GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 22 Jun 2021, 22:34
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

MBA Spotlight – Top 20 Virtual MBA Fair
June 14-30, 2021
Register Schedule
Super Wednesday:
INSEAD AdCom Live Q&A MIT Sloan AdCom Live Q&A Goizueta AdCom Live Q&A How to Pay for Your MBA Landing a Tech PM Job
Close

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
Your Progress

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo
13 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

avatar
NoHalfMeasures
Retired Moderator
Joined: 29 Oct 2013
Posts: 236
Concentration: Finance
GPA: 3.7
WE:Corporate Finance (Retail Banking)
GMAT ToolKit User
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  18 Dec 2015, 06:33
30
Bookmarks
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

64% (02:17) correct 36% (02:22) wrong based on 456 sessions

Hide Show timer Statistics

If a, b, c, and d are positive numbers and \(\frac{a}{b} < \frac{c}{d}\) , which of the following must be true?

I. \(\frac{(a+c)}{(b+d) }< \frac{c}{ d}\)

II. \(\frac{(a+c)}{(b+d)} < \frac{a}{b}\)

III. \(\frac{(a+c)}{(b+d)} = \frac{a}{b} + \frac{c}{d}\)

A. none
B. I only
C. II only
D. I and II
E. I and III
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
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
Signature Read More
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Community Reply
avatar
NoHalfMeasures
Retired Moderator
Joined: 29 Oct 2013
Posts: 236
Concentration: Finance
GPA: 3.7
WE:Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  18 Dec 2015, 06:36
4
Kudos
1
Bookmarks
a/b<c/d implies

ad<bc

Consider 1) a+c/b+d < c/d is true
then, cross multiplying
ad+dc<bc+cd
thus, ad<bc which is true and hence 1) is true.

Consider 2) a+c/b+d < a/b
implies

ab+bc<ba+ad
bc<ad
which we know to be false

3) We can't prove equality from inequality. Hence can't be 'must be true'. Bunuel, is my logic correct in here?

Hence correct answer is B
_________________
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
Signature Read More
General Discussion
avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2474
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  18 Dec 2015, 06:54
1
Kudos
NoHalfMeasures wrote:
If a, b, c, and d are positive numbers and a/b < c/d , which of the following must be true?

I. (a+c) / (b+d) < c/ d

II. (a+c) / (b+d) < a/b

III. (a+c) / (b+d) = a/b + c/d

a) none
b) I only
c) II only
d) I and II
e) I and III

Pls press kudos if you like the question and would like me to discuss more such questions


Your method is correct as well as all the 4 numbers are positive.

This question can be tackled easily by the method below:

You are given a/b < c/d ---> as all the numbers are positive you can cross multiply to get , a/c < b/d ---> (a/c) + 1 < (b/d) + 1 ---> (a+c)/c < (b+d)/d ---> (a+c) / (b+d) < c/ d which is statement I and is hence true.

Now, again consider a/b < c/d ---> d/b < c/a ---> (d/b) + 1 < (c/a) + 1 ---> (d+b)/b < (c+a)/a ---> a/b < (c+a)/(b+d) but this is not what statement II mentions, making statement II false.

Finally, for (a+c) / (b+d) = a/b + c/d , you can clearly prove this wrong by taking a,b,c,d as 1,2,3,4. So this is also not true.

For a MUST BE TRUE question, you need to get a yes ALWAYS.

Thus, only statement I is true , making B the correct answer.

Hope this helps.
_________________
My Kellogg Journey (2016-2018): https://gmatclub.com/forum/my-kellogg-journey-325661.html
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html
Signature Read More
avatar
NoHalfMeasures
Retired Moderator
Joined: 29 Oct 2013
Posts: 236
Concentration: Finance
GPA: 3.7
WE:Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  18 Dec 2015, 07:04
Thanks for your reply.

But can you also comment on the following-
St3) We can't prove equality from inequality. Hence st3 can't be 'must be true'. Is my logic correct specifically for st3?
_________________
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
Signature Read More
avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2474
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  18 Dec 2015, 07:16
2
Kudos
NoHalfMeasures wrote:
Thanks for your reply.

But can you also comment on the following-
St3) We can't prove equality from inequality. Hence can't be 'must be true'. Is my logic correct specifically for st3?


No this is a very broad statement that you are mentioning. Take a simpler example: If I say x<3 and then ask whether x =2 is true ? You will say "yes" but here you used the inequality to arrive at your answer for an equality.

I have shown 1 way of using particular values to see that III is NOT must be true.

The other way is to assume that (a+c) / (b+d) = a/b + c/d is indeed true.

Then you end up getting \(b^2*c+a*d^2=0\) ---> \(-(a/c)= b^2/d^2\) but this can not possible as a and c are given to be of the same sign (both are positive) and as such this will make -(a/c) a negative quantity.

Additionally, you also know that \(b^2/d^2\) can never be <0 . Thus you have this contradiction, making this statement not a must be true.

Hope this helps.
_________________
My Kellogg Journey (2016-2018): https://gmatclub.com/forum/my-kellogg-journey-325661.html
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html
Signature Read More
avatar
B
vtomar20
Intern
Intern
Joined: 25 Apr 2013
Posts: 4
GMAT 1: 660 Q48 V33
Reviews Badge
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  23 Mar 2017, 09:10
bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.


