It is currently 12 Dec 2017, 21:15

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 and a/b < c/d , which of the fo

Author Message
TAGS:

Hide Tags

Retired Moderator
Joined: 29 Oct 2013
Posts: 285

Kudos [?]: 503 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

18 Dec 2015, 06:33
6
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:38) correct 42% (01:26) wrong based on 138 sessions

HideShow timer Statistics

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
[Reveal] Spoiler: OA

_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 503 [0], given: 197

Retired Moderator
Joined: 29 Oct 2013
Posts: 285

Kudos [?]: 503 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

18 Dec 2015, 06:36
a/b<c/d implies

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

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

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?

_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 503 [0], given: 197

Current Student
Joined: 20 Mar 2014
Posts: 2673

Kudos [?]: 1789 [1], given: 796

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

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.

Kudos [?]: 1789 [1], given: 796

Retired Moderator
Joined: 29 Oct 2013
Posts: 285

Kudos [?]: 503 [0], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

18 Dec 2015, 07:04

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?
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 503 [0], given: 197

Current Student
Joined: 20 Mar 2014
Posts: 2673

Kudos [?]: 1789 [1], given: 796

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

18 Dec 2015, 07:16
1
KUDOS
NoHalfMeasures wrote:

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.

Kudos [?]: 1789 [1], given: 796

Non-Human User
Joined: 09 Sep 2013
Posts: 14883

Kudos [?]: 287 [0], given: 0

Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

24 Dec 2016, 00:52
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.
_________________

Kudos [?]: 287 [0], given: 0

Intern
Joined: 25 Apr 2013
Posts: 4

Kudos [?]: [0], given: 0

GMAT 1: 660 Q48 V33
Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

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 -

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 !

Kudos [?]: [0], given: 0

Manager
Joined: 27 Aug 2014
Posts: 57

Kudos [?]: 6 [0], given: 6

Concentration: Strategy, Technology
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]

Show Tags

27 Mar 2017, 21:14
I used real values and came to the answer. Used 1/2 and 3/4.

Kudos [?]: 6 [0], given: 6

Intern
Joined: 16 Jul 2013
Posts: 4

Kudos [?]: [0], given: 168

If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]

Show Tags

06 Nov 2017, 07:17
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 -

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

Kudos [?]: [0], given: 168

If a, b, c, and d are positive numbers and a/b < c/d , which of the fo   [#permalink] 06 Nov 2017, 07:17
Display posts from previous: Sort by