CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Puzzle
× CAT Questions

CAT Quantitative Aptitude
HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Geometry Coordinate Geometry Mensuration Trigonometry Linear & Quadratic Equations Functions Inequalities Polynomials Progressions
CAT Verbal
Para Jumble Sentence Correction Sentence Elimination Paragraph Completion Reading Comprehension Critical Reasoning Word Usage Para Summary Text Completion
DI LR: Bar Graphs DI LR: Pie Charts DI LR: Multiple Graphs DI LR: Word Problems DI LR: Line Graphs DI LR: Sequencing DI LR: Grid Puzzles DI LR: Math Puzzles DI LR: Visualization DI LR: Other Patterns DI LR: CAT 2017 Cet DI LR: CAT 2017 Rural Survey DI LR: CAT 2017 Happiness DI LR: CAT 2017 Airlines DI LR: CAT 2017 Travel Route DI LR: CAT 2017 Food Delivery DI LR: CAT 2017 Square Layout DI LR: CAT 2017 Team Project DI LR: CAT 2017 Assets DI LR: CAT 2017 Pizza DI LR: CAT 2017 Electives DI LR: CAT 2017 Chess DI LR: CAT 2017 Dorms DI LR: CAT 2017 Tea DI LR: CAT 2017 Friends DI LR: CAT 2017 Security Scan

CAT Online Coaching
CAT Question MenuCAT Questions

The question is from Permutation and Combination. It is more like a puzzle than a question. Some conditions are given and we need to find the number of ordered triplets. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 4: a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?

  1. 8
  2. 6
  3. 2
  4. 4

2IIM : Best Online CAT Coaching

Signup and sample 5 classes
for free

Best CAT Coaching in Chennai

Batches filling fast.
Starts Sat, June 8th, 2019

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: This is more a puzzle than a challenging question. But is a very interesting puzzle nevertheless :)

Exactly one of ab, bc and ca is odd => Two are odd and one is even.

abc is a multiple of 4 => the even number is a multiple of 4.
The arithmetic mean of a and b is an integer => a and b are odd.
and so is the arithmetic mean of a, b and c. => a + b + c is a multiple of 3.

c can be 4 or 8.
c = 4; a, b can be 3, 5 or 5, 9
c = 8; a, b can be 3, 7 or 7, 9
Four triplets are possible.

The question is "How many such triplets are possible (unordered triplets)?"

Hence the answer is "4"

Choice D is the correct answer.


CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube

Other useful sources for Permutation and Combination Questions | Probability Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now