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12 Days of Christmas GMAT Competition 2025 - Day 1: Each of the two

1 2 3 4 5 6 7

Bunuel

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Updated on: 12 Jan 2026, 05:50

Originally posted by Bunuel on 15 Dec 2025, 09:00.
Last edited by Bunuel on 12 Jan 2026, 05:50, edited 1 time in total.

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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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Bunuel

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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.

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15 Dec 2025, 09:09

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hint is the odd range in set 1
set 1 - 2 3 5 7 11
set 2 7 11 13 17 19

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Updated on: 16 Dec 2025, 10:43

Originally posted by ManifestDreamMBA on 15 Dec 2025, 09:11.
Last edited by ManifestDreamMBA on 16 Dec 2025, 10:43, edited 1 time in total.

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Let the first set be A with a,b,c,d,e
Let the second set be B with d,e,f,g,h
Since the range of A is odd, then a must be 2

so, A = 2,3,5,7,11
B = 7,11,13,17,19
Range of B = 19-7 = 12

Bunuel

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15 Dec 2025, 09:12

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only 2 is eve prime number , so e-o=o that the only possiblity
so lowest number is 2 in set a
a{2,3,5,7,11}
b since two is same{7,11,13,17,19}
19-7=12

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15 Dec 2025, 09:12

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The first thing that comes to mind after reading this problem is to write out first five consecutive prime numbers: 2,3,5,7,11. The range is 11-2=9. And this is the only case where the range of consecutive prime numbers can be odd because it has to be odd-even (which is 2)= odd. So, we know that there are only two overlapping numbers, which means the next set is 7,11,13,17,19. Thus, the range is 19-7=12

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15 Dec 2025, 09:15

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For the range to be odd, even number has to be there given that Odd - Even is Odd otherwise range would have been an even number
It is consecutive thus 2,3,5,7,11,13,17,19.

First set has to start from 2 going upto 11 and second set has two common number thus 7,11,13,17,19 leading to 19-7 = 12

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15 Dec 2025, 09:17

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Since the both sets consist of consecutive integers, with 2 common prime, it means last two prime of first set(smaller sum set) are the first two primes of second set.
Also since range of smaller set is odd, the prime number 2 must be in this set.
2 being the smallest prime, the first set is {2,3,5,7,11}
Hence second set becomes {7,11,13,17,19}
Range of second set = 19-7 = 12

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15 Dec 2025, 09:18

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Since the range of the set with the smaller sum of terms is odd, even prime number 2 is part of the set since all other primes are odd.

Set with smaller sum of terms = {2,3,5,7,11}
Set with larger sum of terms = {7,11,13,17,19}

Range of the other set = 19 - 7 = 12

IMO D

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Odd - Even = Odd and Odd - odd = even
So the smaller set must include 2 in it, so the range can be an odd number
Smaller set must include= (2,3,5,7,11) and 11-2=9 odd
The second set have 2 terms in common with set one, sk second set = (7,11,13,17,19)
Range of second set = 19-7=12

D

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Let one set of primes be the following (smaller set): {2, 3, 5, 7, 11} - Range is odd (11 - 2 = 9 [ODD]).

If exactly two primes are exactly the same, then it this set must start at 7. Set two: {7, 11, 13, 17, 19}. The range of this set is 19 - 7 = 12.

Answer D.

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Bunuel

Assume 1st set of prime numbers as (2,3,5,7,11) and in the second set should have exactly 2 primes in common so assume the set to be (7,11,13,17,19)
Now the Range of 1st set is 11-2= 9 (odd) and the Range of 2nd set is 19-7 = 12 (even)
So, answer is 12

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If I were to take the the first set which is smaller as
2,3,5,7,11 the sum comes up to be even. So I cannot consider 2 as the first term.
The better way to consider the first set will be :
S1: 3,5,7,11, 13
S2: 11, 13, 17, 19, 23 Keeping two terms common.

So range of the other set is 12 (23 -11 = 12)

Bunuel

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Bunuel

Range is odd indicates that one of the prime number is even

Set A = {2, 3, 5, 7, 11}

Set B = {7, 11, 13,17,19}

19 - 7 = 12

Option D

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the answer is 10

as mentioned the range of first set is odd, which means, it is either even-odd or odd-even, given there is no even prime number except for 2, so we will go with the second possibility.
Going with the same the first set would be- [2,3,5,7,9] and given there are 2 prime numbers that overlap so they must be the last two ones because these are consecutive primes. So the second set would be- [7,9,11,13,17]; which means the range of second set is 17-7=10

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15 Dec 2025, 09:26

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Let's assume
Set1 P1 P2 P3 P4 P5
Set2 P6 P7 P8 P9 P10

here P1 to P5 and P6 to P10 are consecutive prime number
And given that only 2 number are common in both the sets, So

Set1 P1 P2 P3 P4 P5
Set2 P4 P5 P6 P7 P8

and if the range of the set with smaller sum of set is odd,

Above case is possible when
Odd - Even = odd
and 2 is the only prime number that is even

SET1 = 2 3 5 7 11
SET2 = 7 11 13 17 19

Range of set2 = 19-7 = 12
So option D is correct answer

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15 Dec 2025, 09:29

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set 1: 2,3,5,7,11
set 2: 7,11,13,17,19
range in set 1 is odd which is 9
range in set 2 is 19-7=12
answer=12

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15 Dec 2025, 09:31

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Odd - Even = Odd always

Since the range of the set with smaller sum of terms is odd, one prime is definitely 2, and since there are consecutive primes.

Smaller sum set: 2, 3, 5, 7, 11

The other set has exactly 2 common terms hence

Other Set: 7, 11, 13, 17, 19

Range = 19 - 7 = 12

Ans (D) 12

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Bunuel

Since the range is odd for the first set, it must include an even number in it, which is 2.
There fore the set should include, 2, 5, 7, 11, & 13
Since there are two primes common, next set should be 11, 13, 15, 17, & 19

Therefore the range of the second set should be, 19 - 11 = 8

Correct option is option B

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15 Dec 2025, 09:34

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set S1 and S2 both have prime consecutive numbers
range of set 1 (smaller one) is odd (highest - lowest) = odd (possible only when odd - even) - 2 is the only even prime
hence S1: {2, 3, 5, 7, 11}
only 2 common terms w.r.t S2
hence S2: {7, 11, 13, 17, 19}
range of set 2: 19-7 = 12