The " lumper " of a number is equal to the sum of all the prime numbers less than that number. If the lumper of x is equal to the lumper of x + 3, which of the following is a possible value of x ?
a. 7
b. 8
c. 9
d. 10
e. 11
please answer and explain
oops. less than, not less or equal, so (B)
2,3,5,7 are less than 8, and also less than 11.
the primes are
2 3 5 7 11 ...
The first time there is a gap of at least 3 is at n=7, so (A)
To find the lumper of a number, we need to calculate the sum of all prime numbers less than that number.
Let's consider each option one by one:
a. For x = 7:
The prime numbers less than 7 are 2, 3, 5.
The sum of these prime numbers is 2 + 3 + 5 = 10.
b. For x = 8:
The prime numbers less than 8 are 2, 3, 5, 7.
The sum of these prime numbers is 2 + 3 + 5 + 7 = 17.
c. For x = 9:
The prime numbers less than 9 are 2, 3, 5, 7.
The sum of these prime numbers is 2 + 3 + 5 + 7 = 17.
d. For x = 10:
The prime numbers less than 10 are 2, 3, 5, 7.
The sum of these prime numbers is 2 + 3 + 5 + 7 = 17.
e. For x = 11:
The prime numbers less than 11 are 2, 3, 5, 7.
The sum of these prime numbers is 2 + 3 + 5 + 7 = 17.
Looking at the above calculations, we can see that the lumper of x is equal to the lumper of x+3 for options b, c, d, and e, all of which have a lumper value of 17. However, option a with x = 7 has a lumper value of 10, which is different.
Therefore, the only possible value of x is option a: 7.