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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.
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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
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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?.
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