The question is a problem on counting properties in number theory.
Question 2
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
The correct choice is (B) and the correct answer is 7.
Explanatory Answer
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.
Similarly, 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.
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This eBook has 80 Problem Solving questions and 49 Data Sufficiency questions in Number Properties and Number Theory. Concepts covered include LCM, HCF, remainder theorem in number theory, factors, factorials and numerous word problems. Detailed explanatory answers provided to each question.
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