AAPL wrote:Veritas Prep
x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be
A. Between 1 and 10
B. Between 11 and 15
C. Between 15 and 20
D. Between 20 and 25
E. Greater than 25
OA E
x = (2)(4)(6)....(46)(48)(50)
= (
1)(2)(
2)(2)(
3)(2).....(
23)(2)(
24)(2)(
25)(2)
Notice that:
x is divisible by
2. This tells us that
x+1 is 1 greater than a multiple of
2. In other words, x+1 is NOT divisible by
2
x is divisible by
3. This tells us that
x+1 is 1 greater than a multiple of
3. In other words, x+1 is NOT divisible by
3
x is divisible by
4. This tells us that
x+1 is 1 greater than a multiple of
4. In other words, x+1 is NOT divisible by
4
x is divisible by
5. This tells us that
x+1 is 1 greater than a multiple of
5. In other words, x+1 is NOT divisible by
5
.
.
.
x is divisible by
23. This tells us that
x+1 is 1 greater than a multiple of
23. In other words, x+1 is NOT divisible by
23
x is divisible by
24. This tells us that
x+1 is 1 greater than a multiple of
24. In other words, x+1 is NOT divisible by
24
x is divisible by
25. This tells us that
x+1 is 1 greater than a multiple of
25. In other words, x+1 is NOT divisible by
25
We see that x+1 is NOT divisible by
2 to
25
In other words, all integers from
2 to
25 are NOT factors of x+1
So, if a number IS a factor of x+1, that number must be greater than
25
Answer: E
Cheers,
Brent
