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

 It is currently 22 Feb 2019, 08:27

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If a, b and c are integers such that b > a, is b+c > a

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

### Hide Tags

SVP
Joined: 04 May 2006
Posts: 1647
Schools: CBS, Kellogg
If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

Updated on: 09 Aug 2012, 23:22
1
38
00:00

Difficulty:

95% (hard)

Question Stats:

34% (02:27) correct 66% (02:03) wrong based on 1659 sessions

### HideShow timer Statistics

If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0

_________________

Originally posted by sondenso on 26 May 2009, 01:46.
Last edited by Bunuel on 09 Aug 2012, 23:22, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

10 Aug 2012, 00:15
13
8
If a, b and c are integers such that b > a, is b+c > a ?

Question: is $$b+c > a$$ ? --> or: is $$b+c-a > 0$$?

(1) c > a. If $$a=1$$, $$b=2$$ and $$c=3$$, then the answer is clearly YES but if $$a=-3$$, $$b=-2$$ and $$c=-1$$, then the answer is NO. Not sufficient.

(2) abc > 0. Either all three unknowns are positive (answer YES) or two unknowns are negative and the third one is positive. Notice that in the second case one of the unknowns that is negative must be $$a$$ (because if $$a$$ is not negative, then $$b$$ is also not negative so we won't have two negative unknowns). To get a NO answer for the second case consider $$a=-3$$, $$b=1$$ and $$c=-4$$ and . Not sufficient.

(1)+(2) We have that $$b > a$$, $$c > a$$ ($$c-a>0$$) and that either all three unknowns are positive or $$a$$ and any from $$b$$ and $$c$$ is negative. Again for the first case the answer is obviously YES. As for the second case: say $$a$$ and $$c$$ are negative and $$b$$ is positive, then $$b+(c-a)=positive+positive>0$$ (you can apply the same reasoning if $$a$$ and $$b$$ are negative and $$c$$ is positive). So, we have that in both cases we have an YES answer. Sufficient.

_________________
##### General Discussion
Senior Manager
Joined: 27 Jun 2008
Posts: 485
WE 1: Investment Banking - 6yrs

### Show Tags

26 May 2009, 06:18
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0

E

a = -4 or 3
b = -3 or 4

The above satifies b>a, using - or + as examples.

(1) c>a
c = -2 or 4
Insuff
(2) abc>0
This means either 2 of the intergers are negative or all of the intergers are positive.
Insuff
Manager
Joined: 13 May 2009
Posts: 186
Schools: Stanford, Harvard, Berkeley, INSEAD

### Show Tags

26 May 2009, 10:34
1
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?
(1) c > a
(2) abc > 0

b>a <==> 0>a-b <==> a-b is negative
Question:(b+c>a)?
Question:(c>a-b)?
Question:(c >= 0)?

(1) Insufficient, as a-b<0 could mean that a<0 or a>0, which means c<0 or c>=0.

(2) We have an even # of negatives, ie 0/2. If we have 0 negatives, then sufficient. Again if we have 2 insufficient.

I can see the pattern, the answer is E.

Here are the Yes/No cases:

Yes: 4 5 7
No: -9 3 -10

Final Answer, $$E$$.
_________________

Manager
Joined: 11 Apr 2009
Posts: 136

### Show Tags

27 May 2009, 10:27
2
why cant it be C?

1. b>a and c>a and abc>0:

If a<0, b can be less than or greater than 0.

If a<0, b<0 then c>0 (a=-6, b=-4, c=2) => b+c >a
If a<0, b>0, c<0 (a=-3, b=5, c=-1) => b+c >a

If all are positive, then also b+c >a.

Hence, C.

Are there any assumptions which do not satisfy both conditions simultaneously?

What is the OA?
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
Posts: 195
Schools: Harvard, Penn, Maryland

### Show Tags

27 May 2009, 13:20
1
2
The answer is C

statement 1 does work for positives, but not for negatives. a= -2 b= -1 c= -1.

statement 2 doesnt work on its own because c could be way less than a, negating b,
a= -3 b=2 c= -5

however, both together mean that there can only be two negatives, and c must be larger than A.
for any value A, negative or not, two values that are greater than it with one positive are going to together be greater than A.
if A is positive = a=2, c=3, b=3, a=1 b=2 c=2
if A is negative = a= -3, c= -2, b=1, a= -2 b=-1 c=1

There is no solution with (1) and (2) true that doesn't end up with B + C > A

gmatprep is right
Senior Manager
Joined: 08 Jan 2009
Posts: 291

### Show Tags

27 May 2009, 19:18
1
b>a
stmt 1 :

c>a so b+c>2a
we cannot tell whether b+c >a may or may not. So insufficient.

stmt 2 :
abc>0 and b >a
a = +ve b = +ve c =+ve so definetly b+c > a
a = -ve b = -ve c = +ve so definetly b+c > a. ( since c =+ve and b>a)
a = -ve b = +ve c = -ve ( here it is just the opposite u know b =+ve but do not know c>a).so u cant tell whether b+c > a

Combing : yes u know you have got what u wanted so C.

