It is currently 10 Dec 2018, 13:37
My Tests

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.

How many integers between 2,000 and 3,999 have a ones digit

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

CAT Tests
How many integers between 2,000 and 3,999 have a ones digit [#permalink] New post 05 Aug 2018, 14:32
Expert's post
00:00

Question Stats:

75% (01:10) correct 25% (00:27) wrong based on 8 sessions
How many integers between 2,000 and 3,999 have a ones digit that is a prime number?

[Reveal] Spoiler: OA
800

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

CAT Tests
Re: How many integers between 2,000 and 3,999 have a ones digit [#permalink] New post 08 Aug 2018, 18:05
Expert's post
Explanation

This is a combinatorics problem. Make four “slots” (since the numbers are all four-digit numbers), and determine how many possibilities there are for each slot:

__ __ __ __

Since the number must begin with 2 or 3, there are two possibilities for the first slot. Because the ones digit must be prime and there are only four prime one-digit numbers (2, 3, 5, and 7), there are four possibilities for the last slot:

2........... 4
__ __ __ __


The other slots have no restrictions, so put 10 in them, since there are ten digits from 0–9:

2 10 10 4
__ __ __ __

Multiply to get 800.

Alternatively, figure out the pattern and add up the number of qualifying four-digit integers. In the first ten numbers, 2000–2009, there are exactly four numbers that have a prime units digit: 2002, 2003, 2005, and 2007.

The pattern then repeats in the next group of ten numbers, 2010–2020, and so on. In any group of ten numbers, then, four qualify. Between 2,000 and 3,999 there are \(3,999 – 2,000 + 1 = 2,000\) numbers, or \(\frac{2000}{10}= 200\) groups of ten numbers, so there are a total of \(400 \times 2 = 800\) numbers that have a prime units digit.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Intern
Joined: 22 Jul 2018
Posts: 41
Followers: 0

Kudos [?]: 9 [0], given: 5

Re: How many integers between 2,000 and 3,999 have a ones digit [#permalink] New post 14 Oct 2018, 01:58
2. How many integers between 0 and 1570 have a prime tens digit and a prime units digit??
3. How many integers between 1 and 10^21 are such that the sum of their digits is 2?
4. How many 3-digit integers between 100 and 200 have a digit that is the average (arithmetic mean) of the other 2 digits?
5. How many integers between 324,700 and 458,600 have tens digit 2 and units digit 1?
6. How many four-digit numbers have at least one digit repeating?
7. In how many no. between 100 and 1000 at least one of their digits is 7?
Re: How many integers between 2,000 and 3,999 have a ones digit   [#permalink] 14 Oct 2018, 01:58
Display posts from previous: Sort by

How many integers between 2,000 and 3,999 have a ones digit

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.