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Number Theory - December 13, 2004
The GMAT Sample Math question for the day is from the topic Number Theory.
Question
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 result of the present case.
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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