BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Positive Integers Less than 10,000 --> Not Easy

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Wed Feb 03, 2010 5:21 pm
GMAT Score:720

Positive Integers Less than 10,000 --> Not Easy

by skalevar » Fri Oct 15, 2010 2:45 pm
How many positive integers are less than 10,000 in which the sum of the digits is equals 5?

A. 31
B. 51
C. 56
D. 62
E. 93

I got started on this, but could only try to count up the ways manually. There must be a trick. Please help!

OA. is C. From Ready for GMAT.com Advanced Quant download.
Top
Source: — Problem Solving |
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Fri Oct 15, 2010 6:55 pm
skalevar wrote:How many positive integers are less than 10,000 in which the sum of the digits is equals 5?

A. 31
B. 51
C. 56
D. 62
E. 93

I got started on this, but could only try to count up the ways manually. There must be a trick. Please help!

OA. is C. From Ready for GMAT.com Advanced Quant download.
easy easy... not difficult...
the numbers which its sum is 5 can be
0005=4!/3!1!=4 combinations
1004=4!/2!=12
2003=12 comnibations
1103=12 combinations
1112=4 combinations
2201=12 comninations
total =12+12+12+12+$+4=56
Top
User avatar
Legendary Member
Posts: 1172
Joined: Wed Apr 28, 2010 6:20 pm
Thanked: 74 times
Followed by:4 members

by uwhusky » Fri Oct 15, 2010 7:52 pm
Yo, easy on the "easy comments."

We're here to share knowledge.
Yep.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 16, 2010 8:02 am
skalevar wrote:How many positive integers are less than 10,000 in which the sum of the digits is equals 5?

A. 31
B. 51
C. 56
D. 62
E. 93

I got started on this, but could only try to count up the ways manually. There must be a trick. Please help!

OA. is C. From Ready for GMAT.com Advanced Quant download.
Here is an efficient way to solve this problem.

Let's say that we have the 5 letters DDDDD.

However we separate the 5 letters, we will still have 5 letters:

DD DD D
D DDD D
DDDD D
DD DDD

We can think of these various groups of D's as digits that add up to 5:

DD DD D means 2 2 1
D DDD D means 1 3 1
DDDD D means 4 1
DDDDD means 5

So any grouping of the 5 letters DDDDD will give us a number the sum of whose digits is 5:

DD DD D will give us 221, 2021, 2201, or 2210.
etc.

So the question becomes:

How many ways can the 5 letters DDDDD be divided into groups?

We can have at most 4 groups, because if we divide DDDDD into 5 groups (D-D-D-D-D), we'll have a 5-digit number. Thus we can divide DDDDD at most 3 times. Let | = separation between groups.

D|D|D|DD = 1112
DD||D|DD = 2012
DD|D||DD = 2102
|DD|D|DD = 0212 = 212
DD|D|DD| = 2120
etc.

So any arrangement of the 8 elements DDDDD||| represents a number the sum of whose digits is 5.

Number of ways to arrange DDDDD||| = 8!/(5!*3!) = 56.

The correct answer is C.

By extension, the number of positive integers less than 10,000 the sum of whose digits is 4 = number of ways to arrange DDDD||| = 7!/(4!*3!) = 35.
Last edited by GMATGuruNY on Sun Oct 17, 2010 3:10 am, edited 2 times in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Sat Oct 16, 2010 10:21 am
uwhusky wrote:Yo, easy on the "easy comments."

We're here to share knowledge.
:( ????????? ??????????
Top
User avatar
Legendary Member
Posts: 1172
Joined: Wed Apr 28, 2010 6:20 pm
Thanked: 74 times
Followed by:4 members

by uwhusky » Sat Oct 16, 2010 11:51 am
Imagine every question you asked in verbal that you thought were tough, and someone responded by saying, "oh that one is easy, it's A."

How does that make you feel? Drop the attitude and stick with sharing information.
Yep.
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Sat Oct 16, 2010 5:59 pm
uwhusky wrote:Imagine every question you asked in verbal that you thought were tough, and someone responded by saying, "oh that one is easy, it's A."

