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27 Oct 2023, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:15) correct
34%
(02:05)
wrong
based on 176
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Not Attempted Yet
Let x = 36,721. If y is formed by rearranging the digits in x at random (such that x≠y), then what is the probability that y > x ?
A. 2/5
B. 54/119
C. 1/2
D. 65/119
E. 3/5
A. 2/5
B. 54/119
C. 1/2
D. 65/119
E. 3/5
27 Oct 2023, 04:54
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Bunuel
OA is B
Posted from my mobile device
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28 Oct 2023, 10:53
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Number of values y can obtain by rearranging digits = 5! = 120
Since y =/= x, subtract one from 120 (value of x itself), which becomes 119.
Digits: 1, 2, 3, 6, 7
To calculate all values bigger than x, start with the left most digit:
Digits greater than 3: 6, 7 ( 2 numbers)
Therefore, numbers greater than x can be anything which start with either 6 or 7 = 2 * 4! (To arrange the rest of the digits)
= 48
In case left most digit is 3:
the second-most left digit should be greater than 6 (i.e. 7) ( only one number)
Therefore, numbers greater than x with 3 at left = 1 * 1 * 3! = 6
Similarly, moving on to the next place:
7 (Here, there is no number greater than 7)
If we stop and look, we can see that 721 is the greatest number which can be formed even of we rearrange the digits.
Hence, number of values greater than x = 48 + 6 = 54
Therefore, P(y > x) = 54/119
Answer: (B) 54/119
Since y =/= x, subtract one from 120 (value of x itself), which becomes 119.
Digits: 1, 2, 3, 6, 7
To calculate all values bigger than x, start with the left most digit:
Digits greater than 3: 6, 7 ( 2 numbers)
Therefore, numbers greater than x can be anything which start with either 6 or 7 = 2 * 4! (To arrange the rest of the digits)
= 48
In case left most digit is 3:
the second-most left digit should be greater than 6 (i.e. 7) ( only one number)
Therefore, numbers greater than x with 3 at left = 1 * 1 * 3! = 6
Similarly, moving on to the next place:
7 (Here, there is no number greater than 7)
If we stop and look, we can see that 721 is the greatest number which can be formed even of we rearrange the digits.
Hence, number of values greater than x = 48 + 6 = 54
Therefore, P(y > x) = 54/119
Answer: (B) 54/119
