The GMAT Math practice question given below is a sequences and series question based on Arithmetic Progressions about finding number of terms of an Arithmetic sequence. An easy question - GMAT 600 to 650 level problem solving question.
Question 17: How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?
The smallest 3-digit positive integer that leaves a remainder of 5 when divided by 7 is 103.
The largest 3-digit positive integer that leaves a remainder of 5 when divided by 7 is 999.
The series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an A.P (arithmetic progression) with 103 as the first term and 999 as the last term. The common difference of the sequence is 7.
In an A.P, the last term l = a + (n - 1) * d, where 'a' is the first term, 'n' is the number of terms of the series and 'd' is the common difference.
Therefore, 999 = 103 + (n - 1) * 7
Or 999 - 103 = (n - 1) * 7
Or 896 = (n - 1) * 7
So, n - 1 = 128 or n = 129
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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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