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# If a, b, c, and d, are positive numbers, is a/b < c/d?

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Intern
Joined: 10 Nov 2016
Posts: 5
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

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27 Apr 2017, 03:06
catty2004 wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

(1) 0 < (c-a) / (d-b)

This is perhaps off topic but it caught my attention. How can a square of a number x be strictly less than x? I can't seem to find it logical.
Math Expert
Joined: 02 Sep 2009
Posts: 44388
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

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27 Apr 2017, 03:13
samia33 wrote:
catty2004 wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

(1) 0 < (c-a) / (d-b)

This is perhaps off topic but it caught my attention. How can a square of a number x be strictly less than x? I can't seem to find it logical.

x^2 < x is true for 0 < x < 1.

For example, (1/2)^2 < 1/2.

Check the links below for more:
Inequality tips

Solving Quadratic Inequalities - Graphic Approach

Wavy Line Method Application - Complex Algebraic Inequalities

DS Inequalities Problems
PS Inequalities Problems

Hope it helps.
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Senior Manager
Joined: 29 Jun 2017
Posts: 265
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

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14 Jul 2017, 08:03
for number property problem, we at first try to change the form of the expression.
if we can not change, or the change dose not bring any result, thinking of PICKING THE SPECIFIC NUMBERS.

choice A dose not imply a change in form of expression. so, we pick the specific numbers
Manager
Joined: 30 Apr 2013
Posts: 92
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

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14 Oct 2017, 08:36
Statement 2 is clearly sufficient but for statement 1 am bit confused- can someone clarify?

1) 0 < c-a/d-b

Can we simplify it to a+d < c + b ? If yes, am stuck here. how do I go forward?
Director
Joined: 17 Dec 2012
Posts: 630
Location: India
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

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14 Oct 2017, 19:59
catty2004 wrote:
If a, b, c, and d, are positive numbers, is $$\frac{a}{b} < \frac{c}{d}$$?

(1) $$0 < \frac{(c-a)}{(d-b)}$$

(2) $$(\frac{ad}{bc})^2 < \frac{(ad)}{(bc)}$$

Plug in Approach

Statement 1: a and b and also c and d can each be different numbers for the same value of a/b and c/d resp. Hence will give different answers and not sufficient

Statement 2: At least one of a/b or d/c is less than 1 and the other has a ceiling on its value. For convenience we will round values to one decimal.

If d/c =0.9, a/b should be less than 1.1. Since d/c=0.9, c/d=1.1. Hence c/d >a/b
If a/b=0.9, d/c should be less than 1.1, and c/d>0.9. Hence c/d>a/b
If both are less than 1, then c/d>a/b
Hence c/d in all the cases gretaer than a/b. Sufficient

Hence B.
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Srinivasan Vaidyaraman
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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?   [#permalink] 14 Oct 2017, 19:59

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