May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 30 May 2008
Posts: 51

If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
Updated on: 12 May 2017, 01:29
Question Stats:
74% (02:06) correct 26% (02:26) wrong based on 2571 sessions
HideShow timer Statistics
If a, b, c, and d, are positive numbers, is \(\frac{a}{b} < \frac{c}{d}\)? (1) \(0 < \frac{(ca)}{(db)}\) (2) \((\frac{ad}{bc})^2 < \frac{(ad)}{(bc)}\)
Official Answer and Stats are available only to registered users. Register/ Login.
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: 636
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
catty2004 wrote: 92. If a, b, c, and d, are positive numbers, is a/b < c/d?
1) 0 < (ca) / (db)
2) (ad/bc)^2 < (ad)/(bc) 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 crossmultiplying. This will be useful laters. Statement 1) is not useful, however. (ca) and (db) 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 crossmultiply to get ad < bc. That answers our question with a definite yes, so it's sufficient and the answer is (B)
_________________




Senior Manager
Joined: 13 Aug 2012
Posts: 418
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
catty2004 wrote: If a, b, c, and d, are positive numbers, is a/b < c/d?
(1) 0 < (ca) / (db)
(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) (ca)/(db)  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 61406 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: 12

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?



Intern
Joined: 19 Sep 2012
Posts: 12

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
20 Sep 2012, 01:51
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: 418
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: 102

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 crossmultiply 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: 55271

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
18 Jun 2014, 08:48
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 crossmultiply 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: 102

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: 55271

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
19 Jun 2014, 00:55
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: 549

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



Senior Manager
Joined: 10 Mar 2013
Posts: 495
Location: Germany
Concentration: Finance, Entrepreneurship
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 casame and d<b or db  same and c>a... 1) (ca)/(db) > 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: 257
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/myjourneyto46onverbal750overall171722.html#p1367876



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7372
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
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 < (ca) / (db) (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 < (ca) / (db), and if we multiply (db)^2 on both sides, 0<(ca)(db). 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 spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Manager
Joined: 04 Dec 2015
Posts: 96
WE: Operations (Commercial Banking)

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: 82

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
26 Dec 2015, 16:59
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 \(\frac{ca}{db}>0\), i.e. \(ca\) and \(db\) 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: 114

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 db ? 1. 0 < ca/db > multiply by db > 0 < ca > 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: 12

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
21 Apr 2017, 03:15
daviddaviddavid wrote: hey,
for statement 1:
can't we just multiply the equation by db ?
1. 0 < ca/db > multiply by db > 0 < ca > a < c so a < c but we don't know whether a/b < c/d
Is that correct ? We cannot multiply the equation by db because we do not know if db is less or greater than zero. For instance, d=3 and b=4, then 34 = 1. Rule of thumb: we cannot manipulate inequalities without knowing the signs. (and as I mentioned before we don't know the sign of db). Hope it helps



Director
Joined: 02 Sep 2016
Posts: 659

Re: If a, b, c, and d, are positive numbers, is a/b < c/d?
[#permalink]
Show Tags
21 Apr 2017, 03:26
The question is asking whether ad<bc ? 1) Not sufficient 2) (ad/bc)^2 <ad/bc 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: 114

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 db ?
1. 0 < ca/db > multiply by db > 0 < ca > a < c so a < c but we don't know whether a/b < c/d
Is that correct ? We cannot multiply the equation by db because we do not know if db is less or greater than zero. For instance, d=3 and b=4, then 34 = 1. Rule of thumb: we cannot manipulate inequalities without knowing the signs. (and as I mentioned before we don't know the sign of db). Hope it helps ok thanks so but we could still change the inequality and consider both cases, right ? 1a. 0 < ca/db > multiply by db > 0 < ca > a < c so a < c but we don't know whether a/b < c/d 1b. 0 < ca/db > multiply by db > 0 > ca > 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 ]



