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?

- 128
- 142
- 143
- 141
- 129

From INR

Find the first and last term of the series

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.

Compute the number of terms

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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