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
MAth Number problem -
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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
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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I believe the answer is Cvarun289 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
![Image](https://s8.postimage.org/6t49myq29/sum_of_5.jpg)
More on this question here: https://www.beatthegmat.com/very-tricky- ... 25349.html
Cheers,
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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.)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 number of natural number solutions for a+b+c+d=5 is 8C3=56 and hence the answer.
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
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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Check here for similar problems:
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https://www.beatthegmat.com/tricky-counting-t92069.html
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https://www.beatthegmat.com/combinations-t120668.html
https://www.beatthegmat.com/tricky-counting-t92069.html
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Numbers less than 100,000 will be 5-digit numbers (or less).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
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
Cheers,
Brent