GMAT Changed on April 16th - Read about the latest changes here

 It is currently 25 May 2018, 23:25

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 30 May 2008
Posts: 64
If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

Updated on: 12 May 2017, 01:29
3
KUDOS
45
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:38) correct 27% (01:50) wrong based on 1777 sessions

### HideShow timer Statistics

If a, b, c, and d, are positive numbers, is $$\frac{a}{b} < \frac{c}{d}$$?

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

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

Originally posted by catty2004 on 08 Jul 2012, 18:20.
Last edited by Bunuel on 12 May 2017, 01:29, edited 2 times in total.
Edited the question.
Kaplan GMAT Instructor
Joined: 25 Aug 2009
Posts: 640
Location: Cambridge, MA
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

08 Jul 2012, 18:46
10
KUDOS
Expert's post
5
This post was
BOOKMARKED
catty2004 wrote:
92. If a, b, c, and d, are positive numbers, is a/b < c/d?

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

Hi catty,

We're looking for whether a/b < c/d. Fortunately, we're told a useful bit of info in the question stem. All four terms are positive. That's very important with inequalities, because it means that we can multiply and divide without having to worry about the direction of the inequality signs. In this case, we could rephrase the question to whether ad < bc by cross-multiplying. This will be useful laters.

Statement 1) is not useful, however. (c-a) and (d-b) could both be positive or negative; that means that when me multiply to get rid of a term, we might or might not have to flip the terms. Since any of the variables could be greater or less than any of the other variables, this statement is insufficient.

Statement 2) gives us exactly what we want. Here, with no subtraction, everything stays positive. That means we can divide out (ad/bc) from both sides without flipping the inequality. We get ad/bc < 1, and can cross-multiply to get ad < bc. That answers our question with a definite yes, so it's sufficient and the answer is (B)
_________________

