Kimberly77 wrote:
BrentGMATPrepNow wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionFor any integer n greater than 1, [n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between [6 + 2 and [6 + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
[6 + 2 = (6)(5)(4)(3)(2)(1) + 2 =
2[(6)(5)(4)(3)(1) + 1], which is a multiple of
2. So, [6 + 2 is NOT prime
[6 + 3 = (6)(5)(4)(3)(2)(1) + 3 =
3[(6)(5)(4)(2)(1) + 1], which is a multiple of
3. So, [6 + 3 is NOT prime
[6 + 4 = (6)(5)(4)(3)(2)(1) + 4 =
4[(6)(5)(3)(2)(1) + 1], which is a multiple of
4. So, [6 + 4 is NOT prime
[6 + 5 = (6)(5)(4)(3)(2)(1) + 5 =
5[(6)(4)(3)(2)(1) + 1], which is a multiple of
5. So, [6 + 5 is NOT prime
[6 + 6 = (6)(5)(4)(3)(2)(1) + 6 =
6[(5)(4)(3)(2)(1) + 1], which is a multiple of
6. So, [6 + 6 is NOT prime
Answer: A
Cheers,
Brent
Hi
BrentGMATPrepNow, not quite understand the way factorization work here. Why is the need for factorization and not sure why is not 2[(3)(5/2)(2)(3/2)(1/2) + 1] like usual factorization?
Thanks Brent
You are missing using the distributive property.
The distributive property applies when we are
multiplying an expression consisting of ADDING and SUBTRACTING.
In these cases, we multiply each term inside the brackets by the term outside the brackets.
For example 2(3x + 5) = 6x + 10
[ here we multiplied 3x by 2, and we multiplied 5 by 2]Important: Notice that I treated 3x as a
single expression. That is, I did not multiply 3 by 2 AND x by 2. Instead, I multiplied the single term, 3x, by 2.
Similarly, the expression (6)(5)(4)(3)(2)(1) + 2 has two terms: (6)(5)(4)(3)(2)(1) and 2.
When we factor out a 2 we get: 2[(6)(5)(4)(3)(1) + 1]
In your factorization, 2[(3)(5/2)(2)(3/2)(1/2) + 1], you are assuming that we multiply (3) by 2, and multiply (5/2) by (2), which is incorrect.
To see the problem with your calculations first recognize that (1)(1)(1)(1)(1) = 1
So, we would expect that (2)(1)(1)(1)(1)(1) = 2
However, the way you are multiplying suggest that we multiply each 1 by 2 to get: (2)(1)(1)(1)(1)(1) = (2)(2)(2)(2)(2) = 32