How does that make you feel? Drop the attitude and stick with sharing information.
i just dont feel anything... dont be so sensitive and emotional... if you read it with another emotional such as joking type or something, you would feel different... its all about typing....
and well, i just dont feel anything about it because i dont care.... if they say that, i will think.. ok, so its an easy one, thus i am not good enough to do the test now...
anyways... its all about your emotional when you read someone.... i dont care...
Top
User avatar
Legendary Member
Posts: 1172
Joined: Wed Apr 28, 2010 6:20 pm
Thanked: 74 times
Followed by:4 members

by uwhusky » Sat Oct 16, 2010 11:24 pm
It's one thing to "respect others" and another to "not care for disrespect." What you need to learn is how to show some respect for others.
Yep.
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Sun Oct 17, 2010 8:34 am
uwhusky wrote:It's one thing to "respect others" and another to "not care for disrespect." What you need to learn is how to show some respect for others.
youre going too far to say whether someone respects a stranger via the way she/he types....just relax and dont be so emotional... thats what i did and will say...sad things that some men are so emotional...
and thank for the unnecessary advance...i wont waste my time on this so move on, mr annoying!
Top
User avatar
Legendary Member
Posts: 1172
Joined: Wed Apr 28, 2010 6:20 pm
Thanked: 74 times
Followed by:4 members

by uwhusky » Sun Oct 17, 2010 9:59 am
Son, good luck with your application. You have much to learn.

I don't care about what you write, because quite honestly, I don't understand half of what you wrote. I was merely trying to tell you that you should try to be helpful instead of making snarky "easy" comments. But I guess that went nowhere.
Yep.
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Sun Oct 17, 2010 3:28 pm
uwhusky wrote:Son, good luck with your application. You have much to learn.

I don't care about what you write, because quite honestly, I don't understand half of what you wrote. I was merely trying to tell you that you should try to be helpful instead of making snarky "easy" comments. But I guess that went nowhere.
son??? if you say so! he called me son! lol its all about culture and your english level thing... lol... i dont bother anything what you said and dun feel anything hard.... human has to learn for the whole life... thats what i always think... but for what you wrote, i think you've done your learning! congratulation, mr knowledger! lol
by the way, one question. if you dont care why are you so talkative? or you care me? are you ghey? lol
Top
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Sun Oct 17, 2010 3:33 pm
uwhusky wrote:It's one thing to "respect others" and another to "not care for disrespect." What you need to learn is how to show some respect for others.
and dont bother,,, the more you write and say something to me, the more i tease what you wrote... lol...
Top
Legendary Member
Posts: 537
Joined: Fri Jan 22, 2010 10:06 pm
Thanked: 14 times
Followed by:1 members

by frank1 » Sun Oct 17, 2010 8:23 pm
I agree it was not as easy as it was presented(considering will have 2 minutes to solve it)
GMAT score is equally counted as your GPA and 78 clicks can change you life.
Top
User avatar
Legendary Member
Posts: 866
Joined: Mon Aug 02, 2010 6:46 pm
Location: Gwalior, India
Thanked: 31 times

by goyalsau » Tue Oct 19, 2010 8:37 am
frank1 wrote:I agree it was not as easy as it was presented(considering will have 2 minutes to solve it)
Absolutely agree with you, Question was not easy.
I think it is of 700+ , And if it not, Then God Help Me,
Because i was not able to solve it in 2 minutes.
Saurabh Goyal
[email protected]
-------------------------


EveryBody Wants to Win But Nobody wants to prepare for Win.
Top
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Thu Oct 14, 2010 1:21 pm

by phoenixhazard » Tue Oct 19, 2010 2:15 pm
GMATGuruNY wrote:
skalevar wrote:How many positive integers are less than 10,000 in which the sum of the digits is equals 5?

A. 31
B. 51
C. 56
D. 62
E. 93

I got started on this, but could only try to count up the ways manually. There must be a trick. Please help!

OA. is C. From Ready for GMAT.com Advanced Quant download.
Here is an efficient way to solve this problem.

Let's say that we have the 5 letters DDDDD.

However we separate the 5 letters, we will still have 5 letters:

DD DD D
D DDD D
DDDD D
DD DDD

We can think of these various groups of D's as digits that add up to 5:

DD DD D means 2 2 1
D DDD D means 1 3 1
DDDD D means 4 1
DDDDD means 5

So any grouping of the 5 letters DDDDD will give us a number the sum of whose digits is 5:

DD DD D will give us 221, 2021, 2201, or 2210.
etc.

So the question becomes:

How many ways can the 5 letters DDDDD be divided into groups?

We can have at most 4 groups, because if we divide DDDDD into 5 groups (D-D-D-D-D), we'll have a 5-digit number. Thus we can divide DDDDD at most 3 times. Let | = separation between groups.

D|D|D|DD = 1112
DD||D|DD = 2012
DD|D||DD = 2102
|DD|D|DD = 0212 = 212
DD|D|DD| = 2120
etc.

So any arrangement of the 8 elements DDDDD||| represents a number the sum of whose digits is 5.

Number of ways to arrange DDDDD||| = 8!/(5!*3!) = 56.

The correct answer is C.

By extension, the number of positive integers less than 10,000 the sum of whose digits is 4 = number of ways to arrange DDDD||| = 7!/(4!*3!) = 35.
Sorry, I don't get why you can't have D-D-D-D-D (1 1 1 1 1), that equals 5?
Top
Post new topic Post Reply