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13 Mar 2023, 13:42
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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45% (02:45) correct
55%
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Nancy is asked to select integers, between \(0\) and \(10^{13}\). If she is instructed to select only those integers whose sum of digits is 3, then how many different integers can she select within the given range?
A) 235
B) 340
C) 377
D) 455
E) 533
A) 235
B) 340
C) 377
D) 455
E) 533
15 Mar 2023, 17:17
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D) should be the answer to this:
1. 10^13 has 13 digits.
2. The possible digits of that number to get [ ∑(digits(10^13)) = 3 ] are 1+1+1+10*0, 1+2 + 11*0, and 3 + 12*0
3. The first option, 1+1+1+10*0 can be attained in 13!/(10! * 3!) = 11*12*12/3! = 11*2*13 = 286 ways
4. The second option, 1+2+11*0 can be attained in 13!/11! = 12*13 = 156 ways
5. The last option, 3+12*0 can be attained in 13!/12! = 13 ways
6. Finally, ∑(ways to attain a number whose numbers sum up to 3) = 286+156+13 = 455
-> The final answer should be 455
1. 10^13 has 13 digits.
2. The possible digits of that number to get [ ∑(digits(10^13)) = 3 ] are 1+1+1+10*0, 1+2 + 11*0, and 3 + 12*0
3. The first option, 1+1+1+10*0 can be attained in 13!/(10! * 3!) = 11*12*12/3! = 11*2*13 = 286 ways
4. The second option, 1+2+11*0 can be attained in 13!/11! = 12*13 = 156 ways
5. The last option, 3+12*0 can be attained in 13!/12! = 13 ways
6. Finally, ∑(ways to attain a number whose numbers sum up to 3) = 286+156+13 = 455
-> The final answer should be 455
samarpan.g28
10 Jul 2024, 07:25
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gmatophobia
\(10^{13}\) means 13 digits thus we can pick numbers from 0 to \(10^{13}\) where the sum of their digits=3.
How will the sum be 3? When the digits will include any of the below.
a. 1,2
b. 1,1,1
c. 3
Rest, we will fill with zeroes. There is nothing to worry about initial zeroes as we already know that the numbers can be anything from a single-digit to a 13-digit number.
For a, we need to add eleven zeroes apart from 1 and 2 thus the possible ways to get numbers are 13!/11!=156.
For b, we need to add ten zeroes so 13!/(10!*3!)=286.
For c, we need to add twelve zeroes so 13!/12!=13.
156+286+13=455. Option (D) is correct.
