Data Sufficiency

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

Zoser wrote:

Statement 2: 11! - 12 < y < 11! - 2
Let's examine a few possible values for y.

y = 11! - 11

Why you started with 11!-11 not 11!-12?

We're told that 11! - 12 < y, so y cannot equal 11! - 12

So, the smallest possible value of y is 1 greater than 11! - 12
In other words, the smallest possible value of y is 1 greater than 11! - 11

Cheers,
Brent