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It is said that there are 5 consecutive prime numbers in each set and 1 set has a range as even. We Know since prime numbers are odd except 2., so Odd-Odd= Even. Hence 2 is in one set... Now the set is [2,3,5,7,11]
Another set has 2 numbers in common of 1st set.. So it should be 7,11 bcz if we take any other number consecutive numbers criteria would be ruled out.
Ex: taking 5,7,11,13,17,19... this set have 3 numbers in common as we can only take consecutive prime number.
Hence, set is [7,11,13,17,19] of which range is 19-7=12.
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Range of the set with the smaller sum of terms is odd means that the largest prime is odd and the smallest prime is even. This narrows down the possibilities for the first set because 2 is the only even prime.

So Set 1 is the set of 2, 3, 5, 7, 11.

For Set 2 to have 2 primes in common, it must start with 7 and 11. So Set 2 is 7, 11, 13, 17, and 19.

The range of Set 2 is 19 - 7 which is 12.
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**The set has to be exactly 2 prime numbers in common**
First set has to start with 2 because all other pime numbers are odd and ODD - ODD = EVEN
so the get an odd range 1st set = {2,3,5,7,11}
to have atleast 2 numbers in common we can start with: {7,11} not {3,5,7,11} --> which will have 4 numbers in common.
So range of the next set will be: {7,11,13,17,19} = 12 (Even number)
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First set has a range as an odd number. This is only possible if the set starts from 2 since all other prime numbers are odd, therefore, their range will always be even. E.g. 31,37,41,43 has range of 12. This is true for all sets of prime numbers starting from 3.
So, first set is 2,3,5,7,11. Second set has 2 common prime numbers and is also consecutive, so only option is 7,11,13,17,19 and hence the range 12 is the answer.
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Hi,

IMO Ans D. As 1st set range is odd, which means 2 is in the set, hence we can find the consecutive Prime no set for the 2 sets. Please let me know if my logic is correct. Thanks
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Since, the sets are "consecutive primes", the last two items of one set will be the first two items in the other set. Like,

Set A = {p1, p2, p3, p4, p5}

Set B = {p4, p5, P1, P2, P3}

Also, given the range of the set with smaller sum of terms is odd:

Range is the difference between the maximum and minimum value in a set. Any addition or subtraction between odds is always even, and since the range here is odd, it must be that the difference is between an odd and an even number, and since 2 is the only prime, Set A & B must be:
Set A = {2,3,5,7,11}
Set B = {7,11,13,17,19}

Range of Set B = 19 - 7 = 12

Option D
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Facts given in the question -
1. There are two different sets containing five consecutive prime numbers
2. The sets contain 2 common primes
3. The set with the smaller sum of terms has an even range

We will start the question by cornering the statement which can help us identify one of the sets. In this case that is statement 3 as explained below:

Apart from 2 all the other primes are odd and hence the range can only be odd if 2 is involved (odd-even = odd and vice versa). So smaller set => {2,3,5,7,11}

As we have only 2 primes common (statement 2) the other set => {7,11,13,17,19}

Range of the other set => 19 - 7 =12 => Correct answer is D
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Let us assume that the first set = 2, 3, 5, 7, 11.

Now since the other set has exactly 2 numbers in common, the other set can be 7, 11, 13, 17, 19

The range is 19-7=12
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Set 1 = (2,3,5,7,11) & Set 2 = (7,11,13,17,19) Range (set 2) = 19-7 = 12

Since set with smaller sum has an odd range, it should be Odd-Even = Odd and only even prime no is 2
Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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Solution:

Suppose in set 1, five consecutive primes are 2, 3, 5, 7, 11, and in set 2, the five consecutive primes where two primes are in common are 7, 11, 13, 17, 19. If the range in the first set is 9, which is odd, then the range in the second set is 12. So, the answer is option D.
Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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Let the smaller set of consecutive primes be S1 and the larger set of consecutive primes be S2.
Given that range of S1 is ODD which means ODD-EVEN= ODD. The only even prime is 2. Hence set S1 is (2,3,5,7,9)
Given that set S2 and set S1 have exactly two common primes that means set S2 must be from (7,9,11,13,15). The range of S2 is 17-7=10.

Answer is 10

Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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samalest 5 cosecutive prime are 2,3,5,7,11 and overlaping 7 & 11 other set least possible sume would be 7,11,13,17,19. so 7-19=12

Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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Hello,
As the range is odd no it means that it has even no as prime in it
so sets will have (2,3,5,7,11)
so other set have exactly two common so that will have ( 7,11,13,17,19)
so range will be 12
Option D is correct
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Given two sets of consecutive primes with smaller set's range being odd.
If range is odd -> that means [highest - small value] is odd

This is possible if only one of them is even and other is odd because
even \(+/-\) odd is odd
and in all other cases, sum or subtraction will lead to even value

\(2\) is the only even prime. So this set should have \(2\) in it so that the range becomes odd. Since the set is a consecutive set of 5 primes, therefore the set will be
{\(2, 3, 5, 7, 11\)}

The other set is also consecutive set of 5 primes but it has only 2 overlapping. To be consecutive + only two overlapping, the set has to start from last two of the previous set
i.e {\(7, 11, 13, 17, 19\)}
range of this set
= 19-7
=12
Ans: Option D
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I’m bit confused how two sets can share exactly two primes

Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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Range is odd so atlease one even prime no. 2 is present.
Set will be {2,3,5,7,11}
To have exactly 2 matching element, only 7 & 11 is possible. The other set can be {7,11,13, 17, 19}
Range 19 - 7 = 12

Ans is 12
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The key inference to make here is the difference between two numbers will be odd, only if, one of them is even.
Since the range of the first set of prime numbers is odd and two is the only existing even prime number it must be part of the set.
Hence, the first set will be

2,3,5,7,11

And since the second set has two numbers in common and there can be no negative primes the second set is

7,11,13,17,19

That is why the range is 19-7 = 12

Bunuel
Each of the two sets consists of five consecutive prime numbers, and the sets have exactly two primes in common. If the range of the set with the smaller sum of terms is odd, what is the range of the other set?

A. 3
B. 8
C. 10
D. 12
E. 17
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