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

It is currently 25 Mar 2019, 21:20

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

How many integers n between 100 and 299 are there such that the hundre

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53831
How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 27 Nov 2018, 00:33
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (02:35) correct 42% (02:20) wrong based on 111 sessions

HideShow timer Statistics

How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

A. 48
B. 49
C. 50
D. 51
E. 52

_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Director
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 762
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 27 Nov 2018, 02:30
1
1
First number N such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n is 123.
Then 124 ,125 ,126, 127, 128, 129 - Total 7 numbers.
Next is 134-139 - Total 6 numbers.
145-149 - 5 numbers.
156-159 - 4 numbers.
167-169 - 3 numbers.
178-179 - 2 numbers.
180 - 1 number.
total of 28 numbers between 100-200.

Similarly from 200 to 299.
234-239 - 6 numbers.
245-249 - 5 numbers.
256-259 - 4 numbers.
267-269 - 3 numbers.
278-279 - 2 numbers.
289 - 1 number.
total of 21 numbers.

Total is 28+21 = 49 numbers.

B is the answer.
_________________
Press +1 Kudo If my post helps!
SVP
SVP
User avatar
P
Joined: 18 Aug 2017
Posts: 2497
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 27 Nov 2018, 10:53
Bunuel wrote:
How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

A. 48
B. 49
C. 50
D. 51
E. 52


GMATinsight :
Sir is there any other method to solve such question, where we dont end up counting every number?

N : (100A+10B+C)
so we need to find such specific no. ie 100A<10B<C

123,124,125,126,127,128,129,134,135,136.... so on..

this is a very time consuming method is there any short cut??
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1162
How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post Updated on: 16 Dec 2018, 20:53
Bunuel wrote:
How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

A. 48
B. 49
C. 50
D. 51
E. 52


this is a triangular number sequence:
0,1,3,6,10,15,21,28...
here is the relationship between the hundreds block and number of compliant integers in each:
800-0
700-1
600-3
500-6
400-10
300-15
200-21
100-28
because the value for term n=n(n-1)/2,
the 7th term (200 block) will have 7*6/2=21 compliant integers
and the 8th term (100 block) will have 8*7/2=28 compliant integers
21+28=49 total compliant integers between 100 and 299
B

Originally posted by gracie on 28 Nov 2018, 16:14.
Last edited by gracie on 16 Dec 2018, 20:53, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 10 Oct 2017
Posts: 3
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 30 Nov 2018, 00:25
If the hundreds digit is 1, the tens digit has 7 cases, the units digit has 7 cases => has total 28 numbers
If the hundreds digit is 2, the tens digit has 6 cases, the units digit has 6 cases => has total 21 numbers
--> has 49 numbers
--> B
Manager
Manager
avatar
S
Joined: 09 Jul 2018
Posts: 65
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 30 Nov 2018, 00:31
duynguyen612 wrote:
If the hundreds digit is 1, the tens digit has 7 cases, the units digit has 7 cases => has total 28 numbers
If the hundreds digit is 2, the tens digit has 6 cases, the units digit has 6 cases => has total 21 numbers
--> has 49 numbers
--> B


Can you please explain how you get 28 and 21 numbers?
Manager
Manager
avatar
D
Joined: 17 May 2015
Posts: 249
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 30 Nov 2018, 03:00
1
1
Bunuel wrote:
How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

A. 48
B. 49
C. 50
D. 51
E. 52


Hi,

We can divide the whole range into the two parts: 100 to 199 and 200 to 299.

100 to 199

Hundreds digit is fixed in this case,i.e. 1. Tens digit can be 2,3,4,5,6,7, and 8.
For example, when tens digit is 2 we have the following possibilities:
Attachment:
Number_counting1.png
Number_counting1.png [ 4.05 KiB | Viewed 813 times ]


Number of ways = 1*1*7 = 7 ways.

Similarly, when tens digit is 3 we have the following possibilities:

Attachment:
Number_counting2.png
Number_counting2.png [ 3.9 KiB | Viewed 807 times ]


Number of ways = 1*1*6 = 6 ways.

Hence, the total number of ways = \(7 + 6 + \dots + 1 = \frac{7\times8}{2} = 28\) numbers.

200 to 199

Hundreds number is 2. Tens digit can be 3,4,5,6,7, and 8. Hundreds digit can be 4,5,6,7,8, and 9.

Hence, the total number in this case = \(6 + 5 + \dots + 1 = \frac{6\times7}{2} = 21\) numbers.

Total number = 28 + 21 = 49 numbers.

Thanks.
Manager
Manager
avatar
S
Joined: 08 Oct 2018
Posts: 64
Location: India
GPA: 4
WE: Brand Management (Health Care)
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

New post 06 Jan 2019, 12:50
Bunuel wrote:
How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?

A. 48
B. 49
C. 50
D. 51
E. 52


Solving using counting principle:

abc is a number in between 100 and 299, a is hundreds, b is tens and c is units place.
0<a<b<c<9
So, c is atleast 3.

✓c can take values between 3-9, inclusive = 7 values.
AND
✓b can take values between 2 and 8, inclusive (b is atleast 2) = 7 values.
AND
✓a can take 1 value = 1

Total possibilities = 7x7x1 = 49

Posted from my mobile device
_________________
We learn permanently when we teach,
We grow infinitely when we share.
GMAT Club Bot
Re: How many integers n between 100 and 299 are there such that the hundre   [#permalink] 06 Jan 2019, 12:50
Display posts from previous: Sort by

How many integers n between 100 and 299 are there such that the hundre

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


Copyright

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®.