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Which must be greate than 1?

This topic has 5 expert replies and 2 member replies
LulaBrazilia Master | Next Rank: 500 Posts Default Avatar
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Which must be greate than 1?

Post Sun Feb 16, 2014 9:51 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

    A) root(p/q)

    B) p/(p^2)

    C) p/2q

    D) q/(p^2)

    E) q/p

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    Post Sun Feb 16, 2014 10:09 am
    Since we're dealing with positive integers, we can cross multiply to find that p < q. As a result, q/p must be greater than 1 (answer E). The full solution below is taken from the GMATFix App. It discusses each answer choice in detail



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    Thanked by: Pazoki
    Post Sun Feb 16, 2014 10:15 am
    LulaBrazilia wrote:
    If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

    A) √(p/q)
    B) p/(p²)
    C) p/2q
    D) q/(p²)
    E) q/p
    Given: p/q < 1
    Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
    Also, since p and q are both positive, we can conclude that 0 < p < q

    Which of the following MUST be greater than 1?

    IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

    E) q/p
    If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
    So, the correct answer must be E

    ----------------------------------------------------------------

    ANOTHER APPROACH
    The question asks, "Which of the following MUST be greater than 1?"
    So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

    A) √(p/q)
    Let p = 1 and q = 4 to get: √(1/4) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE A

    B) p/(p²)
    Let p = 2 to get: 2/(2²) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE B

    C) p/2q
    Let p = 1 and q = 2 to get: 1/2(2) = 1/4
    1/4 is NOT greater than 1, so ELIMINATE C

    D) q/(p²)
    Let p = 1 and q = 2 to get: 2/(1²) = 4
    4 IS greater than 1, so KEEP D

    E) q/p
    Let p = 1 and q = 2 to get: 2/1 = 2
    2 IS greater than 1, so KEEP E

    We have eliminated A, B, and C. So, we must try a DIFFERENT set of values for answer choices D and E.

    D) q/(p²)
    Let p = 2 and q = 3 to get: 3/(2²) = 3/4
    3/4 is NOT greater than 1, so ELIMINATE D

    So, the correct answer must be E

    Cheers,
    Brent

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    Last edited by Brent@GMATPrepNow on Tue Nov 17, 2015 10:50 am; edited 1 time in total

    Thanked by: rohitberia
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    Abhishek009 Master | Next Rank: 500 Posts
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    Post Sun Feb 16, 2014 10:18 am
    LulaBrazilia wrote:
    If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

    A) root(p/q)

    B) p/(p^2)

    C) p/2q

    D) q/(p^2)

    E) q/p
    Plug in some values

    p/q < 1 and p and q are positive integers

    Let P = 2 and q = 3

    p/q = 0.667 < 1

    Now check each options matter of just 10 seconds -

    A) root(p/q) root 2/3

    B) p/(p^2)= 2/4

    C) p/2q = 2/6

    D) q/(p^2) = 3/4

    E) q/p = 3/2 => 1.5 This is the answer...


    IMO (E)

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    Post Sun Feb 16, 2014 9:02 pm
    Hi LulaBrazilia,

    Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a faster way of looking at it though…

    Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship…so Q/P > 1. The question ask which of the 5 options is greater than 1….

    That's answer E

    GMAT assassins aren't born, they're made,
    Rich

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    Thanked by: Pazoki
    Priyaranjan Junior | Next Rank: 30 Posts Default Avatar
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    Post Mon Nov 16, 2015 8:09 pm
    In answer choice D, if p=1, q=2, then q/(p²)= 2/1²= 2/1=2 >1

    Brent@GMATPrepNow wrote:
    LulaBrazilia wrote:
    If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

    A) √(p/q)
    B) p/(p²)
    C) p/2q
    D) q/(p²)
    E) q/p
    Given: p/q < 1
    Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
    Also, since p and q are both positive, we can conclude that 0 < p < q

    Which of the following MUST be greater than 1?

    IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

    E) q/p
    If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
    So, the correct answer must be E

    ---------------------------------

    ANOTHER APPROACH
    The question asks, "Which of the following MUST be greater than 1?"
    So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

    A) √(p/q)
    Let p = 1 and q = 4 to get: √(1/4) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE A

    B) p/(p²)
    Let p = 2 to get: 2/(2²) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE B

    C) p/2q
    Let p = 1 and q = 2 to get: 1/2(2) = 1/4
    1/4 is NOT greater than 1, so ELIMINATE C

    D) q/(p²)
    Let p = 1 and q = 2 to get: 1/(2²) = 1/4
    1/4 is NOT greater than 1, so ELIMINATE D

    STOP.
    Since we have eliminated A, B, C and D, the correct answer must be E

    Cheers,
    Brent

    Thanked by: Brent@GMATPrepNow
    Post Tue Nov 17, 2015 10:12 am
    Hi Priyaranjan,

    You are correct; Brent's example doesn't actually eliminate Answer D. You could use P=2 and Q=3 though - and THAT example would eliminate Answer D.

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Post Tue Nov 17, 2015 10:51 am
    Priyaranjan wrote:
    In answer choice D, if p=1, q=2, then q/(p²)= 2/1²= 2/1=2 >1

    Brent@GMATPrepNow wrote:
    LulaBrazilia wrote:
    If p/q < 1 and p and q are positive integers, which of the following must be greater than 1?

    A) √(p/q)
    B) p/(p²)
    C) p/2q
    D) q/(p²)
    E) q/p
    Given: p/q < 1
    Since q is POSITIVE, we can multiply both sides of the inequality by q to get p < q
    Also, since p and q are both positive, we can conclude that 0 < p < q

    Which of the following MUST be greater than 1?

    IMPORTANT TIP: To answer this question, we'll need to examine every answer choice. Given this, where would a crafty test-maker place the correct answer? He/she would place it near the bottom, because most people check the answer choices from top to bottom. So, whenever we have such a question, I suggest that we start from the bottom and work our way to the top.

    E) q/p
    If 0 < p < q, we know that q/p is POSITIVE and we know that q/p must be greater than 1.
    So, the correct answer must be E

    ---------------------------------

    ANOTHER APPROACH
    The question asks, "Which of the following MUST be greater than 1?"
    So, if we can find values for p and q such that an answer choice yields a value that is NOT greater than 1, we can ELIMINATE that answer choice.

    A) √(p/q)
    Let p = 1 and q = 4 to get: √(1/4) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE A

    B) p/(p²)
    Let p = 2 to get: 2/(2²) = 1/2
    1/2 is NOT greater than 1, so ELIMINATE B

    C) p/2q
    Let p = 1 and q = 2 to get: 1/2(2) = 1/4
    1/4 is NOT greater than 1, so ELIMINATE C

    D) q/(p²)
    Let p = 1 and q = 2 to get: 1/(2²) = 1/4
    1/4 is NOT greater than 1, so ELIMINATE D

    STOP.
    Since we have eliminated A, B, C and D, the correct answer must be E

    Cheers,
    Brent
    Nice catch, Priyaranjan!

    I have edited my response.

    Cheers,
    Brent

    _________________
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