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How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
- a)6
- b)7
- c)5
- d)8
- e)18
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many different positive integers exist between 106 and 107, the su...
Method 1: Find the number of such integers existing for a lower power of 10 and extrapolate the results.
Between 10 and 100, that is 101 and 102, we have 2 numbers, 11 and 20.
Between 100 and 1000, that is 102 and 103, we have 3 numbers, 101, 110 and 200.
Therefore, between 106 and 107, one will have 7 integers whose sum will be equal to 2.
Alternative approach
All numbers between 106 and 107 will be 7 digit numbers.
There are two possibilities if the sum of the digits has to be '2'.
There are two possibilities if the sum of the digits has to be '2'.
Possibility 1: Two of the 7 digits are 1s and the remaining 5 are 0s.
The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.
So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.
The left most digit has to be one of the 1s. That leaves us with 6 places where the second 1 can appear.
So, a total of six 7-digit numbers comprising two 1s exist, sum of whose digits is '2'.
Possibility 2: One digit is 2 and the remaining are 0s.
The only possibility is 2000000.
The only possibility is 2000000.
Total count is the sum of the counts from these two possibilities = 6 + 1 = 7
Choice B is the correct answer.
Most Upvoted Answer
How many different positive integers exist between 106 and 107, the su...
Understanding the Problem
To find the different positive integers between 106 and 107 whose sum of digits is equal to 2, we need to analyze and determine the possible numbers that satisfy this condition.
Identifying the Numbers
- The numbers between 106 and 107 are 107, 106.
- To find the sum of digits equal to 2, the possible numbers are 107, 106, 17.
Calculating the Sum of Digits
- For the number 107: 1 + 0 + 7 = 8 (Not equal to 2)
- For the number 106: 1 + 0 + 6 = 7 (Not equal to 2)
- For the number 17: 1 + 7 = 8 (Not equal to 2)
Determining the Correct Answer
After analyzing the possible numbers between 106 and 107 and checking their sum of digits, we can see that there are 2 numbers (106 and 17) whose sum of digits is equal to 2.
Therefore, the correct answer is option B) 7.
To find the different positive integers between 106 and 107 whose sum of digits is equal to 2, we need to analyze and determine the possible numbers that satisfy this condition.
Identifying the Numbers
- The numbers between 106 and 107 are 107, 106.
- To find the sum of digits equal to 2, the possible numbers are 107, 106, 17.
Calculating the Sum of Digits
- For the number 107: 1 + 0 + 7 = 8 (Not equal to 2)
- For the number 106: 1 + 0 + 6 = 7 (Not equal to 2)
- For the number 17: 1 + 7 = 8 (Not equal to 2)
Determining the Correct Answer
After analyzing the possible numbers between 106 and 107 and checking their sum of digits, we can see that there are 2 numbers (106 and 17) whose sum of digits is equal to 2.
Therefore, the correct answer is option B) 7.
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How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?a)6b)7c)5d)8e)18Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?a)6b)7c)5d)8e)18Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?a)6b)7c)5d)8e)18Correct answer is option 'B'. Can you explain this answer?.
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