Thanks gmatprep09 and dk94588.
Manager
Joined: 13 May 2009
Posts: 186
Schools: Stanford, Harvard, Berkeley, INSEAD

### Show Tags

28 May 2009, 10:53
1
1
Whoops the answer is C

If you look at both together,

we have that b>a & c>a.

from (1) we get b+c>2a and we're almost sufficient, but only if 2a>a.
Well if a<0, no, but if a>0, yes.

(2) tells us that 0 or 2 are negative. If all 3 are positive, sufficient.
Now if 2 are negative, then a has to be negative as well. Suppose a were positive-- then b/c would be negative, and b>a & c>a would be false. Hence a has to be positive.

(C)

Very tricky
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

05 Jul 2013, 01:44
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

_________________
Manager
Joined: 02 Jul 2012
Posts: 187
Location: India
Schools: IIMC (A)
GMAT 1: 720 Q50 V38
GPA: 2.6
WE: Information Technology (Consulting)
If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

21 Oct 2014, 21:12
1
sondenso wrote:
If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0

The question stem says that b > a. There are following possibilities for this
a. Both Positive Lets say $$b = 5 and a = 2$$

b. Both Negative, lets say $$b = -3 and a = -5$$

c. One positive one negative, lets say $$b = 3 and a = -1$$

d. Either of the two zero

1. c > a

C can be positive or negative and can fit in any of the above mentioned scenarios.

Insufficient

2. abc > 0

This means either all are positive or any two are negative. Since b > a, there are numerous possibilities for c.

So, Insufficient.

c > a and abc > 0

This would mean that either all are positive - b + c > a

or two negatives and one one positive - a has to be negative, either of b and c has to be negative and the other one positive. This would also mean that c + b > a

Ans - C
_________________

Give KUDOS if the post helps you...

Manager
Joined: 24 May 2013
Posts: 79
If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

16 Mar 2016, 21:41
If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a
(2) abc > 0
Either two are negative and one positive or all are positive.

Individually both the statements are not sufficient.
Combining 1 and 2 Sufficient.

Hence C.
Attachments

abc integer.png [ 6.31 KiB | Viewed 16120 times ]

Intern
Joined: 14 Nov 2015
Posts: 11
Re: If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

18 Mar 2016, 07:08
Bunuel

In this problem can we subtract the following inequalities?

b>a
b+c>a

and arrive at 'is c>0??'
CEO
Joined: 20 Mar 2014
Posts: 2629
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

18 Mar 2016, 07:21
.rr1990 wrote:
Bunuel

In this problem can we subtract the following inequalities?

b>a
b+c>a

and arrive at 'is c>0??'

Let me try to answer.

The answer is NO you can not.

b>a and b+c>a can mean both c<0 and c>0 by taking the following cases:

b=5, c=-3 and a=1 but the given conditions are also true for b=5, c=3 and a=1. So you have both the cases possible.

With,

b>a and b+c>a, you can not directly subtract the 2 inequalities as the sign for b>a MUST be reversed. You can only ADD in inequalities without thinking about the signs.

If I give you,

b>a and b+c>a ---> then the only MUST be true statement will be ---> b+b+c > 2a ---> 2b+c > 2a

BUT,

If you are given, b<a and b+c > a, as you can not add 2 inequalities with dissimilar inequality signs ---> you must do an additional operation (b<a ---> -b>-a) before you add the 2.

After the manipulation you get,

-b > -a and this added to b+c > a --> -b+b+c > 0 ---> c>0

Hope this helps.
Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

18 Mar 2016, 08:11
.rr1990 wrote:
Bunuel

In this problem can we subtract the following inequalities?

b>a
b+c>a

and arrive at 'is c>0??'

Hi,

NO you cannot..
if
b>a...I
b+c>a..II

I-II
b-(b+c)>a-a
-c>0
or c<0

II-I
b+c-b>a-a
c>0

so you see, you have two opposite answer depending on the way you subtract..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Intern
Joined: 11 Jun 2017
Posts: 22
If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

01 Oct 2017, 08:32
If a, b and c are integers such that b > a, is b+c > a ?

(1) c > a

lets say b=-1 and a=-2. If c=-1 then -1+-1 = -2 ---> is b+c > a NO. If c=1 then -1+1>-2 YES.

Hence insufficient.

(2) abc > 0

Only tell us either a,b,c are all positive or 2 negative and 1 positive, besides this info we get nothing. Hence insufficient.

IF two combines. When b is positive a, c must be negative (all three are positive will be a straight answer. And all three negative will never happen because abc > 0) (abc>0, b>a, c>a). Either outcome makes b+c > a. (C) Correct
Non-Human User
Joined: 09 Sep 2013
Posts: 9894
Re: If a, b and c are integers such that b > a, is b+c > a  [#permalink]

### Show Tags

10 Oct 2018, 23:32
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.
_________________
Re: If a, b and c are integers such that b > a, is b+c > a   [#permalink] 10 Oct 2018, 23:32
Display posts from previous: Sort by

# If a, b and c are integers such that b > a, is b+c > a

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

 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®.