GMAT Questionbank | Number Properties Q2

GMAT Sample Questions | Counting Methods

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?

  1. 6
  2. 7
  3. 5
  4. 8
  5. 18

Get to Q51 in GMAT Quant

Online GMAT Course
From INR 2500

Video Explanation

GMAT Live Online Classes

Starts Sun, April 9, 2023

Explanatory Answer

Method 1 to solve this GMAT Number Properties Question: Find the number of such integers existing for a lower power of 10 and extrapolate the results.

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.

Alternative approach

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.

Total count is the sum of the counts from these two possibilities = 6 + 1 = 7

Choice B 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 April 9, 2023

★ GMAT Live Info

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

Work @ Wizako

How to reach Wizako?

Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Leave A Message