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is y prime?

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sanju09 GMAT Instructor
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is y prime? Post Wed Jul 23, 2014 9:44 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If y is a positive integer, is y prime?
    (1) y > 4!.
    (2) 11! - 12 < y < 11! - 2.



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    Post 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 B

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    Post 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: http://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

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