Last visit was: 21 May 2024, 16:08 It is currently 21 May 2024, 16:08
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
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93373
Own Kudos [?]: 625629 [17]
Given Kudos: 81918
Send PM
Most Helpful Reply
Retired Moderator
Joined: 19 Oct 2018
Posts: 1877
Own Kudos [?]: 6382 [6]
Given Kudos: 704
Location: India
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 22 Nov 2018
Posts: 445
Own Kudos [?]: 494 [1]
Given Kudos: 292
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 740 Q49 V41
Send PM
Current Student
Joined: 16 Jan 2019
Posts: 630
Own Kudos [?]: 1448 [4]
Given Kudos: 144
Location: India
Concentration: General Management
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Send PM
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
4
Kudos
For a number to be divisible by 20, the units digit must be 0 and the tens digit must be an even number except 0 to avoid repetition.

This way, the units digit has only 1 possibility and tens digit has 4 possibilities.

Now the thousands digit has only 8 options (1-9 except a even number that was picked as the tens digit) and the hunderds digit has 7 options

Therefore positive 4-digit integers that are divisible by 20 without repetition of digits = 8*7*4*1 = 224

Answer is (C)

Hit Kudos if this helped!

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8027
Own Kudos [?]: 4126 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
Bunuel wrote:
How many positive 4-digit integers are divisible by 20 if the repetition of digits is not allowed?

(A) 168
(B) 196
(C) 224
(D) 288
(E) 360


last digit = 0; 1
and tens place ; 2,4,6,8; 4
hunderes ; 7 placs
thousands; 8 placses
8*7*4*1 ; 224
IMO C
Intern
Intern
Joined: 30 Mar 2017
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 6
Send PM
How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
1
Kudos
Can someone please explain the logic behind A being able to take only 8 values and B only 7 (when the 4-digit integer is written as ABCD). I know it has to do with the fact that repetition is not allowed but how can we logically deduce this?
Senior Manager
Senior Manager
Joined: 22 Nov 2018
Posts: 445
Own Kudos [?]: 494 [0]
Given Kudos: 292
Location: India
GMAT 1: 640 Q45 V35
GMAT 2: 740 Q49 V41
Send PM
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
RuZu wrote:
Can someone please explain the logic behind A being able to take only 8 values and B only 7 (when the 4-digit integer is written as ABCD). I know it has to do with the fact that repetition is not allowed but how can we logically deduce this?


RuZu Only 10 integers are there from 0,1,2,3...9. So C and D as repetition is not allowed will take 2 out. So max available for A will be 8 and B will be 7

Posted from my mobile device
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11282
Own Kudos [?]: 32668 [0]
Given Kudos: 306
Send PM
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
Expert Reply
Bunuel wrote:
How many positive 4-digit integers are divisible by 20 if the repetition of digits is not allowed?

(A) 168
(B) 196
(C) 224
(D) 288
(E) 360



For any number to be divisible by 20, the last two digits should be 00, 20, 40, 60 and 80.
As repetition is not allowed we can have only 4 possibilities: 20, 40, 60 and 80.

Now, for each case, say 20, two digits gone and the A and B in ABCD can be fixed from remaining 8 digits. => 8*7

Total cases for all 4 possibilities = 8*7*4 = 224

C
Intern
Intern
Joined: 08 Oct 2022
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 7
Send PM
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
Why "B" can only take values from 10-3?
GMAT Club Bot
Re: How many positive 4-digit integers are divisible by 20 if the repetiti [#permalink]
Moderator:
Math Expert
93373 posts