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

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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 27 Apr 2017, 02:06
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catty2004 wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

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

(2) (ad/bc)^2 < (ad)/(bc)



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.
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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 27 Apr 2017, 02:13
samia33 wrote:
catty2004 wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

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

(2) (ad/bc)^2 < (ad)/(bc)



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

Inequalities Made Easy!

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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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 14 Jul 2017, 07:03
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
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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 14 Oct 2017, 07:36
2
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?
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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 14 Oct 2017, 18:59
1
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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Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

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New post 25 May 2018, 02:34
(1) 0 < (c-a) / (d-b)
for this statement I done like this: 0 < (c-a) / (d-b)=>0<c-a
c>a - substituted values and got to know insufficient.
I want to know if the first is correct as I did not see any explanation like the above and less time consuming.
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Re: If a, b, c, and d, are positive numbers, is a/b < c/d? &nbs [#permalink] 25 May 2018, 02:34

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