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by varun289 » Wed Dec 05, 2012 8:38 pm
38. How many positive integers less than 10,000 are there in which sum of digits equals 5?
(a) 31
(b) 51
(c) 56
(d) 62
(e) 93
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by Jim@StratusPrep » Thu Dec 06, 2012 8:10 am
0- 99 ---- 6
100 - 199 --- 4
300 - 399 --- 3
400 - 499 --- 2
500 - 599 --- 1

1000 - 1099 --- 5
1100 - 1199 --- 4
1200 - 1299 --- 3
1300 - 1399 --- 2
1400 - 1499 --- 1

2000 - 2099 --- 4
2100 - 2199 --- 3
2200 - 2299 --- 2
2300 - 2399 --- 1

The pattern will continue to drop the highest number so ther are 6 between 3000 and 3999, 3 between 4000 and 4999 and then just 1 at 5000

Your total is 16 + 15 + 10 + 6 + 3 + 1 = 51
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by Brent@GMATPrepNow » Thu Dec 06, 2012 8:17 am
varun289 wrote:38. How many positive integers less than 10,000 are there in which sum of digits equals 5?
(a) 31
(b) 51
(c) 56
(d) 62
(e) 93
I believe the answer is C

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More on this question here: https://www.beatthegmat.com/very-tricky- ... 25349.html

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by The Iceman » Thu Dec 06, 2012 9:38 am
varun289 wrote:38. How many positive integers less than 10,000 are there in which sum of digits equals 5?
(a) 31
(b) 51
(c) 56
(d) 62
(e) 93
The best way to see this problem is to imagine abcd as any generic number from 1 to 9999, such that a+b+c+d=5 (e.g. 5 can be represented as 0005, 122 can be represented as 0122, etc.)
The number of natural number solutions for a+b+c+d=5 is 8C3=56 and hence the answer.
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by varun289 » Thu Dec 06, 2012 9:59 am
brent logic is best ,
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by ritind » Sat Dec 08, 2012 2:15 am
Brent if the question would have been
How many positive integers less than 100,000 are there in which sum of digits equals 6?
Will the ans be 9C3 i.e. 84
Just wanted to know if i got the logic rite or wrong. Pl. help
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by GMATGuruNY » Sat Dec 08, 2012 6:03 am
Check here for similar problems:

https://www.beatthegmat.com/permutation- ... 23007.html

https://www.beatthegmat.com/combinations-t120668.html

https://www.beatthegmat.com/tricky-counting-t92069.html
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by Brent@GMATPrepNow » Sat Dec 08, 2012 9:15 am
ritind wrote:Brent if the question would have been
How many positive integers less than 100,000 are there in which sum of digits equals 6?
Will the ans be 9C3 i.e. 84
Just wanted to know if i got the logic rite or wrong. Pl. help
Numbers less than 100,000 will be 5-digit numbers (or less).
So, using my technique, we need xC4 to take x things and divide it into 5 regions.
To get a sum of 6, we need x to be such that, when we choose 4 items, there must be 6 items left.
So, we need x to be 10.

So, my long-winded answer to your question is....

How many positive integers less than 100,000 are there in which sum of digits equals 6?
Answer = 10C4

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by ritind » Sun Dec 09, 2012 9:54 pm
Thanks Brent I gt the logice now
Thanks GMATGuruNY: I was looking for more question on P&C topic
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