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18 Jun 2018, 00:49
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D
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Difficulty:
85%
(hard)
Question Stats:
45% (02:31) correct
55%
(02:59)
wrong
based on 47
sessions
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In the 6-digit integer \(543,2xy\), \(x\) and \(y\) are chosen from the digits 0, 2, 4, 6 and 8. What is the probability that \(543,2xy\) is divisible by 8?
A. \(\frac{1}{5}\)
B. \(\frac{6}{25}\)
C. \(\frac{7}{25}\)
D. \(\frac{8}{25}\)
E. \(\frac{9}{25}\)
A. \(\frac{1}{5}\)
B. \(\frac{6}{25}\)
C. \(\frac{7}{25}\)
D. \(\frac{8}{25}\)
E. \(\frac{9}{25}\)
18 Jun 2018, 00:49
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Official Solution:
In the 6-digit integer \(543,2xy\), \(x\) and \(y\) are chosen from the digits 0, 2, 4, 6 and 8. What is the probability that \(543,2xy\) is divisible by 8?
A. \(\frac{1}{5}\)
B. \(\frac{6}{25}\)
C. \(\frac{7}{25}\)
D. \(\frac{8}{25}\)
E. \(\frac{9}{25}\)
An integer with three or more digits is divisible by 8 if and only if its last three digits from a number that is divisible by 8.
The values of \(2xy\) that are divisible by 8 are 200, 208, 224, 240, 248, 264, 280, and 288.
The total number of 6-digit integers of the form \(543,2xy\) is equal to the number of ways of choosing two digits from 0, 2, 4, 6 and 8, which is 5*5 = 25.
Thus, the probability that \(543,2xy\) is divisible by 8 is \(\frac{8}{25}\).
Answer: D
In the 6-digit integer \(543,2xy\), \(x\) and \(y\) are chosen from the digits 0, 2, 4, 6 and 8. What is the probability that \(543,2xy\) is divisible by 8?
A. \(\frac{1}{5}\)
B. \(\frac{6}{25}\)
C. \(\frac{7}{25}\)
D. \(\frac{8}{25}\)
E. \(\frac{9}{25}\)
An integer with three or more digits is divisible by 8 if and only if its last three digits from a number that is divisible by 8.
The values of \(2xy\) that are divisible by 8 are 200, 208, 224, 240, 248, 264, 280, and 288.
The total number of 6-digit integers of the form \(543,2xy\) is equal to the number of ways of choosing two digits from 0, 2, 4, 6 and 8, which is 5*5 = 25.
Thus, the probability that \(543,2xy\) is divisible by 8 is \(\frac{8}{25}\).
Answer: D
01 Aug 2019, 09:51
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Max value = 288
Min value = 200
Both these numbers are divisible by 8, therefore
>>> 288 - 200 = 88
> 88/8 = 11
Meaning there are a total of 11+1 = 12 numbers and the probability would be 12/25!
In this set "200, 208, 224, 240, 248, 264, 280, and 288" you have missed: 216, 232, 256 and 272 making a total of 12 numbers that are divisible by 8
Min value = 200
Both these numbers are divisible by 8, therefore
>>> 288 - 200 = 88
> 88/8 = 11
Meaning there are a total of 11+1 = 12 numbers and the probability would be 12/25!
In this set "200, 208, 224, 240, 248, 264, 280, and 288" you have missed: 216, 232, 256 and 272 making a total of 12 numbers that are divisible by 8
