Problem Solving

Gmat_mission wrote:What is the positive difference between the sum of the squares of the first 4 positive integers and the sum of the prime numbers between the first square and fourth square?

A) 11
B) 12
C) 13
D) 14
E) 15

Sum of the squares of the first 4 positive integers = 1² + 2² + 3² + 4²
= 1 + 4 + 9 + 16
= 30

Prime numbers between 1 and 16 are 2, 3, 5, 7, 11 and 13.
Sum = 2 + 3 + 5 + 7 + 11 + 13 = 41

Positive difference = 41 - 30 = 11

Answer: A

Cheers,
Brent

Gmat_mission wrote:What is the positive difference between the sum of the squares of the first 4 positive integers and the sum of the prime numbers between the first square and fourth square?

A) 11
B) 12
C) 13
D) 14
E) 15

[spoiler]OA=A[/spoiler]

Source: EMPOWERgmat

The sum of the squares of the first 4 positive integers is 1 + 4 + 9 + 16 = 30.

The sum of the primes between 1 and 16 is 2 + 3 + 5 + 7 + 11 + 13 = 41.

Therefore, the positive difference is 41 - 30 = 11.

Answer: A

Hi Gmat_mission,

Certain Quant questions on Test Day are just about doing organized work and making sure that you're following the 'instructions' in the prompt.

Here, we're asked to compare two sums:
1) The sum of the squares of the first 4 positive integers
2) The sum of the prime numbers between the first square and fourth square

For the first sum, we need the SQUARES of the first four positive integers. That sum is....

1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30

For the second sum, we need the PRIMES between 1 and 16. That sum is...

2 + 3 + 5 + 7 + 11 + 13 = 41

The positive difference between those sums is 41 - 30 = 11

Final Answer: A

GMAT assassins aren't born, they're made,
Rich