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If p/q < 1, and p and q are positive integers, which of the

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If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:16
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If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p
[Reveal] Spoiler: OA
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:21
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If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p

Since p and q are positive integers, then q/p>0. Now, multiply p/q < 1 by q/p to get 1 < q/p.

Answer: E.

Or: since this is a must be true question, then even if we find only one example for which an option is not true, it'll mean that this option is not always true, thus not a correct answer.

Say p=2 and q=3. In this case, no option is correct but E.

Answer: E.

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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Dec 2012, 05:33
Expert's post
Walkabout wrote:
If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A) \sqrt{\frac{p}{q}}
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p


Given:
p/q <1. Since p and q are positive integers, we can multiply by q on both sides.
The relation becomes:
p<q.

Now if we divide the entire relation by p, then:
p/p < q/p or 1< q/p

Hence q/p > 1.
+1 E.

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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 21 Jan 2013, 10:46
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If p/q < 1 then q>p.

A) \sqrt{\frac{p}{q}} will obviously be less than 1.
(B) p/q^2 Will increase the denominator and still makes it less than 1.
(C) p/2qWill increase the denominator and still makes it less than 1.
(D) q/p^2Still less than 1. Suppose p =2 and q =3
(E) q/p Since q > p, q/p >1

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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 22 May 2014, 21:29
When we know the signs of fraction in an inequality and want to take the reciprocal here is a handy rule: flip the inequality when taking reciprocal unless both sides have different signs.
Thus we can flip the inequality in the given relation p/q<1, to get q/p>1. E it is!

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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 23 May 2014, 06:25
Not sure if it is solved this way:

\frac{p}{q} < 1,

As p and q are positive, Denominator should be greater than numerator.

Therefore, q>p

Hence, \frac{q}{p} > 1

Rgds,
Rajat

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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 17 Jun 2014, 21:03
Did anyone solve this with smart numbers? Used p = 1 and q = 2 which narrowed it down to D and E and then tested those with p = 5 and q = 9? This gave me E.
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink] New post 18 Jun 2014, 00:27
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carolinanmd wrote:
Did anyone solve this with smart numbers? Used p = 1 and q = 2 which narrowed it down to D and E and then tested those with p = 5 and q = 9? This gave me E.


The second approach in my solution here: if-p-q-1-and-p-and-q-are-positive-integers-which-of-the-144262.html#p1156616 uses p=2 and q=3 to discard all options but E.

Hope it helps.

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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If p/q < 1, and p and q are positive integers, which of the   [#permalink] 18 Jun 2014, 00:27
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