sanju09 wrote:If y is a positive integer, is y prime?
(1) y > 4!
(2) 11! - 12 < y < 11! - 2
This question is VERY similar to this one:
https://www.beatthegmat.com/wrong-answer-t277820.html
Target question: is y prime?
Statement 1: y > 4!
In other words, y > 24
This does not help us determine whether or not y is prime. Consider these two conflicting cases:
Case a: y = 29, in which case
y IS prime
Case b: y = 25, in which case
y is NOT prime
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 11! - 12 < y < 11! - 2
Let's examine a few possible values for y.
y = 11! - 11
y = (
11)(10)(9)....(5)(4)(3)(2)(1) -
11
y =
11[(10)(9)....(5)(4)(3)(1) - 1]
Since y is a multiple of
11,
y is NOT prime
y = 11! - 10
y = (11)(
10)(9)....(5)(4)(3)(2)(1) -
10
y =
10[(11)(9)....(5)(4)(3)(1) - 1]
Since y is a multiple of
10,
y is NOT prime
y = 11! - 9
y = (11)(10)(
9)....(5)(4)(3)(2)(1) -
9
y =
9[(11)(10)....(5)(4)(3)(1) - 1]
Since y is a multiple of
9,
y is NOT prime
As you can see, this pattern can be repeated all the way up to y = 11! - 1. In EVERY case,
y is NOT prime
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
