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

It is currently 18 Jul 2018, 05:54

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.

Close

Request Expert Reply

Confirm Cancel

Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47077
Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 23 Sep 2015, 03:29
1
8
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (01:33) correct 47% (01:56) wrong based on 144 sessions

HideShow timer Statistics

1 KUDOS received
Manager
Manager
avatar
Joined: 10 Aug 2015
Posts: 103
GMAT ToolKit User
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post Updated on: 23 Sep 2015, 14:06
1
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C


Kudos for a correct solution.


Solution: For problems such as this, it is sometimes better to simplify the question.
(A + B) / (C + B) > A/C --->(1)
Subtract 1 on both sides.
==> (A - C) / (C + B) > (A - C)/C .Numerators are same .
If A = C , then then (1) is always true.
Else, for this to be true C+B<C ==>B<0.
So we have find whether B<0.

Statement1 : B>0. But we dont know whether a=c. Insufficient

Statement2 : It says nothing about B. Insufficient.

Combined : A != C and B>0. No. Sufficient.
Option C

Originally posted by anudeep133 on 23 Sep 2015, 04:47.
Last edited by anudeep133 on 23 Sep 2015, 14:06, edited 1 time in total.
2 KUDOS received
Intern
Intern
avatar
Joined: 17 Oct 2012
Posts: 3
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 23 Sep 2015, 13:20
2
@anudeep123:

A is wrong. what if a=b=c=1? Combining both, the left side is always going to be greater than A/C by 1. Correct answer is C.
2 KUDOS received
Intern
Intern
avatar
Joined: 23 Sep 2015
Posts: 4
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 24 Sep 2015, 03:57
2
Since we are told that A and C are both greater than zero, that means we can freely multiply and divide these two variables in the inequality but not B since we aren't told if B is positive or negative.

With that in mind, lets play around with the question first.
(A+B) A
------- > ---
(C+B) C

Since we can multiply/divide A and C around the inequality lets cross multiply

AC + AB > AC + BC

Subtract AC on both sides and we're left with "is AB > BC"

Now on to the choices

1) B>0
Insufficient since this doesn't tell us anything about C and A.

2) A<C
Again, insufficient since if you consider this statement alone, we aren't told anything about the value of B. If B is positive then BC will be be greater than AB if C > A. However, if B is a negative value then BC will be less than AB if C > A

1) and 2)
Sufficient. We know B is positive. This fills the gap in the second statement. If B is positive then having C > A ensure that BC > AB

So answer is C
Intern
Intern
User avatar
Joined: 13 Nov 2014
Posts: 48
GMAT 1: 590 Q42 V29
GMAT 2: 630 Q47 V29
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 24 Sep 2015, 21:18
Additions of B in numerator and denominator can be tricky,

I guess answer should be E
_________________

-----------------------------------------
Consider Cudos if you like this post.
-----------------------------------------

Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 173
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 24 Sep 2015, 22:24
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C

st1 -- B is positive given
also A and C are positive

hence (A + B) / (C + B) > A/C

We can cross multiply

AC + BC > AC + AB
BC > AB
BC - AB > 0
B( C-A) >0

already that B is >0 hence --- C >A

Therefore ---- We got the relation between c and a .

Now

(A + B) / (C + B) > A/C Use number any positve number that satisfy C>A and B is also positive .We will get a definitive ans .

ST B . Not sufficient . NO clues given for B

Hence Ans is A .
_________________

Regards ,

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47077
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 05 Oct 2015, 02:39
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

For (1), we are only given that b is a positive number. Picking values is a good strategy here. If we can choose values such that we get a “yes” and choose values so that we get a “no” then we can quickly eliminate. If a = 1 and c = 1 and b = 1, then the inequality is NOT correct. However, if a = 1 and c = 2, and b = 3, we get 4/5 > 1/2, which IS correct. (2) can be proved insufficient similarly. Combined, if b is positive and a < c, then it will continue to INCREASE the left-hand side of the inequality no matter what values we pick.

The answer is (C).

Remember, even the most seemingly complex Data Sufficiency questions can be overcome with solid strategy!
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2724
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 28 Apr 2016, 19:03
Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C


Kudos for a correct solution.


I solved it by remembering that if 0 < x/y < 1, then adding same positive number to the numerator and denominator, the value will increase.

1. B>0
just listed 2 possible options
A=C
B=2
A+2/C+2 = A/C so equal

A=3
C=5
B=1
3+1/5+1 = 4/6 = 2/3 > 3/5

2 outcomes, A alone is not sufficient.

2. A<C
ok, so 0<A/C<1 but what about B? if B is negative, then adding it to numerator and denominator would decrease the new fraction.
clearly 2 alone is not sufficient.

1+2
A<C
and B>0
sufficient.
Intern
Intern
avatar
Joined: 14 Mar 2014
Posts: 21
Schools: HBS '17
GMAT ToolKit User Reviews Badge
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 29 Apr 2016, 00:22
1
whenever we add something to numerator and denominator, percentages come into play! like if the percentage increase in Numerator is more than the percentage increase in denominator, ratio increases and vice versa.

So here we are adding a number B to numerator (A) and denominator (C) but we don't know which one is larger so as know whose percentage increase is more.

St1: B>0 now we know that we are adding a number and not subtracting since B is positive but we don't know whether A >C or C>B so we can't comment on the change in ratio.

St2: A<C but this does not tell about B( whether we are subtracting a number or adding a number)

1 & 2 combined: now B>0 so we are adding something. and A<C so percentage change in numerator(A) would be more as compared to percentage change in denominator(C) . So the ratio will increase.

Hence C.

Bunuel wrote:
Given that A > 0 and C > 0, is (A + B) / (C + B) > A/C?

(1) B > 0

(2) A < C


Kudos for a correct solution.
Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 302
GMAT 1: 600 Q44 V27
Reviews Badge
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 29 Jun 2016, 04:58
The first temptation is to cross-multiply the expressions, but we can't do it because we only know that A, C are positive, but we don't know the sign of B.
So for start let the question stem as it is.

from 1) \(b>0\) Now we know all the signs and we can cross multiply. We get:

\(CA+CB>CA+AB\)
CA+CB>CA+AB
\(CB>AB\)
\(CB-AB>0\)
\(B(C-A)>0\)
Now we have that B multiplied by (C-A) is positive. How can that be? only if B>0 and (C-A)>0 or B<0 and (C-A)<0

From the stem we are told that B>0, so the question becomes "Is (C-A) positive?" From 1) we can't extract any info on C-A so it's insufficient.

from 2) A<C, so 0<C-A We don't know the sign of B, so we can't cross-multiply and that impairs us from working on the question. Insufficient.

1) + 2) from 1 we got our rephrased question, "Is (C-A) positive?" and from 2) we get that A<C, so 0<C-A and we now have enough info to answer.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7283
Premium Member
Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C? [#permalink]

Show Tags

New post 09 Apr 2018, 11:41
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?   [#permalink] 09 Apr 2018, 11:41
Display posts from previous: Sort by

Given that A > 0 and C > 0, is (A + B)/(C + B) > A/C?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.