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TAGS: Senior Manager Joined: 20 May 2014
Posts: 282
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Kudos [?]: 50  , given: 220

How many integers between 1 and 10^21 are such that the sum [#permalink]
2
KUDOS 00:00

Question Stats: 36% (01:36) correct 63% (00:58) wrong based on 33 sessions
How many integers between 1 and $$10^{21}$$ are such that the sum of their digits is 2?

A. 190
B. 210
C. 211
D. 230
E. 231

Kudos for correct solution.
[Reveal] Spoiler: OA Director Joined: 20 Apr 2016
Posts: 826
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 603  , given: 124

Re: How many integers between 1 and 10^21 are such that the sum [#permalink]
1
KUDOS
Bunuel wrote:
How many integers between 1 and 10^21 are such that the sum of their digits is 2?

A. 190
B. 210
C. 211
D. 230
E. 231

Kudos for correct solution.

10^21 here we have two option

1. 1+1 = 2

2. 2+0 =2

Now for the first option ,

10^21 can be written as = 1,000,000,000,000,000,000,000 i.e 21 zero's

Here we have to fill two places with 1 out of 21 places i.e 11,1001,100001 ....(since the number has to be less than 10^21)

so we can use the combination formula as 21C2 as we are choosing two places from the 21 places of zero's
=210 ways.

Now for the option 2, choosing 2
we have 21 ways i.e 02,020,200,2000 ....(i.e we can fill up the 21 zero's places with 2,as the number has to be less than 10^21)

Therefore total no of ways =210+21=231 ways.
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Intern Joined: 22 Jul 2018
Posts: 41
Followers: 0

Kudos [?]: 10 , given: 5

1. How many integers between 2,000 and 3,999 have a ones digit??
2. How many integers between 0 and 1570 have a prime tens digit and a prime units digit?
Director Joined: 20 Apr 2016
Posts: 826
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 603 , given: 124

Re: Similar problems [#permalink]
ruposh6240 wrote:
1. How many integers between 2,000 and 3,999 have a ones digit??
2. How many integers between 0 and 1570 have a prime tens digit and a prime units digit?

The first ques- is not complete

2. there are 252 integers.

Next time would request you to read the rules before posting, as this type of post are not encouraged

https://greprepclub.com/forum/rules-for ... -1083.html
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Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 107 , given: 4

Re: How many integers between 1 and 10^21 are such that the sum [#permalink]
Expert's post
Bunuel wrote:
How many integers between 1 and $$10^{21}$$ are such that the sum of their digits is 2?

A. 190
B. 210
C. 211
D. 230
E. 231

Kudos for correct solution.

How many digits will 10^n have ;- n+1, so 10^21 will have 22 digits - 1 of one and 21 of zeroes
but we are looking for < 10^21, so we will have 22-1=21 digits to fill up..

we can get 2 in two forms
1) 1+1
2) 2+0

so
1) 1+1..... choose 2 places out of 21 for two 1s....21C2=21*10=210
2) 2+0...... choose one place out of 21 for one 2.... 21C1=21

total = 210+21=231
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Intern Joined: 27 Oct 2018
Posts: 49
Followers: 0

Kudos [?]: 12 , given: 27

Re: How many integers between 1 and 10^21 are such that the sum [#permalink]
231 is the right answer
Intern Joined: 02 Oct 2018
Posts: 31
Followers: 0

Kudos [?]: 2 , given: 0

Re: How many integers between 1 and 10^21 are such that the sum [#permalink]
231 ways. 21C2+ 21C1 Re: How many integers between 1 and 10^21 are such that the sum   [#permalink] 04 Nov 2018, 22:38
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