Author 
Message 
TAGS:

Hide Tags

SVP
Joined: 04 May 2006
Posts: 1877
Schools: CBS, Kellogg

If a, b and c are integers such that b > a, is b+c > a [#permalink]
Show Tags
26 May 2009, 01:46
1
This post received KUDOS
27
This post was BOOKMARKED
Question Stats:
35% (04:54) correct 65% (01:25) wrong based on 1393 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT Club Premium Membership  big benefits and savings
Last edited by Bunuel on 09 Aug 2012, 23:22, edited 1 time in total.
Edited the question.



Director
Joined: 27 Jun 2008
Posts: 538
WE 1: Investment Banking  6yrs

Re: Integers [#permalink]
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: 191
Schools: Stanford, Harvard, Berkeley, INSEAD

Re: Integers [#permalink]
Show Tags
26 May 2009, 10:34
1
This post received KUDOS
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>ab <==> ab is negative Question:(b+c>a)? Question:(c>ab)? Question:(c >= 0)? (1) Insufficient, as ab<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, \(E\).
_________________
Hades



Manager
Joined: 11 Apr 2009
Posts: 159

Re: Integers [#permalink]
Show Tags
27 May 2009, 10:27
2
This post received KUDOS
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: 208
Schools: Harvard, Penn, Maryland

Re: Integers [#permalink]
Show Tags
27 May 2009, 13:20
1
This post received KUDOS
1
This post was BOOKMARKED
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: 324

Re: Integers [#permalink]
Show Tags
27 May 2009, 19:18
1
This post was BOOKMARKED
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: 191
Schools: Stanford, Harvard, Berkeley, INSEAD

Re: Integers [#permalink]
Show Tags
28 May 2009, 10:53
1
This post received KUDOS
1
This post was BOOKMARKED
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
_________________
Hades



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
Show Tags
10 Aug 2012, 00:15
10
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
If a, b and c are integers such that b > a, is b+c > a ?Question: is \(b+c > a\) ? > or: is \(b+ca > 0\)? (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 \(b > a\), \(c > a\) (\(ca>0\)) 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 \(b+(ca)=positive+positive>0\) (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. Answer: C.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 43892

Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
Show Tags
05 Jul 2013, 01:44



Current Student
Joined: 02 Jul 2012
Posts: 211
Location: India
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
This post received KUDOS
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. Adding the two 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: 85

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 10917 times ]



Intern
Joined: 14 Nov 2015
Posts: 12

Re: If a, b and c are integers such that b > a, is b+c > a [#permalink]
Show Tags
18 Mar 2016, 07:08
BunuelIn this problem can we subtract the following inequalities? b>a b+c>a and arrive at 'is c>0??'



Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
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: BunuelIn 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: 5660

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: BunuelIn 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
III b(b+c)>aa c>0 or c<0
III b+cb>aa c>0
so you see, you have two opposite answer depending on the way you subtract..
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
BANGALORE/



Intern
Joined: 11 Jun 2017
Posts: 34

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




If a, b and c are integers such that b > a, is b+c > a
[#permalink]
01 Oct 2017, 08:32






