The concept tested in this GMAT practice question is counting method and elementary number properties. A GMAT 650 to 700 level problem solving sample question.
Question 2: How many different positive integers exist between 106 and 107, the sum of whose digits is equal to 2?
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.
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'.
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'.
Possibility 2: One digit is 2 and the remaining are 0s.
The only possibility is 2000000.
1. Number Systems | Types of Numbers | Chart
2. Number Properties | Rational & Irrational Numbers
3. GMAT Number Properties | Indices & Rule of Exponents
4. Number Systems | Surds & Conjugates
5. Number Properties | Tests of divisibility
6. Number Properties | How to check whether a number is prime?
7. Number Properties | How to prime factorize a number?
8. GMAT Number Theory | Prime factorization | Properties of squares & cubes
9. Number Properties | What is HCF? | How to find HCF?
10. Number Properties | What is LCM? | How to find LCM?
11. 3 important properties of LCM & HCF | LCM & HCF of fractions
12. Number Properties | When to use LCM and HCF?
13. Number Theory | How to find number of factors?
14. Number Theory | Number of ways to express as a product of 2 factors
15. Number Theory | Sum of all factors of a number
16. Number Theory | Product of all factors of a number
17. Number Theory | Remainders of sum & product
18. Number Theory | Remainder of dividing xn by 'd'
19. Polynomials | Remainder when a monomial divides it
20. Number Theory | Highest power of a prime that divides factorial of 'n'
21. Number Theory | Highest power of a composite number that divides factorial of 'n'
22. Number Theory | Number of trailing zeroes in a number
23. Number Theory | Unit digit of higher powers of numbers
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