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11 Nov 2023, 03:06
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74% (02:04) correct
26%
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How many integers in a set of 5 consecutive positive integers are divisible by 4?
(1) The median of the set is odd.
(2) The average (arithmetic mean) of the set is a prime number.
Nice and tricky question!
M12-21
(1) The median of the set is odd.
(2) The average (arithmetic mean) of the set is a prime number.
Nice and tricky question!
M12-21
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19 Nov 2023, 08:00
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How many integers in a set of 5 consecutive positive integers are divisible by 4?
(1) The median of the set is odd.
When a set has an odd number of terms, the median is simply the middle term. In this case, our set of 5 consecutive numbers follows the pattern: {Odd, Even, Odd, Even, Odd}. Among two consecutive even integers, only one will be a multiple of 4. This information is sufficient to determine that there is exactly one integer in the set of 5 consecutive positive integers that is divisible by 4.
(2) The average (arithmetic mean) of the set is a prime number.
In any evenly spaced set, the arithmetic mean (average) is equal to the median. Thus, we have mean = median = prime. Since it's not possible for the median to be equal to the even prime number 2 (in this case, not all 5 numbers will be positive), the median must be an odd prime. This results in the same pattern as the first statement: {Odd, Even, Odd, Even, Odd}. This statement is also sufficient.
Answer: D
(1) The median of the set is odd.
When a set has an odd number of terms, the median is simply the middle term. In this case, our set of 5 consecutive numbers follows the pattern: {Odd, Even, Odd, Even, Odd}. Among two consecutive even integers, only one will be a multiple of 4. This information is sufficient to determine that there is exactly one integer in the set of 5 consecutive positive integers that is divisible by 4.
(2) The average (arithmetic mean) of the set is a prime number.
In any evenly spaced set, the arithmetic mean (average) is equal to the median. Thus, we have mean = median = prime. Since it's not possible for the median to be equal to the even prime number 2 (in this case, not all 5 numbers will be positive), the median must be an odd prime. This results in the same pattern as the first statement: {Odd, Even, Odd, Even, Odd}. This statement is also sufficient.
Answer: D
General Discussion
11 Nov 2023, 03:28
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Bunuel
The set has only 5 integers, hence the median will be the 3rd term in the set.
S = { A, B, C, D, E}
Hence, C is the median in the set.
Statement 1
(1) The median of the set is odd.
If the median of the set is odd, the remainder of the term when divided by 4 will be either 1 or 3, i.e the median will be of the form
N = 4p + 1 or N = 4p + 3
In both cases, the set can only have one number which is divisible by 4.
Hence, this statement alone is sufficient and we can eliminate B, C, and E.
Statement 2
(2) The average (arithmetic mean) of the set is a prime number.
As the members of the set are equally spaced, the mean of the set is equal to the median of the set. Hence, we can infer this statement as "The
The median can either be even or odd.
The median cannot be even, i.e. the median cannot be 2 because of the given constraint that members of the set are positive. Hence, the median of the set is odd.
Hence, statement 2 provides the same information as Statement 1. We already know that Statement 1 is sufficient.
Hence, statement 2 is also sufficient.
Option D
