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

 It is currently 19 Oct 2019, 02:55 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

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 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 V
Joined: 02 Sep 2009
Posts: 58452
How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags 00:00

Difficulty:   65% (hard)

Question Stats: 59% (02:32) correct 41% (02:21) wrong based on 117 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

_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

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 Kudos If my post helps!
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5020
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

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??
VP  P
Joined: 07 Dec 2014
Posts: 1224
How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

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  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

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  S
Joined: 09 Jul 2018
Posts: 63
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

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  D
Joined: 17 May 2015
Posts: 247
Re: How many integers n between 100 and 299 are there such that the hundre  [#permalink]

Show Tags

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 [ 4.05 KiB | Viewed 2166 times ]

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

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

Attachment: Number_counting2.png [ 3.9 KiB | Viewed 2160 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  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

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. 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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  