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To solve this, we need to remember that:
Odd - odd = even
Odd - even = odd.

Thus, because the range of the set with the smaller sum is odd, we can deduce that said set starts with 2

Thus, the 1st set will be :
2, 3, 5, 7, 11

And because there are ONLY 2 prime in common, the 2nd set will be

7, 11, 13, 17, 19

Thus, the range of the 2nd set is \(19 - 7 = 12, \)thus D
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We know that there are 2 sets with 5 consecutive prime numbers and they have 2 prime numbers in common.
One of the set's is smaller in sum and also its range is odd

Given what we know, what we can conclude is there is an even numbered prime number in the smaller sum set as its range is odd (smaller number and larger number should be even or odd) and this is possible if the set is
Set 1 = {2,3,5,7,11}

We know that 2 primes are common between the sets and the sets have consecutive primes, the 2 sets have overlapping and adjacent primes
=> Set 2 = {7,11,13,17,19}

Since we require the range of the other set
Range 2 = 19 - 7 = 12

D. 12
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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 Set 1 = [2,3,5,7,11]
Let set 2 = [7,11,13,17,19]

As can be seen, sum of Set 1 < Sum of set 2.
set 1 range = 11 - 2 = 9 (odd)
The range of the other set is 19 - 7 = 12
Option D.
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I think the answer is D. first set 2,3,5,7,11 range is 9 7,11,13,17,19 range is 12
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First set - (2,3,5,7,11)
Range of this is 9 which is odd.
As 2 is the only prime number which will result in odd range.

Second set - (7,11,13,17,19)
Range - 12. Answer
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So the question has mentioned two sets with 5 consecutive integers and two common prime numbers. So the last 2 numbers of the first set should be the first two numbers of the 2nd set. And looking after the difference is odd the first number should be an even prime number which is '2', So first set becomes 2,3,5,7,11 and second set 7,11,13,17,19. So range is 19-7 = 12
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Since the range is odd, it is only possible if it has 2 in the set
so, first set = { 2, 3, 5, 7 , 11}
and because the second set has 2 common prime
the second set = {7, 11, 13, 17, 19}
range = 19-7=12
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I think the answer is D:12. Since the range can only be odd if there is an even number on the subtraction, and 2 is the only even number, the range would be 19 - 7 = 12
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let the first set of the prime number be
p1, p2,p3,p4,p5

since the second set has 2 prime number common with the first let them be
p4,p5,p6,p7,p8

The set with smaller sum will be the one with smaller primes . ( set 1)

so the range is
p5 - p1 ( largest number - the smallest number )

The the range of this set is odd , as told in the question .

this set must have 2 in it as , all other prime numbers are odd and odd - odd is always even

so the first set is
2,3,5,7,11
range 11-2 = 9 (odd )

second set will be
7,11,13,17,19
range 19 - 7 = 12

Range of other set = 12
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Set 1 parameters because it has an odd range: [2,3,5,7,11]
Set 2 parameters because they have exactly two primes in common: [7,11,13,17,19]

Range of set 2 = 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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Since the range of the smaller set is odd, the set must be {2, 3, 5, 7, 11} (2 is the only even prime number)
Therefore the larger set is {7, 11, 13, 17, 19} => Range = 19 - 7 = 12

Answer: 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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we can get odd number by subtacting even number from odd number also all the prime numbers apart from 2 are odd so the first set will be {2,3,5,7,11} and range is 9 for this which is odd
now to make the 2nd set with 2 common prime numbers it will be {7,11,13,17,19} range of this is 12
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Bunuel

GMAT Club Official Explanation:



Two sets of five consecutive primes that share exactly two must be:

Smaller set: {p1, p2, p3, p4, p5}
Larger set: {p4, p5, p6, p7, p8}

For the smaller set to have an odd range, p5 - p1 must be odd, so p5 must be odd and p1 must be even. All primes except 2 are odd, so this happens only if p1 = 2. That forces the smaller set to be {2, 3, 5, 7, 11}, whose range is 9.

The overlapping larger set is then {7, 11, 13, 17, 19}, and its range is 12.

Answer: D.

but why can we not take 5 and 7 common?, the question says exactly two primes overlapping but does not specify which
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quaevoluptate

but why can we not take 5 and 7 common?, the question says exactly two primes overlapping but does not specify which

If one set is {2, 3, 5, 7, 11}, how can it overlap with another set of five consecutive primes with only 5 and 7 in common?
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Set 1 = {2,3,5,7,11}
Set 2 ={7,11,13,17,19}
2 conditions are : 1. exactly two primes in common = 7,11 and the second condition the range of the smaller set which is set 1 has to be odd that is Range =Highest-Lowest which is 11-2 =9, which is odd and hence both the conditions are satisfied
So Range of set2 will be 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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