Quant Exam > Quant Questions > A seven-digit number comprises of only 2s and...
Start Learning for Free
A seven-digit number comprises of only 2's and 3's. How many of these are multiples of 12?
- a)10
- b)22
- c)12
- d)11
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A seven-digit number comprises of only 2s and 3s. How many of these ar...
Number should be a multiple of 3 and 4. So, the sum of the digits should be a multiple of 3. We can either have all seven digits as 3, or have three 2's and four 3's, or six 2's and a 3.
(The number of 2's should be a multiple of 3).
For the number to be a multiple of 4, the last 2 digits should be 32. Now, let us combine these two.
All seven 3's - No possibility.
Three 2's and four 3's - The first 5 digits should have two 2's and three 3's in some order.
No of possibilities = 5!3!2!5!3!2! = 10
Six 2's and one 3 - The first 5 digits should all be 2's. So, there is only one number 2222232.
So, there are a total of 10 + 1 = 11 solutions.
(The number of 2's should be a multiple of 3).
For the number to be a multiple of 4, the last 2 digits should be 32. Now, let us combine these two.
All seven 3's - No possibility.
Three 2's and four 3's - The first 5 digits should have two 2's and three 3's in some order.
No of possibilities = 5!3!2!5!3!2! = 10
Six 2's and one 3 - The first 5 digits should all be 2's. So, there is only one number 2222232.
So, there are a total of 10 + 1 = 11 solutions.
Hence the answer is "11"
Choice D is the correct answer.
Most Upvoted Answer
A seven-digit number comprises of only 2s and 3s. How many of these ar...
Value of 100P2:
The value of 100P2 can be calculated using the formula for permutation. Permutation is the arrangement of objects in a specific order. The formula for permutation is given by:
nP r = n! / (n-r)!
Where n is the total number of objects and r is the number of objects to be arranged in a specific order.
Substituting the values of n and r, we get:
100P2 = 100! / (100-2)!
Simplifying the expression, we get:
100P2 = (100 x 99 x 98 x ... x 1) / (98 x 97 x ... x 1)
100P2 = 100 x 99
100P2 = 9900
Therefore, the value of 100P2 is 9900.
The value of 100P2 can be calculated using the formula for permutation. Permutation is the arrangement of objects in a specific order. The formula for permutation is given by:
nP r = n! / (n-r)!
Where n is the total number of objects and r is the number of objects to be arranged in a specific order.
Substituting the values of n and r, we get:
100P2 = 100! / (100-2)!
Simplifying the expression, we get:
100P2 = (100 x 99 x 98 x ... x 1) / (98 x 97 x ... x 1)
100P2 = 100 x 99
100P2 = 9900
Therefore, the value of 100P2 is 9900.
Free Test
FREE
| Start Free Test |
Community Answer
A seven-digit number comprises of only 2s and 3s. How many of these ar...
B/z nCr = n!/(n-r)! So 100P2=100!/(100-2)! =100×99×98!/(98)! =9900
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer?
Question Description
A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer?.
A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer?.
Solutions for A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A seven-digit number comprises of only 2s and 3s. How many of these are multiples of 12?a)10b)22c)12d)11Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup