GMAT Quant Practice | Set Theory Q2

Union of 3 sets & its complement | Set Theory | GMAT Sample Questions

The GMAT practice question is a problem solving question from the topic Set Theory. Concept tested: Compute the union of 3 sets and compute its complement. A medium difficulty, GMAT 600 level, Set Theory sample question.

Question 2: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

  1. 0
  2. 20
  3. 10
  4. 18
  5. 25

Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3500


Video Explanation


GMAT Live Online Classes


Starts Tue, Oct 12, 2021


Explanatory Answer | GMAT Set Theory Practice

Objective: Compute number of candidates who had none of the three.

Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three.

Total number of candidates = 200.

Number of candidates who had at least one of the three = n(A ∪ B ∪ C),
where A is the set of those who have a two wheeler, B is the set of those who have a credit card, and C is the set of those who have a mobile phone.

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - {n(A ∩ B) + n(B ∩ C) + n(C ∩ A)} + n(A ∩ B ∩ C)

Therefore, n(A ∪ B ∪ C) = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or n(A ∪ B ∪ C) = 190.

n(A ∪ B ∪ C) is the number of candidates who had at least one of three.
As 190 candidates who attended the interview had at least one of the three,
(200 - 190 = 10) candidates had none of three.

Choice C 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 Set Theory Videos On YouTube


Additional Practice Questions in Set Theory

  1. Wizako's GRE Sample Question in Set Theory
  2. 2IIM's CAT Set Theory Practice Questions
  3. Ascent's Set Theory Questionbank

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
Nungambakkam
Chennai 600 034. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message