Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Two numbers are chosen from the set <img alt="\{1,3,5,7, \ldots, 143,145,147\}" src="https://en

Two numbers are chosen from the set \{1,3,5,7, \ldots, 143,145,147\}, Determine the number of ways these numbers can be multiplied together to obtain a product that is a multiple of 7.

 

Option: 1

3276

 


Option: 2

3568

 


Option: 3

4296

 


Option: 4

6246


Answers (1)

best_answer

To determine the number of ways two numbers can be multiplied together to obtain a product that is a multiple of 7 from the set \{1,3,5,7, \ldots, 143,145,147\},  we need to consider the factors of 7 .

Since 7 is a prime number, a product will be a multiple of 7 if and only if at least one of the chosen numbers is divisible by 7 .

Let's analyze the given set: \{1,3,5,7, \ldots, 143,145,147\}
Numbers divisible by 7: 7,14,21, \ldots, 147

Now, we can count the number of ways to choose two numbers from this set such that their product is a multiple of 7 .
1. Choose one number divisible by 7 and any other number from the set:
There are 21 numbers divisible by 7(7,14,21, \ldots, 147). So, there are 21 \times 146=3066  ways.

2. Choose two numbers divisible by 7 :
There are 21 numbers divisible by 7(7,14,21, \ldots, 147). So, there 21 \times(21-1) / 2=210 ways.

Therefore, the total number of ways to choose two numbers from the set \{1,3,5,7, \ldots, 143,145,147\}such that their product is a multiple of 7 is 3066+210=3276 ways.

Thus, there are 3276 ways to choose two numbers from the given set such that their product is a multiple of 7.

 

Posted by

Irshad Anwar

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: NTA reopens Session 2 registration; apply by March 13 at jeemain.nta.nic.in
anam-khan

JEE Mains 2026 LIVE: NTA session 2 registration last day, city slip soon; here's how to prepare
anam-khan

JEE Main 2026 session 2 application correction begins on jeemain.nta.nic.in; edit details by tomorrow

Latest Question