Eli Meyer
Kaplan Teacher
http://www.kaptest.com/GMAT

Prepare with Kaplan and save $150 on a course! Kaplan Reviews Intern Joined: 19 Sep 2012 Posts: 13 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 19 Sep 2012, 15:56 First of all, I have rephrased the statement. I have become "a/b < c/d" to "ad < cb". Then, I have answered (B) due to the fact that I know that the result of a proper fraction to the power of 2 is always less than the result of the proper fraction. Thus, in this case (ad/bc)^2 < (ad)/(bc), the fraction ad/bc must be a proper fraction and therefore it must be true that ad<bc. Is it right this reasoning? Senior Manager Joined: 13 Aug 2012 Posts: 443 Concentration: Marketing, Finance GPA: 3.23 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags Updated on: 20 Sep 2012, 07:21 7 This post received KUDOS 5 This post was BOOKMARKED 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) We know that a,b,c and d are positive numbers. This is a Yes/No DS question type - is a/b < c/d. Since we are certain that we have no negative values, we can manipulate the inequality question to - is ad < bc? It's much easier to look at. (1) (c-a)/(d-b) - a positive fraction or whole number Say c=d=5 and a=2 and b=1 for 3/4, then ad < bc is false Say c=d=5 and a=1 and b=2 for 4/3, then ad < bc is true thus (1) is INSUFFICIENT (2) Thus, YES! SUFFICIENT. See attachment. Answer: B Attachments photo.JPG [ 259.84 KiB | Viewed 43822 times ] _________________ Impossible is nothing to God. Originally posted by mbaiseasy on 19 Sep 2012, 21:02. Last edited by mbaiseasy on 20 Sep 2012, 07:21, edited 2 times in total. Intern Joined: 19 Sep 2012 Posts: 13 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 20 Sep 2012, 01:51 1 This post received KUDOS I agree with your approach to the problem. But is not it easier to realize about the rule of proper fraction to the power of 2 instead of manipulate the ecuation in the stem 2? Senior Manager Joined: 13 Aug 2012 Posts: 443 Concentration: Marketing, Finance GPA: 3.23 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 20 Sep 2012, 07:13 racingip wrote: I agree with your approach to the problem. But is not it easier to realize about the rule of proper fraction to the power of 2 instead of manipulate the ecuation in the stem 2? You are right. That's what I did. I did cancelling of of the powers of . Sorry my explanation is not clear. haha! I just summarized that when you start cancelling out, it's like multiplying that fraction I put up. _________________ Impossible is nothing to God. Manager Joined: 04 Jan 2014 Posts: 114 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 18 Jun 2014, 07:11 KapTeacherEli wrote: catty2004 wrote: 92. If a, b, c, and d, are positive numbers, is a/b < c/d? Statement 2) gives us exactly what we want. Here, with no subtraction, everything stays positive. That means we can divide out (ad/bc) from both sides without flipping the inequality. We get $$ad/bc$$ < 1, and can cross-multiply to get $$ad < bc$$. That answers our question with a definite yes, so it's sufficient and the answer is (B) Hi could you please explain the part on cross multiplication? I am getting $$a/b$$ > $$b/c$$. Math Expert Joined: 02 Sep 2009 Posts: 45423 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 18 Jun 2014, 08:48 1 This post received KUDOS Expert's post 2 This post was BOOKMARKED pretzel wrote: KapTeacherEli wrote: catty2004 wrote: 92. If a, b, c, and d, are positive numbers, is a/b < c/d? Statement 2) gives us exactly what we want. Here, with no subtraction, everything stays positive. That means we can divide out (ad/bc) from both sides without flipping the inequality. We get $$ad/bc$$ < 1, and can cross-multiply to get $$ad < bc$$. That answers our question with a definite yes, so it's sufficient and the answer is (B) Hi could you please explain the part on cross multiplication? I am getting $$a/b$$ > $$b/c$$. $$(\frac{ad}{bc})^2 < \frac{ad}{bc}$$ --> reduce by ad/bc: $$\frac{ad}{bc} <1$$ --> multiply by bc: $$ad<bc$$. Hope it's clear. _________________ Manager Joined: 04 Jan 2014 Posts: 114 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 18 Jun 2014, 18:20 Bunuel wrote: $$(\frac{ad}{bc})^2 < \frac{ad}{bc}$$ --> reduce by ad/bc: $$\frac{ad}{bc} <1$$ --> multiply by bc: $$ad<bc$$. Hope it's clear. If $$ad<bc$$, then $$\frac{a}{b}$$ < $$(\frac{c}{d})$$? Math Expert Joined: 02 Sep 2009 Posts: 45423 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 19 Jun 2014, 00:55 1 This post received KUDOS Expert's post pretzel wrote: Bunuel wrote: $$(\frac{ad}{bc})^2 < \frac{ad}{bc}$$ --> reduce by ad/bc: $$\frac{ad}{bc} <1$$ --> multiply by bc: $$ad<bc$$. Hope it's clear. If $$ad<bc$$, then $$\frac{a}{b}$$ < $$(\frac{c}{d})$$? For positive values, yes. _________________ Director Joined: 23 Jan 2013 Posts: 596 Schools: Cambridge'16 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 11 Sep 2014, 21:29 we can conceive logically that (ad/bc)^2<ad/bc only when ad/bc<1, so ad<bc B Director Joined: 10 Mar 2013 Posts: 563 Location: Germany Concentration: Finance, Entrepreneurship GMAT 1: 580 Q46 V24 GPA: 3.88 WE: Information Technology (Consulting) Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 21 May 2015, 09:05 Is a/b<c/d or (because all the values are >0) ad<bc ? Prethinking: c/d>a/b if ca-same and d<b or db - same and c>a... 1) (c-a)/(d-b) --> c>a and d>b Not suff. yes and no.. see explanation above... 2) (ad/bc)^2 < ad/bc this means we have a proper fraction here (1/2^2 < 1/2) this also means that ad<bc Sufficient --> see underlined part above _________________ When you’re up, your friends know who you are. When you’re down, you know who your friends are. Share some Kudos, if my posts help you. Thank you ! 800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660 Retired Moderator Joined: 29 Oct 2013 Posts: 272 Concentration: Finance GPA: 3.7 WE: Corporate Finance (Retail Banking) Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 09 Nov 2015, 08:46 Bunuel, 2) This quite clearly sufficient 1) However, it was not very clear to me how this one is insufficient. Is there any way we know this choice is not sufficient w/o resorting to number picking? Thanks! _________________ Please contact me for super inexpensive quality private tutoring My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5452 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink] ### Show Tags 10 Nov 2015, 11:49 2 This post received KUDOS Expert's post Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. 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) If we modify the question, the sign of the inequality does not change as a,b,c,d are positive integers. Hence, we want to know whether a/b < c/d?, or ad<bc. From condition 1, 0 < (c-a) / (d-b), and if we multiply (d-b)^2 on both sides, 0<(c-a)(d-b). We cannot know whether ad<bc, so this is insufficient. From condition 2, we can divide both sides by (ad)/(bc), which gives us (ad/bc)^2 < (ad)/(bc), or (ad/bc)<1, and when we multiply bc on both sides, (ad/bc)<1, or ad<bc. This answers the question 'yes' so this is sufficient, and the answer becomes (B). Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 04 Dec 2015
Posts: 11
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

