Jun 16 09:00 PM PDT  10:00 PM PDT For a score of 4951 (from current actual score of 40+). AllInOne Standard & 700+ Level Questions (150 questions) Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55618

Question Stats:
65% (01:23) correct 35% (01:24) wrong based on 109 sessions
HideShow timer Statistics
If \(a\) and \(b\) are negative integers, is \(a^b\) negative? (1) \(ab\) is even (2) \(a + b\) is even
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 55618

Re M2406
[#permalink]
Show Tags
16 Sep 2014, 01:20
Official Solution: (1) \(ab\) is even. If \(a=b=2\), then \(a^b=\frac{1}{4} \gt 0\) but if \(a=2\) and \(b=1\), then \(a^b=\frac{1}{2} \lt 0\). Not sufficient. (2) \(a+b\) is even. If \(a=b=2\), then \(a^b=\frac{1}{4} \gt 0\) but if \(a=1\) and \(b=1\), then \(a^b=1 \lt 0\). Not sufficient. (1)+(2) From \(a+b=even\) it follows that \(a\) and \(b\) are either both odd or both even. Now, if both are odd then \(ab=even\) won't hold true, so both \(a\) and \(b\) must be even. Hence \(a^b=negative^{even}=positive\). Sufficient. Answer: C
_________________



Manager
Joined: 08 Feb 2014
Posts: 204
Location: United States
Concentration: Finance
WE: Analyst (Commercial Banking)

Re: M2406
[#permalink]
Show Tags
22 Nov 2014, 19:55
We know that both a and b are negative integers. Therefore, a is being raised to the power of a negative number. This means that for a^b to be positive, b must be even (because a is neg. ex: a=(2), (2)^2 =4, while (2)^3=(8).
stmt 1: all we know is that at least one of a or b is even, because you need a min. of one even number in a set, for the product of a set of numbers to be even. a, or b, or both could be even. Insuff.
stmt 2: all we know is that a and b are either both odd or both even, because o+o=e and e+e=e but o+e=o.
stmts 1&2: stmt 1 tells us that at least a or b is even. combined with stmt 2, we know that both terms are even, therefore, b is even.



Senior Manager
Joined: 08 Jun 2015
Posts: 423
Location: India
GMAT 1: 640 Q48 V29 GMAT 2: 700 Q48 V38
GPA: 3.33

Re: M2406
[#permalink]
Show Tags
13 Apr 2018, 04:16
+1 for option C. The question requires us to find out if b is even or not. St 1 : ie a is even , b is even or both are even. We can't be sure of b is even or not. NS St 2 : i.e both are even or both are odd. NS Both together : Yes , sufficient ! We now know that both are even. Hence the answer is C
_________________
" The few , the fearless "



Intern
Joined: 16 Apr 2018
Posts: 7
Location: India
Concentration: General Management, International Business
Schools: HBS '21, Kellogg 1YR '20, CBS '21, Duke '19, McCombs '21, Tepper '21, LBS '21, IESE '21, ISB '20, IE Sept19 Intake, IIMA PGPX"20, ESMT
GPA: 4
WE: Analyst (Computer Software)

Re M2406
[#permalink]
Show Tags
10 Apr 2019, 18:22
I think this is a highquality question and the explanation isn't clear enough, please elaborate. In statement 2: When A=B=2, that given A+B= 4 which is not even and when A=B=1, then also A+B=2 which is not even. To answer the question, values of A and B are not sufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 55618

Re: M2406
[#permalink]
Show Tags
10 Apr 2019, 21:19
oharsha12 wrote: I think this is a highquality question and the explanation isn't clear enough, please elaborate. In statement 2: When A=B=2, that given A+B= 4 which is not even and when A=B=1, then also A+B=2 which is not even. To answer the question, values of A and B are not sufficient. Both 4 and 2 are even integers.b Even number is an integer, which is divisible by 2 without a remainder.
_________________



CEO
Joined: 18 Aug 2017
Posts: 3834
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: M2406
[#permalink]
Show Tags
11 Apr 2019, 00:29
Bunuel wrote: If \(a\) and \(b\) are negative integers, is \(a^b\) negative?
(1) \(ab\) is even
(2) \(a + b\) is even #1 \(ab\) is even one of integers has to be even so we dont know which one of a or b is even ; insufficient #2 \(a + b\) is even ; both a & b odd or both even ; insufficient from1 & 2 ab both are even so [m]a^b[/m is not negative IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.










