GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 07 Dec 2019, 09:27 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If a, b, c, and d, are positive numbers, is a/b < c/d?

Author Message
TAGS:

### Hide Tags

Intern  Joined: 30 May 2008
Posts: 46
If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

5
86 00:00

Difficulty:   35% (medium)

Question Stats: 74% (02:04) correct 26% (02:23) wrong based on 2229 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: 629
Location: Cambridge, MA
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

22
10
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)
Senior Manager  Joined: 13 Aug 2012
Posts: 398
Concentration: Marketing, Finance
GPA: 3.23
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

14
6
catty2004 wrote:
If a, b, c, and d, are positive numbers, is a/b < c/d?

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

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.

Attachments photo.JPG [ 259.84 KiB | Viewed 71102 times ]

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.
##### General Discussion
Intern  B
Joined: 19 Sep 2012
Posts: 11
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1
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  B
Joined: 19 Sep 2012
Posts: 11
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1
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: 398
Concentration: Marketing, Finance
GPA: 3.23
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

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.
Manager  Joined: 04 Jan 2014
Posts: 94
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1
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 V
Joined: 02 Sep 2009
Posts: 59588
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

5
3
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: 94
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 59588
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1
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  G
Joined: 23 Jan 2013
Posts: 522
Schools: Cambridge'16
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

B
Senior Manager  B
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
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

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
Retired Moderator Joined: 29 Oct 2013
Posts: 248
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

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!
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

2
1
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)

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.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
Manager  B
Joined: 04 Dec 2015
Posts: 145
WE: Operations (Commercial Banking)
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

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  B
Joined: 13 Feb 2011
Posts: 79
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

5
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  B
Joined: 26 Mar 2017
Posts: 105
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

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  B
Joined: 19 Sep 2012
Posts: 11
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1
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  G
Joined: 02 Sep 2016
Posts: 641
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

1) Not sufficient

That means denominator > numerator
bc>ac

Sufficient.
Manager  B
Joined: 26 Mar 2017
Posts: 105
Re: If a, b, c, and d, are positive numbers, is a/b < c/d?  [#permalink]

### Show Tags

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  [ 27 posts ]

Display posts from previous: Sort by

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