4GMAT - GMAT Online Practice Test
topic wise list of questions  Topicwise List of Questions
Other useful links
Share your GMAT Test experience
Testimonials
GMAT Prep Freebies
You are here: Home » GMAT Test Prep Questions » Progressions, AP GP » Question 2
Linear Equations   GMAT Math Practice - Arithmetic Progression
The GMAT Math practice question given below is a sequences and series question based on Arithmetic Progressions

Question
How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?
  1. 128
  2. 142
  3. 143
  4. 141
  5. 129
The correct choice is (E) and the correct answer is 129.

Explanatory Answer
The smallest 3-digit positive integer that when divided by 7 leaves a remainder of 5 is 103.
The largest 3-digit positive integer that when divided by 7 leaves a remainder of 5 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 the first term being 103 and the last term being 999 having a common difference of 7.

We know that in an A.P, 'l' the last term is given by 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
Or n - 1 = 128
Or n = 129

Copyright 2004-07 4GMAT.COM
Test Catalyst (India) Private Limited
All rights reserved
GMAT™ and GMAC™ are registered trademarks of the Graduate Management Admission Council™. The Graduate Management Admission Council™ does not endorse, nor is it affiliated in any way with the owner or any content of this web site.