 3.
Then unit digit will be 0.
Combining is also insufficient.

E is the answer.
_________________

If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point?

GMAT Club Bot
Re: If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s &nbs [#permalink] 04 Nov 2018, 09:33
Display posts from previous: Sort by

If r and s are non negative integers, p = 1.9*10^r and q = 1.9*10^s

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.