GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 17 Jan 2020, 05:43 ### 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 are there between 2 x 10^5 and 9 X 10^5 so that the

Author Message
TAGS:

### Hide Tags

Intern  B
Joined: 25 Apr 2015
Posts: 7
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

1
12 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:37) correct 37% (01:39) wrong based on 244 sessions

### HideShow timer Statistics

How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9
b) 8
c) 7
d) 6
e) 5

Originally posted by franz711 on 26 Jun 2017, 23:45.
Last edited by Bunuel on 27 Jun 2017, 00:10, edited 2 times in total.
Renamed the topic.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4214
Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

5
Top Contributor
2
franz711 wrote:
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9
b) 8
c) 7
d) 6
e) 5

When we check the answer choices (ALWAYS check the answer choices before choosing an approach), we see that all 5 answer choices a small.

In this case, we should consider the straightforward approach of listing and counting
2 x 10^5 = 2 x 100,000 = 200,000
9 x 10^5 = 9 x 100,000 = 900,000

So, we're must consider values between 200,000 and 900,000
The first value whose digits add to 3 is: 200,001
The next one is: 200,010
And: 200,100
201,000
210,000
And there's one more: 300,000

TOTAL = 6

RELATED VIDEOS

_________________
##### General Discussion
Math Expert V
Joined: 02 Aug 2009
Posts: 8340
Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

1
1
franz711 wrote:
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9
b) 8
c) 7
d) 6
e) 5

Hi,

Pl post in Correct format

For the sum of digits to be three, two cases..
1) the first digit is 2, so (3-2) or 1 can take place at any of 5 places after 2..
Example 200001,200010..
So ways = 5
2) 3 in first place, the rest can only be 0..
So 1 way ... 300000

Total 5+1=6
D
_________________
Intern  S
Joined: 11 Aug 2016
Posts: 46
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

franz711 wrote:
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9
b) 8
c) 7
d) 6
e) 5

We need to find integers between 200000 and 900000 such that the sum of the digits is 3

For numbers between 200000 and 299999, the first digit is 2. We need one digit to be 1 and the rest to be all 0's
The number will be of the form 2 _ _ _ _ _ where one place is 1 and the rest are all 0's. 1 can take any of the 5 places after 2, so there will be 5 integers
210000, 201000, 200100, 200010, and 200001 => 5 integers

Next for numbers starting with the digit 3, all the places need to be 0 for the sum to be 3
Hence only one number is possible
300000 => 1 Integer

For any numbers after 300000, the sum of the digits will be greater than 3.

Hence a total of 6 integers are possible. Answer D
Retired Moderator P
Joined: 19 Mar 2014
Posts: 915
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

1
1
How many integers are there between 2 * 10^5 and 9 * 10^5 so that the sum of their digits is 3?

$$2 * 10^5$$ = $$200,000$$

$$9 * 10^5$$ = $$900,000$$

We need to find number of integers, whose some of digits is 3

First Digit: 200,001

We will get the sum of digits 3 for 5 different places of 1 = 200,001, 200,010, 200,100 201,000, 210,000 = 5 Integers

Next and the only number whose digits sun to 3 is: 300,000 = 1 Integer

Hence, Total Integers $$= 5+1 = 6$$

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Director  V
Joined: 04 Dec 2015
Posts: 731
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

1
franz711 wrote:
How many integers are there between 2 x 10^5 and 9 X 10^5 so that the sum of their digits is 3?

a) 9
b) 8
c) 7
d) 6
e) 5

$$2 * 10^5 = 200000$$

$$9 * 10^5 = 900000$$

From the given set of integers, sum of digits to be 3 would be; $$2 + 1 = 3$$. and $$3 + 0 = 3$$.

Numbers would be ;

$$200001,200010,200100,201000,210000 = 5$$ integers.

$$300000 =1$$ integer.

Total number of integers with sum of digits $$3 = 5 + 1 = 6$$. Answer (D)...

_________________
Please Press "+1 Kudos" to appreciate. Non-Human User Joined: 09 Sep 2013
Posts: 13959
Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: How many integers are there between 2 x 10^5 and 9 X 10^5 so that the   [#permalink] 24 Nov 2019, 02:22
Display posts from previous: Sort by

# How many integers are there between 2 x 10^5 and 9 X 10^5 so that the  