GMAT Math Practice | Progressions Q23

GMAT Quant Questions | AP series & LCM

The given question is an easy to moderate level difficulty question combining concepts in Arithmetic Progression and elementary number theory - LCM in particular. It is a GMAT 650 to 700 level problem solving question.

Question 23: In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

  1. 11
  2. 14
  3. 12
  4. 13
  5. 10

Get to Q51 in GMAT Quant

Online GMAT Course
@ INR 3500

Video Explanation

GMAT Live Online Classes

Starts Tue, Oct 12, 2021

Explanatory Answer

Step 1 of solving this GMAT Progressions question: Find the first number common to both the sequences.

The first sequence: Numbers leaving a remainder of 4 when divided by 7: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, ....
The second sequence: Numbers leaving a remainder of 9 when divided by 11: 9, 20, 31, 42, 53, 64, .....

From the listing of the two sequences we can identify the first number that is a part of the both the sequences is 53.

Step 2 of solving this GMAT Progressions question:
Compute common difference of terms common to both sequences and find number of terms

The common difference of the first sequence is 7 and that of the second sequence is 11.
Elements common to both the sequences will have a common difference that is the LCM of 7 and 11.
77 is the LCM of 7 and 11.
Every 77th number after 53 will be a term common to both the series.

So, the terms that are common to both the arithmetic sequences can be expressed as 77k + 53.
Because we are interested in the first 1000 natural numbers, k will take values from 0 to 12.
i.e., a total of 13 values.

Choice D is the correct answer.

GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Oct 12, 2021

★ GMAT Live Info

GMAT Coaching in Chennai

Next Batch
after Lockdown

★ GMAT Class Info

GMAT Coaching in Chennai

Sign up for a Free Demo of our GMAT Classes in Chennai

★ Schedule Demo

GMAT Preparation Online | GMAT Number Properties Videos On YouTube

Other useful sources for Number Properties, Number Systems and Number Theory Sample Questions

GMAT Sample Questions | Topicwise GMAT Questions

Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Chennai 600 034. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Leave A Message