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

1 2 3 4 5 6 7

rakku

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15 Dec 2025, 23:40

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Bunuel

answer is D 12 since it seems the two prime in common are 7 and 11.

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Answer: D

It is given that both the sets consist of prime numbers and the range of the set with smaller sum of terms is odd. In order for a range of prime numbers to be odd, it has to have the number 2 (as 2 is the only even prime number).

Now, the smaller set of consecutive prime numbers would be: 2, 3, 5, 7, 11
Since the other set has exactly 2 primes in common with the above set and is a set of consecutive prime numbers, the only possibility is:
7, 11, 13, 17, 19

Range of this set = 19-7 = 12

Bunuel

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Bunuel

Set 1 - The possibility of the range being odd is when one number is even and the other is odd. Since 2 is only even prime number it has to be part of the set.
Hence Set 1 with 5 consecutive prime numbers -> [ 2, 3, 5, 7, 11]

If Set 2 has 5 consecutive prime numbers and only 2 are common then the set would be [7, 11, 13, 17, 19]

Range of Set 2 -> 19 -7 = 12

Option D

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We are told that the set of the small sum is odd so 2 cant be one of the prime numbers, so the set contains prime number greater than 2
Set A= { 3, 5, 7, 11, 13 }
Set B= { 11, 13, 17, 19, 23}

23-11= 12

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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?

Let set A= (2,3,5,7,11)
Set B = (7,11,13,17,19)
range of set A = 9 which is
range of Set B = 12

OPTION D ; 12

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

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Qn: Two sets of consecutive prime numbers with overlap of last & first term in both (which means the 2nd set is the continuation of 1st, with first term in S2 being the last of S1),

Soln.:

Range of the smaller set is odd (i.e. the 1st term must be 2 - the only even prime number & w.k.t, odd - even = odd)

So the 2 sets are:

S1 {2, 3, 5, 7, 11}
S2 {11, 13, 17, 19, 23}

Range S2 = 23-11 = 12.

Answer: Option D

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S1={P1,P2,P3,P4,P5}
S2={P4,P5,P6,P7,P8}

Since it is mentioned that the range of S1 is odd, it is possible only if there is an even number. Hence, P1 has to be 2. So we get:
S1={2,5,7,9,11} ; Range=9
therefore, S2={9,11,13,17,19}
Range=19-9= 10
Correct Answer: Option C

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16 Dec 2025, 01:18

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Bunuel

For the range of a set of primes to be odd, one of the highest/lowest primes needs to be even. And since there's only one even prime, it's safe to say that set 1 (the one with the smaller sum) would be {2, 3, 5, 7, 11}.

The second set with consecutive primes shares 2 primes with set 1. Set 2 will have to contain larger primes since set 1 starts with the lowest prime possible. Therefore, set 2 would be {7, 11, 13, 17, 19}

Therefore, the range of set 2 is 19-7 = 12

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PLease refer the attached answer Key provided- Key concept- If Odd is difference of two terms then one term MUST BE Even and the only even prime number is 2.

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Given
1. Two sets of consecutive Prime Numbers let Set A and B be the 2 sets
2. Range with smaller sum of terms is Odd. which means it is difference between Odd and even, and there is only one even prime which is 2.
3. Exactly 2 prime no. common in both the set A and B, so for having a consecutive prime, last 2 from set are common in B

So lets say Set A is smaller and has elements (2,3,5,7,11), and Set B is (7,11,13,17,19)

Range of B= Max-Min=19-7=12 Option D

Bunuel

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Bunuel

Here the catch is that only one prime number we have which is even that is 2 and in question it is mentioned that first set is having range as odd.

Now, odd can only possible when odd is getting subtracted by even, that means first set would be {2,3,5,7,11}

And because only two prime number can overlap and since it is a consecutive prime number set second set would be {7,11,13,17,19}

Therefore, range of second set is 12

Hence option D is the ans.

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Bunuel

Let's say two sets are: set A and set B, and set A is the smaller one. If the range of set A is odd, this scenario is only possible when one of the prime numbers is even. There is only one even prime number - 2. Therefore, set A is {2,3,5,7,11}. As set B has exactly two similar prime numbers as in set A, we can say that those two numbers are 7 and 11 because the numbers are consecutive in each set. As a result, set B is {7,11,13,17,19}, and the range is 19-7=12.

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Since the range of set 1 is odd, the two numbers (first and last in the set) have to be odd and even. Since 2 is the only even prime number, set 1 has to start with 2.
Last two numbers in the set will be 7 and 11.
The second set will start with 7 since exactly 2 numbers are same.
Last number in the set will be 19.
Range = 19-7 = 12

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To keep this simple,
Consider first nine prime numbers and divide them into 2 sets keeping 11 as a common element.
Range of the 1st set is calculated as (11-2=9) - Satisfies the condition given in Qn.
Now range of 2nd set is calculated as (23-11=12).
Answer is 12.

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If the range of set of smaller sum of consecutive prime numbers is odd, then one of the nos has to be even and 2 is the only even prime no.
So the 1st set is : {2,3,5,7,9}
There are 2 terms common in both the sets so 2nd set is : {7,9,11,13,17}
And the range of this set is 10.

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16 Dec 2025, 02:36

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A: {2, 3, 5, 7, 11}; B: {7, 11, 13, 17, 19}

Answer would be = 19 - 7 = 12

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p1, p2, p3, p4, p5

the only way set 2 contains exactly 2 primes as set 1 is by starting from p4, p5,p6,p7,p8

range is odd when O-E
so set 1 will start from 2,3,5,7,11
hence set 2 = 7,11,13,17,19

range of set 2 = 19-7=12

ANS-D

Bunuel

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16 Dec 2025, 04:53

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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?

Range of set with smaller sum of terms is odd... In order for for range to be odd we need atleast 1 even prime in range and 2 in only even prime.
Set 1= {2,3,5,7,11} and
Set 2= {7,11,13,17,19}
Range of set 2 = 19-7 =12

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16 Dec 2025, 05:13

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Given that the absolute majority of prime numbers is odd, normally the difference between each two is even. Like, $13-11=2$.

However, in this task the range is odd, which means the subtrahend must be even - and the only even prime number is 2. This is how we get the first set: {2 3 5 7 11}, since the primes need to be consecutive.

The other set consists of three different and two similar numbers, and since they still have to be consecutive, the larger set must start at the 'top' of the previous one: {7 11...} as common numbers, and then {... 13 17 19}.

Therefore, the range of the second set is $R = 19 - 7 = 12$, and the right answer is D.

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16 Dec 2025, 05:19

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Range Set A(5 consec prime number)= Odd
Only 2 is even prime number others are odd. So, range will be odd only when 1st prime number is 2. Set A= 2,3,5,7,11
Set B has 2 common prime to Set A. So, Set B= (7,11,13,17,19). Range = 12

Bunuel

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