Bunuel I am very confused why 3rd statement is not correct. Here is my take on it -

(a+c) / (b+d) = a/b + c/d

Taking LCM -
so, (a+c)/(b+d)= (ad+cb)/(bd)

cross multiplying -
abd + bcd =abd +bcd, which is true. So the answer should be E. Can you please let me know why this approach is wrong. Thanks for all your help !
avatar
S
praneet87
Manager
Manager
Joined: 27 Aug 2014
Posts: 52
Location: Canada
Concentration: Strategy, Technology
Schools: Tepper '20, Johnson '20, Ross '20, Ivey '19
GMAT 1: 660 Q45 V35
GPA: 3.66
WE:Consulting (Consulting)
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  27 Mar 2017, 21:14
I used real values and came to the answer. Used 1/2 and 3/4.
avatar
B
saxena21nov
Intern
Intern
Joined: 16 Jul 2013
Posts: 6
GMAT ToolKit User
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  06 Nov 2017, 07:17
1
Kudos
vtomar20 wrote:
bumpbot wrote:
Hello from the GMAT Club BumpBot!



I am very confused why 3rd statement is not correct. Here is my take on it -

(a+c) / (b+d) = a/b + c/d

Taking LCM -
so, (a+c)/(b+d)= (ad+cb)/(bd)

cross multiplying -
abd + bcd =abd +bcd, which is true. So the answer should be E. Can you please let me know why this approach is wrong. Thanks for all your help !


Hi vtomar20

I see a problem in your algebra.

Even i did the same mistake and eventually found what i was doing wrong.

When you simplify the expression:

(a+c) / (b+d) = a/b + c/d

you will get

abd + bcd =abd +bcd + ad^2 + cb^2

and this however is not true, since in the above expression we have an extra ad^2 + cb^2 on the right side which will make the right side bigger (and we know this because all the a, b, c, and d, are positive numbers ).

so E is out and B is the answer.

I hope its clear :-)

Thankyou
Arunabh saxena
avatar
D
thangvietnam
Director
Director
Joined: 29 Jun 2017
Posts: 969
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  11 Jan 2018, 19:55
a/b<c/d
we multiple two side by bd. remember all number are positive.
ac<cb.

this simple multiply make the fraction from into factors form. this is key to do inequality problem.
avatar
B
Suryangshu
Manager
Manager
Joined: 20 Jun 2016
Posts: 59
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  22 Jul 2018, 23:57
1
Kudos
A good idea to eliminate III is if you look at option 1 it tells (a+c)/(b+d)<c/d, which we have already proved to be true.

Now go to option III (a+c) / (b+d) = a/b + c/d , which denotes (a+c) / (b+d) > c/d hence it is false as we have already proved I to be true !!
_________________
Life is a challenge face it.
Signature Read More
User avatar
P
energetics
Senior Manager
Senior Manager
Joined: 05 Feb 2018
Posts: 405
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  27 Jun 2019, 16:59
1
Kudos
Pick numbers... noticing the LHS is the same for all 3 roman numerals.
a=1/b=1 < c=2/d=1

I. 1+2/1+1 < 2/1
3/2 < 2, TRUE

II. 3/2 < 1, FALSE

III. 3/2 = 3, FALSE

Pick some other numbers to retest I.
a=1/b=3 < c=2/d=3
1+2/3+3 < 2/3
3/6 < 2/3
1/2 < 2/3, TRUE
Good enough, B it is.
avatar
P
sayan640
Manager
Manager
Joined: 29 Oct 2015
Posts: 236
CAT Tests
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  06 Jun 2020, 18:35
NoHalfMeasures wrote:
If a, b, c, and d are positive numbers and a/b < c/d , which of the following must be true?

I. (a+c) / (b+d) < c/ d

II. (a+c) / (b+d) < a/b

III. (a+c) / (b+d) = a/b + c/d

a) none
b) I only
c) II only
d) I and II
e) I and III

Pls press kudos if you like the question and would like me to discuss more such questions


I solved it by taking convenient values.
Lets take a= 4 ; b=2 ; c=12 ; d = 3

c/d = 4 which is greater than a/b=2

I must be true as ,
(a+c) /( b+d) = 16 / 5 = 3.2
c/d = 4
So (a+c) /( b+d) < c/d

II may not be true ,

(a+c) /( b+d) = 16 / 5 = 3.2
a/b = 2
2 is not greater than 3.2

III may not be true ,

(a+c) /( b+d) = 16 / 5 = 3.2

a/b + c/d = 2 +4 =6

Only I must be true.
B is the answer.

Please give me Kudos if you liked my explanation.
avatar
G
basshead
VP
VP
Joined: 09 Jan 2020
Posts: 1069
Premium Member
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink] New post  19 Nov 2020, 10:18
NoHalfMeasures wrote:
If a, b, c, and d are positive numbers and \(\frac{a}{b} < \frac{c}{d}\) , which of the following must be true?

I. \(\frac{(a+c)}{(b+d) }< \frac{c}{ d}\)

II. \(\frac{(a+c)}{(b+d)} < \frac{a}{b}\)

III. \(\frac{(a+c)}{(b+d)} = \frac{a}{b} + \frac{c}{d}\)

A. none
B. I only
C. II only
D. I and II
E. I and III


As each letter represents a positive number, we can cross multiply to get \(ad < cb\).

I. Cross multiply: \(ad + cd < cb + cd\)
\(ad < cb\)

Statement I must be true.

II. Cross multiply: \(ab + bc < ab + ad\)
\(bc < ad\)

We can't say for certain that this is true.

III. \(\frac{(a+c)}{(b+d)} = \frac{a}{b} + \frac{c}{d}\)

let \(a = 1, b = 2, c = 2, d = 3\)

\(\frac{3}{5} = \frac{1}{2 }+ \frac{2}{3}
\)
Not true.

Only statement that must be true is statement I.
_________________
Help me get better -- please critique my responses!
Signature Read More
GMAT Club Bot
gmatclubot
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
19 Nov 2020, 10:18
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10022 posts
Bunuel
Math Expert
77369 posts
GMATBusters
Retired Moderator
2003 posts
nick1816
DS Forum Moderator
2295 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions