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x is an integer such that 1 ≤ x ≤ 100
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22 Aug 2021, 23:20
22 Aug 2021, 23:20
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Question Stats:
16% (02:25) correct
83% (02:31) wrong based on 78 sessions
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\(x\) is an integer such that \(1 ≤ x ≤ 100\)
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Probability that \(x(x + 1)\) is a multiple of 12 and 9 |
\(\frac{1}{10}\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: x is an integer such that 1 x 100
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30 Mar 2022, 03:19
30 Mar 2022, 03:19
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It took some time, I hope my solution is correct.
To be divisible by 9 and 12 means to be divisible by 2*2*3*3 (LCM). Which means that the original pair of numbers should be divisible by 12 and 3 or by 9 and 4 or by 6 and 6. As it is impossible for two neighbor number to be divisible by 6, we have not to examine this case. If we list all number that are divisible by 12 in given range, no neighbor number is divisible by 3. If we list all numbers divisible by 9, there are 5 pairs where neighbor number can be divided by 4, namely pairs: (8,9)(27,28)(44,45)(63,64)(91,92). Which means there are 5 pairs that satisfy the question. Overall there are 100/2=50 possible pairs in the given range, therefore answer is 5/50=1/10, which means correct choice is C
To be divisible by 9 and 12 means to be divisible by 2*2*3*3 (LCM). Which means that the original pair of numbers should be divisible by 12 and 3 or by 9 and 4 or by 6 and 6. As it is impossible for two neighbor number to be divisible by 6, we have not to examine this case. If we list all number that are divisible by 12 in given range, no neighbor number is divisible by 3. If we list all numbers divisible by 9, there are 5 pairs where neighbor number can be divided by 4, namely pairs: (8,9)(27,28)(44,45)(63,64)(91,92). Which means there are 5 pairs that satisfy the question. Overall there are 100/2=50 possible pairs in the given range, therefore answer is 5/50=1/10, which means correct choice is C
