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# A real number N is of the form p/q, where p and q are both distinct po

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Joined: 22 Aug 2013
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A real number N is of the form p/q, where p and q are both distinct po  [#permalink]

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21 Jul 2018, 10:54
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Difficulty:

75% (hard)

Question Stats:

51% (02:13) correct 49% (02:45) wrong based on 61 sessions

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A real number N is of the form p/q, where p and q are both distinct positive integers with a greatest common divisor of 1. If p > q, is N > 1.2 ?

(1) Lowest common multiple of p and q is 28.

(2) Difference between p and q is 3.
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Joined: 02 Aug 2009
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Re: A real number N is of the form p/q, where p and q are both distinct po  [#permalink]

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21 Jul 2018, 19:18
A real number N is of the form p/q, where p and q are both distinct positive integers with a greatest common divisor of 1. If p > q, is N > 1.2 ?

GCD as 1 means both p and q are co-prime.

(1) Lowest common multiple of p and q is 28.
Since the numbers are co-prime, their LCM is nothing but their product.
p*q=28=2^2*7
Only way is either when p=7 and q=4 or when p=28 and q=1.
In both cases, p/q >1.2
Sufficient

(2) Difference between p and q is 3.
Say p and q are small, Ans will be yes.... 8/5=1.4
But if the numbers are bigger, say 103/100=1.03, Ans will be no
Insufficient

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
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Re: A real number N is of the form p/q, where p and q are both distinct po  [#permalink]

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18 Aug 2018, 07:37
2): 28 paired with 1,2,4,7,14
14 paired with 4.
all of these give a N>1.2
Re: A real number N is of the form p/q, where p and q are both distinct po   [#permalink] 18 Aug 2018, 07:37
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