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15 Dec 2025, 09:34
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Given- Two sets of 5 consecutive prime number with two common primes
=>therefore, sets are shifted by 3 primes.
Smaller set: {2,3,5,7,11} => Range=11-2=9(odd)
Larger set shift by three primes {7,11,13,17,19}
Thus, Range=19-7=12(D)
=>therefore, sets are shifted by 3 primes.
Smaller set: {2,3,5,7,11} => Range=11-2=9(odd)
Larger set shift by three primes {7,11,13,17,19}
Thus, Range=19-7=12(D)
Bunuel
15 Dec 2025, 09:35
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Deconstructing the Question
We have two sets, let's call them Set A and Set B.
1. Each set consists of 5 consecutive prime numbers.
2. The sets have exactly 2 primes in common.
3. The range of the set with the smaller sum is odd.
Target: Find the range of the other set (the one with the larger sum).
Step 1: Analyze the "Odd Range" Condition
Theory: Range = Max - Min.
Most prime numbers are odd. The difference between any two odd numbers is always even (Odd - Odd = Even).
The only way to get an odd range is if one number is even and the other is odd (Odd - Even = Odd).
The only even prime number is 2.
Therefore, the set with the odd range must contain the number 2.
Since 2 is the smallest prime, it must be the first term of that set.
Step 2: Construct the First Set (Smaller Sum)
Let Set A be the set starting with 2.
Set A = \(\{2, 3, 5, 7, 11\}\).
Check Range: \(11 - 2 = 9\).
9 is odd. This condition fits perfectly.
Sum of Set A is obviously the smallest possible sum for any set of positive primes.
Step 3: Construct the Second Set (Larger Sum)
The problem states the sets have exactly two primes in common.
Since Set B must have a larger sum, it follows Set A in the sequence of primes.
The overlap must be the last two primes of Set A. Overlap = \(\{7, 11\}\).
So, Set B must start with 7. Set B = \(\{7, 11, 13, 17, 19\}\).
Step 4: Calculate the Range of the Other Set
Target Set: \(\{7, 11, 13, 17, 19\}\).
Max Value = 19.
Min Value = 7.
Range = \(19 - 7 = 12\).
Answer: D
We have two sets, let's call them Set A and Set B.
1. Each set consists of 5 consecutive prime numbers.
2. The sets have exactly 2 primes in common.
3. The range of the set with the smaller sum is odd.
Target: Find the range of the other set (the one with the larger sum).
Step 1: Analyze the "Odd Range" Condition
Theory: Range = Max - Min.
Most prime numbers are odd. The difference between any two odd numbers is always even (Odd - Odd = Even).
The only way to get an odd range is if one number is even and the other is odd (Odd - Even = Odd).
The only even prime number is 2.
Therefore, the set with the odd range must contain the number 2.
Since 2 is the smallest prime, it must be the first term of that set.
Step 2: Construct the First Set (Smaller Sum)
Let Set A be the set starting with 2.
Set A = \(\{2, 3, 5, 7, 11\}\).
Check Range: \(11 - 2 = 9\).
9 is odd. This condition fits perfectly.
Sum of Set A is obviously the smallest possible sum for any set of positive primes.
Step 3: Construct the Second Set (Larger Sum)
The problem states the sets have exactly two primes in common.
Since Set B must have a larger sum, it follows Set A in the sequence of primes.
The overlap must be the last two primes of Set A. Overlap = \(\{7, 11\}\).
So, Set B must start with 7. Set B = \(\{7, 11, 13, 17, 19\}\).
Step 4: Calculate the Range of the Other Set
Target Set: \(\{7, 11, 13, 17, 19\}\).
Max Value = 19.
Min Value = 7.
Range = \(19 - 7 = 12\).
Answer: D
15 Dec 2025, 09:40
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The range of a set is calculated as the difference between the greatest and smallest number in the set.
The only way that a subtraction can result in an odd number is if we subtract an even number from an odd number or viceversa. (eg. 15-8=7) (subtracting an odd number from an odd number or an even number from an even number always results in an even number) (eg 13-3=10, 16-4=12).
This means that in the smallest set of consecutive prime numbers the smallest number must be even, and since the only even prime number is 2, the smallest number in the set must be 2. This means that the set is the following: {2,3,5,7,11}.
Since the other set has 2 numbers in common with the first set, and since it is also composed of consecutive prime integers, it must have in common the numbers 7 and 11.
Therefore the second set is {7,11,13,17,19}.
The range of this set is 19-7=12
The only way that a subtraction can result in an odd number is if we subtract an even number from an odd number or viceversa. (eg. 15-8=7) (subtracting an odd number from an odd number or an even number from an even number always results in an even number) (eg 13-3=10, 16-4=12).
This means that in the smallest set of consecutive prime numbers the smallest number must be even, and since the only even prime number is 2, the smallest number in the set must be 2. This means that the set is the following: {2,3,5,7,11}.
Since the other set has 2 numbers in common with the first set, and since it is also composed of consecutive prime integers, it must have in common the numbers 7 and 11.
Therefore the second set is {7,11,13,17,19}.
The range of this set is 19-7=12
