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

It is currently 18 Sep 2018, 18:50

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

If a and b are positive integers and ab> 13, IS a≠b?

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

Hide Tags

Manager
Manager
avatar
G
Joined: 20 Feb 2017
Posts: 159
Location: India
Concentration: Operations, Strategy
WE: Engineering (Other)
CAT Tests
If a and b are positive integers and ab> 13, IS a≠b?  [#permalink]

Show Tags

New post 25 Jul 2018, 19:52
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:02) correct 72% (01:57) wrong based on 29 sessions

HideShow timer Statistics

If a and b are positive integers and ab> 13, IS a≠b?

1. Exactly three of the numbers ab-4, ab-2,ab+1 & ab+3 have the same ten's digit
2. ab is divisible by 8, but not divisible by 16.

RON PUREWAL

_________________

If you feel the post helped you then do send me the kudos (damn theya re more valuable than $)

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6786
Re: If a and b are positive integers and ab> 13, IS a≠b?  [#permalink]

Show Tags

New post 25 Jul 2018, 20:07
If a and b are positive integers and ab> 13, IS a≠b?

1. Exactly three of the numbers ab-4, ab-2,ab+1 & ab+3 have the same ten's digit
Say the numbers are ab-4,ab-2,ab+1 and ab+3 is not..
ab+3 can have units digit as 0 or 1 since if it is 2, even ab+1 will have same tens digit.
So if ab+3 has units digit as 0 or 1, units digit of ab will be 3 less that is 7 or 8 but no perfect square can have its units digit as 7 or 8 so a≠b as a=b means ab is a perfect square.
Now if ab-2, ab+1 and ab+3 have same tens digit, then ab-4 can have units digit as 8 or 9.
Here units digit of ab will be 4 more that is 8+4 or 9+4 hence 2 or 3, but again no perfect square has its units digit as 2 or 3..
Thus in both cases a≠b
Sufficient

2. ab is divisible by 8, but not divisible by 16.
If a=b, ab will be a perfect square hence the power of prime number will be even but here power of 2 is 3..8=2^3
Hence a≠b
Sufficient

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
B
Joined: 16 Aug 2018
Posts: 29
Concentration: General Management, Strategy
Schools: Guanghua"21 (A)
GMAT 1: 700 Q49 V36
If a and b are positive integers and ab> 13, IS a≠b?  [#permalink]

Show Tags

New post 18 Aug 2018, 01:43
ab-4,ab-2,ab+1,ab+3
ab-4=23,33,43,... > ab=27,37,47,...
or
ab+3=26,36,46,... > ab=23,33,43,...

2)
multiples of 8:
8*1,8*2,8*3,8*4,8*5,8*6,8*7,...
every second of these will be multiples of 16 since the mulitiplier is even (2,4,6,8...)
for the rest, the multiplier (1,3,5..) is odd and does not contain 2 as a factor. hence 8 cannot be root square'd

as we know, the last digit of a square is always 1,4,9,6,5. hence ab cannot be a square or a is not equal to b.
hope that helps
If a and b are positive integers and ab> 13, IS a≠b? &nbs [#permalink] 18 Aug 2018, 01:43
Display posts from previous: Sort by

If a and b are positive integers and ab> 13, IS a≠b?

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

Events & Promotions

PREV
NEXT


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®.