Last visit was: 26 Jul 2024, 23:58 It is currently 26 Jul 2024, 23:58
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the number of 4-digit positive integers where all 4 digits are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644220 [6]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   07 Jul 2021, 06:15
1
Kudos
5
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:07) correct 18% (01:41) wrong based on 177 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
What is the number of 4-digit positive integers where all 4 digits are less than 5?

A. 450
B. 475
C. 500
D. 600
E. 625
ShowHide Answer
Official Answer
C
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9471 [1]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   07 Jul 2021, 06:33
1
Kudos
Expert Reply
The first digit cannot be zero if we'll have a genuine four-digit number. So we have 4 choices for that digit, but we have 5 choices for each of the remaining three digits, and the answer is (4)(5)(5)(5) = 20*25 = 500.
avatar
B
optimusprime07
Intern
Intern
Joined: 01 Oct 2016
Posts: 3
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   07 Jul 2021, 06:35
1
Kudos
ANSWER of this Question should be 500


4 * 5*5*5 = 500
User avatar
P
Showmeyaa
Senior Manager
Senior Manager
Joined: 24 Jun 2019
Posts: 428
Own Kudos [?]: 442 [0]
Given Kudos: 117
Location: India
Concentration: Marketing, Strategy
Send PM
Reviews Badge
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   07 Jul 2021, 07:16
IanStewart wrote:
The first digit cannot be zero if we'll have a genuine four-digit number. So we have 4 choices for that digit, but we have 5 choices for each of the remaining three digits, and the answer is (4)(5)(5)(5) = 20*25 = 500.


Hey IanStewart, what do you think about the way this question is worded?
What is the number of 4-digit positive integers, doesn't this mean we shouldn't be counting 0? Though looking at the options one could make out!
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9471 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   07 Jul 2021, 07:24
Expert Reply
Showmeyaa wrote:
Hey IanStewart, what do you think about the way this question is worded?
What is the number of 4-digit positive integers, doesn't this mean we shouldn't be counting 0? Though looking at the options one could make out!


There are minor issues with the wording (that's true of most unofficial questions though) but I think the meaning of the question is unambiguous. The "4-digit positive integers" are the integers strictly between 1000 and 9999 inclusive, so zero is not a four-digit integer, and I wasn't including zero in my solution, because I insisted we not allow zero to be the first (the thousands) digit of the number. So I was only counting numbers like 1000 and 2222 and 4130, and I wasn't counting numbers like 0123 or 0000, which are not four digit numbers.
User avatar
B
fredmath
Intern
Intern
Joined: 22 Sep 2022
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 32
Send PM
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   27 Oct 2022, 07:05
Hello, I have a question here as well: in a different post, it is said that 0 is not a positive integer, which leads me to saying numbers as 4130 should not be included. What is the ruling opinion on this topic?

Thanks

This is the Post I was relating to: gmatclub/forum/is-zero-a-positive-integer-149242.html
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9471 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink] What is the number of 4-digit positive integers where all 4 digits are   27 Oct 2022, 10:43
Expert Reply
fredmath wrote:
Hello, I have a question here as well: in a different post, it is said that 0 is not a positive integer, which leads me to saying numbers as 4130 should not be included. What is the ruling opinion on this topic?

Thanks

This is the Post I was relating to: gmatclub/forum/is-zero-a-positive-integer-149242.html


Yes, zero is not a positive integer (zero is the only number that is neither positive nor negative). But the question asks us to count how many positive 4-digit integers satisfy a certain property, and a positive 4-digit integer might contain one or more digits that are zero. So 4130, for example, is definitely a positive integer, even if it includes zero as one of its digits.
GMAT Club Bot
gmatclubot
Re: What is the number of 4-digit positive integers where all 4 digits are [#permalink]
27 Oct 2022, 10:43
Moderator:
Bunuel
Math Expert
94619 posts