GMAT Exam > GMAT Questions > For any integer P greater than 1, P! denotes ...
Start Learning for Free
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?
- a)0
- b)1/16
- c)3/8
- d)7/16
- e)7/8
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
For any integer P greater than 1, P! denotes the product of all intege...
Understanding the problem:
Factorial of 8, denoted as 8!, is the product of all integers from 1 to 8.
We need to find the probability of choosing a multiple of 28 from the factors of 8!.
Solution:
Finding the factors of 8!
To find the factors of 8!, we need to first calculate the value of 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Now, find all the factors of 40,320.
Factors of 40,320 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080, 40320
Finding the multiples of 28
Multiples of 28 in the factors of 8! are: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372, 1400, 1428, 1456, 1484, 1512, 1540, 1568, 1596, 1624, 1652, 1680, 1708, 1736, 1764, 1792, 1820, 1848, 1876, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2100, 2128, 2156, 2184, 2212, 2240, 2268, 2296, 2324, 2352
Factorial of 8, denoted as 8!, is the product of all integers from 1 to 8.
We need to find the probability of choosing a multiple of 28 from the factors of 8!.
Solution:
Finding the factors of 8!
To find the factors of 8!, we need to first calculate the value of 8!.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Now, find all the factors of 40,320.
Factors of 40,320 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080, 40320
Finding the multiples of 28
Multiples of 28 in the factors of 8! are: 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232, 1260, 1288, 1316, 1344, 1372, 1400, 1428, 1456, 1484, 1512, 1540, 1568, 1596, 1624, 1652, 1680, 1708, 1736, 1764, 1792, 1820, 1848, 1876, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2100, 2128, 2156, 2184, 2212, 2240, 2268, 2296, 2324, 2352
Free Test
FREE
| Start Free Test |
Community Answer
For any integer P greater than 1, P! denotes the product of all intege...
8! = 27∗32∗5∗7
Any factor of 8! can be written as 2a∗3b∗5c∗7d , where a, b, c and d are integers
a can take 8 values (0 to7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 2 values (0 to 1)
Any factor of 8! can be written as 2a∗3b∗5c∗7d , where a, b, c and d are integers
a can take 8 values (0 to7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 2 values (0 to 1)
Number of factors = 8*3*2*2
If the factor of 8! is multiple of 28, in that case-
a can take 6 values (2 to 7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 1 value (only 1)
a can take 6 values (2 to 7)
b can take 3 values (0 to 2)
c can take 2 values (0 to 1)
d can take 1 value (only 1)
Number of multiples of 28 = 6*3*2*1
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?
Question Description
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?.
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?.
Solutions for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer?, a detailed solution for For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For any integer P greater than 1, P! denotes the product of all integers from 1 to P, inclusive. A number is chosen at random from the list of factors of 8!. What is the probability that the chosen number is a multiple of 28?a)0b)1/16c)3/8d)7/16e)7/8Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Suggested Free Tests
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!
within 7 days!
Takes less than 10 seconds to signup