10 Dec 2015, 07:07
Please correct me if I'm wrong.

1) not sufficient

2) sufficient

Let ab=4 and bc=2 so (ab/bc)^2=4, which cannot be less than (ab/bc)=2. We can try any values such as ab=4 and bc=3.

Therefore we can conclude that ab has to be less than bc.

So 2) is sufficient.

My only problem is that how would I be able to think of such an approach in the main exam , which requires that every question be solved in less than 2 mins ?

Pls help! :p
Manager
Joined: 13 Feb 2011
Posts: 95
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

26 Dec 2015, 16:59
3
KUDOS
NoHalfMeasures wrote:
Bunuel,

2) This quite clearly sufficient
1) However, it was not very clear to me how this one is insufficient. Is there any way we know this choice is not sufficient w/o resorting to number picking?

Thanks!

I know your question is to Bunuel, but I am just sharing how I eliminated the first statement:

Statement 1 tells us that $$\frac{c-a}{d-b}>0$$, i.e. $$c-a$$ and $$d-b$$ have same signs (either both are +ve or both are -ve). However that doesn't tells us anything about their individual values, which makes this statement insufficient.

Hope it helps.
Manager
Joined: 26 Mar 2017
Posts: 146
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

21 Apr 2017, 03:03
hey,

for statement 1:

can't we just multiply the equation by d-b ?

1. 0 < c-a/d-b --> multiply by d-b --> 0 < c-a --> a < c so a < c but we don't know whether a/b < c/d

Is that correct ?
_________________

I hate long and complicated explanations!

Intern
Joined: 19 Sep 2012
Posts: 13
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

21 Apr 2017, 03:15
1
KUDOS
daviddaviddavid wrote:
hey,

for statement 1:

can't we just multiply the equation by d-b ?

1. 0 < c-a/d-b --> multiply by d-b --> 0 < c-a --> a < c so a < c but we don't know whether a/b < c/d

Is that correct ?

We cannot multiply the equation by d-b because we do not know if d-b is less or greater than zero. For instance, d=3 and b=4, then 3-4 = -1. Rule of thumb: we cannot manipulate inequalities without knowing the signs. (and as I mentioned before we don't know the sign of d-b). Hope it helps
Director
Joined: 02 Sep 2016
Posts: 745
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

21 Apr 2017, 03:26
1) Not sufficient

That means denominator > numerator
bc>ac

Sufficient.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Manager
Joined: 26 Mar 2017
Posts: 146
Re: If a, b, c, and d, are positive numbers, is a/b < c/d? [#permalink]

### Show Tags

21 Apr 2017, 03:36
racingip wrote:
daviddaviddavid wrote:
hey,

for statement 1:

can't we just multiply the equation by d-b ?

1. 0 < c-a/d-b --> multiply by d-b --> 0 < c-a --> a < c so a < c but we don't know whether a/b < c/d

Is that correct ?

We cannot multiply the equation by d-b because we do not know if d-b is less or greater than zero. For instance, d=3 and b=4, then 3-4 = -1. Rule of thumb: we cannot manipulate inequalities without knowing the signs. (and as I mentioned before we don't know the sign of d-b). Hope it helps

ok thanks so but we could still change the inequality and consider both cases, right ?

1a. 0 < c-a/d-b --> multiply by d-b --> 0 < c-a --> a < c so a < c but we don't know whether a/b < c/d
1b. 0 < c-a/d-b --> multiply by d-b --> 0 > c-a --> a > c so a > c but we don't know whether a/b > c/d
_________________

I hate long and complicated explanations!

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?   [#permalink] 21 Apr 2017, 03:36

Go to page    1   2    Next  [ 26 posts ]

Display posts from previous: Sort by