Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
Updated on: 13 Aug 2018, 03:10
Originally posted by EgmatQuantExpert on 08 Apr 2015, 10:08.
Last edited by EgmatQuantExpert on 13 Aug 2018, 03:10, edited 5 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 03:10, edited 5 times in total.
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:31) correct
63%
(02:56)
wrong
based on 2221
sessions
History
Date
Time
Result
Not Attempted Yet
If a, b and n are positive integers such that \(n = 3*a\) \(-b^3\), is \(n^2 + 3\) divisible by 2?
(1) \(a^2\) \(-4*b^{3}-5\) \(= 0\)
(2) \(3*\)\(b^3\) \(-a^2\) \(+ 6 = 0\)
This is
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
(1) \(a^2\) \(-4*b^{3}-5\) \(= 0\)
(2) \(3*\)\(b^3\) \(-a^2\) \(+ 6 = 0\)
This is
Ques 2 of The E-GMAT Number Properties Knockout
Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts
Updated on: 07 Aug 2018, 01:08
Originally posted by EgmatQuantExpert on 10 Apr 2015, 05:54.
Last edited by EgmatQuantExpert on 07 Aug 2018, 01:08, edited 2 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 01:08, edited 2 times in total.
Kudos
Bookmarks
Detailed Solution
Step-I: Given Info:
We are given that \(a\), \(b\), \(n >0\) and are integers. Also \(n =3a – b^3\) and we are asked to find if \((n^2 + 3)\) is divisible by 2.
Step-II: Interpreting the Question Statement:
Let’s start from our expression i.e. \((n^2 + 3)\), this expression is divisible by 2 only if it’s even, since 3 is odd, for \(n^2 + 3\) to be even \(n^2\) has to be odd ( as odd + odd =even) and \(n^2\) can be odd only when \(n\) is odd.
Now, we know that \(n = 3a – b^3\) , for \(n\) to be odd, one of the \(3a\) or \(b^3\) has to be odd and other has to be even as the difference of an even and an odd number will always be odd. The even/odd nature of \(3a\) would depend on the even/odd nature of \(a\) and similarly the even odd nature of \(b^3\) would depend on the even/odd nature of \(b\). So, if we can establish that the even/odd nature of \(a\) and \(b\) are either similar or opposite, we will find our answer.
Step-III: Statement-I
Statement-I tells us that \(a^2 – 4b^3 = 5\), it tells us that difference of two numbers is odd. Since \(4b^3\) would always be even, for the difference of \(a^2\) and \(4b^3\) to be odd, \(a^2\) would have to be odd. For \(a^2\) to be odd, \(a\) has to be odd. But St-I does not tell us anything about the even/odd nature of \(b\).
So, Statement-I alone is insufficient.
Step-IV: Statement-II
Statement-II tells us that \(a^2 - 3b^3= 6\), it tells us that difference of two numbers is even. This is only possible in two cases:
a) When both \(a^2\) and \(3b^3\) are odd, for this to happen both \(a\) and \(b\) have to be odd or
b) When both \(a^2\) and \(3b^3\) are even, for this to happen both \(a\) and \(b\) have to be even
But, we know that for n to be odd, both \(a\) and \(b\) have to of opposite even/odd natures. We see that in St-II, in both the cases \(a\) and \(b\) are of the same nature, thus in both the cases, \(n\) would be even.
Hence, Statement-II is sufficient to answer our question.
Step-V: Combining Statements I & II
Since, we have a unique answer from Statement-II alone, we don’t need to combine the information from Statement-I and II.
Thus, the answer is Option B.
Key Takeaways
1. In even-odd questions, simplify complex expressions into simpler expressions using the properties of even-odd combinations.
2. Know the properties of even/odd combinations to save the time spent deriving them in the test
3. The even/odd nature of some expressions can be determined without knowing the exact even/odd nature of the variables of the expressions by using the even/odd combination property
Regards
Harsh
Step-I: Given Info:
We are given that \(a\), \(b\), \(n >0\) and are integers. Also \(n =3a – b^3\) and we are asked to find if \((n^2 + 3)\) is divisible by 2.
Step-II: Interpreting the Question Statement:
Let’s start from our expression i.e. \((n^2 + 3)\), this expression is divisible by 2 only if it’s even, since 3 is odd, for \(n^2 + 3\) to be even \(n^2\) has to be odd ( as odd + odd =even) and \(n^2\) can be odd only when \(n\) is odd.
Now, we know that \(n = 3a – b^3\) , for \(n\) to be odd, one of the \(3a\) or \(b^3\) has to be odd and other has to be even as the difference of an even and an odd number will always be odd. The even/odd nature of \(3a\) would depend on the even/odd nature of \(a\) and similarly the even odd nature of \(b^3\) would depend on the even/odd nature of \(b\). So, if we can establish that the even/odd nature of \(a\) and \(b\) are either similar or opposite, we will find our answer.
Step-III: Statement-I
Statement-I tells us that \(a^2 – 4b^3 = 5\), it tells us that difference of two numbers is odd. Since \(4b^3\) would always be even, for the difference of \(a^2\) and \(4b^3\) to be odd, \(a^2\) would have to be odd. For \(a^2\) to be odd, \(a\) has to be odd. But St-I does not tell us anything about the even/odd nature of \(b\).
So, Statement-I alone is insufficient.
Step-IV: Statement-II
Statement-II tells us that \(a^2 - 3b^3= 6\), it tells us that difference of two numbers is even. This is only possible in two cases:
a) When both \(a^2\) and \(3b^3\) are odd, for this to happen both \(a\) and \(b\) have to be odd or
b) When both \(a^2\) and \(3b^3\) are even, for this to happen both \(a\) and \(b\) have to be even
But, we know that for n to be odd, both \(a\) and \(b\) have to of opposite even/odd natures. We see that in St-II, in both the cases \(a\) and \(b\) are of the same nature, thus in both the cases, \(n\) would be even.
Hence, Statement-II is sufficient to answer our question.
Step-V: Combining Statements I & II
Since, we have a unique answer from Statement-II alone, we don’t need to combine the information from Statement-I and II.
Thus, the answer is Option B.
Key Takeaways
1. In even-odd questions, simplify complex expressions into simpler expressions using the properties of even-odd combinations.
2. Know the properties of even/odd combinations to save the time spent deriving them in the test
3. The even/odd nature of some expressions can be determined without knowing the exact even/odd nature of the variables of the expressions by using the even/odd combination property
Regards
Harsh
09 Apr 2015, 03:11
Kudos
Bookmarks
EgmatQuantExpert
From this question
\(n = 3*a\) \(-b^3\), is \(n^2 + 3\) divisible by 2
we can remake this question in more convinient form:
firstly change N on \(n = 3*a\) \(-b^3\)
\((3*a -b^3)^2 + 3 = even?\)
As we know that A and B integers we can eliminate all powers because they don't have any influence on parity
and we have such question: \(3*a -b + 3 = even?\)
1) \(a^2 -4*b^{3}-5 = 0\)
remove powers: a-4b-5=0
0 is even
so we know that 4b even and 5 is odd
so a is odd but we need information about b and we don't have it because B can be odd and can be even, after multiplying on 4 it will even result
Insufficient
2) \(3*b^3-a^2 + 6 = 0\)
remove powers: 3b-a+6=0
and we see that a and b will be equal parity: both even or both odd
And it seems like insufficient but if we check question we will see that we don't need to know if b odd or even
we need to know about result of a-b+3
and from this statement we know that a-b equal even result and plus 3 will be odd result
Sufficient
Answer is B
