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is y prime?

by sanju09 » Wed Jul 23, 2014 9:44 pm
If y is a positive integer, is y prime?
(1) y > 4!.
(2) 11! - 12 < y < 11! - 2.



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by GMATinsight » Thu Jul 24, 2014 12:17 am
sanju09 wrote:If y is a positive integer, is y prime?
(1) y > 4!.
(2) 11! - 12 < y < 11! - 2.
Question : Is y Prime?

Statement 1: y > 4!
i.e. y > (4x3x2x1)
i.e. y > 24
but y can be 25 NON PRIME or y can be 29 Prime as well

INSUFFICIENT

Statement 2) 11! - 12 < y < 11! - 2

11!-11 = 11(1x2x3x4x5x6x7x8x9x10 - 1) i,e, multiple of 11 i.e. NON PRIME NO.
Similary all the numbers in the given range in statement 2 are NON-PRIME

SUFFICIENT

Answer: Option [spoiler]B[/spoiler]
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by Brent@GMATPrepNow » Thu Jul 24, 2014 8:51 am
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

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Brent
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by Zoser » Sat Apr 15, 2017 6:13 am
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?
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by Brent@GMATPrepNow » Sat Apr 15, 2017 12:20 pm
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

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