Author 
Message 
TAGS:

Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
24 Feb 2013, 20:18
Archit143 wrote: Hi bunuel can you help with this question.....the book has given statement 1 is sufficient...it says that since b^2 is always positive so "a" must also be positive......but i think a can be negative also......
regards Archit Responding to a pm: A response above clarifies that this is an errata. The correct statement 1 is a = b^2 instead of a^2 = b^2. In that case If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) a = b^2 (2) a^2 = b^4 Is\(\frac{1}{a} > \frac{a}{(b^4 + 3)}\) ? Is \(\frac{(b^4 + 3)}{a} > a\) ? Is \(\frac{(b^4 + 3)}{a}  a > 0\) ? Is \(\frac{(b^4 + 3  a^2)}{a} > 0\) ? (1) a = b^2 This tells us that 'a' must be positive. Further, squaring, we get a^2 = b^4 Hence, the question becomes: Is 3/a > 0. It must be since a is positive. Sufficient (2) a^2 = b^4 Doesn't tell us anything about the sign of a. The question becomes: Is 3/a > 0? We cannot say. Not Sufficient Answer (A)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1083
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
25 Feb 2013, 04:46
VeritasPrepKarishma wrote: Archit143 wrote: Hi bunuel can you help with this question.....the book has given statement 1 is sufficient...it says that since b^2 is always positive so "a" must also be positive......but i think a can be negative also......
regards Archit Responding to a pm: A response above clarifies that this is an errata. The correct statement 1 is a = b^2 instead of a^2 = b^2. In that case If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) a = b^2 (2) a^2 = b^4 Is\(\frac{1}{a} > \frac{a}{(b^4 + 3)}\) ? Is \(\frac{(b^4 + 3)}{a} > a\) ? Is \(\frac{(b^4 + 3)}{a}  a > 0\) ? Is \(\frac{(b^4 + 3  a^2)}{a} > 0\) ? (1) a = b^2 This tells us that 'a' must be positive. Further, squaring, we get a^2 = b^4 Hence, the question becomes: Is 3/a > 0. It must be since a is positive. Sufficient (2) a^2 = b^4 Doesn't tell us anything about the sign of a. The question becomes: Is 3/a > 0? We cannot say. Not Sufficient Answer (A) Hi karishma Statement 1 is a^2 = b^2 and not a = b^2 Can you clear something that i am missing here... by the way thanks for explaining and statement is insufficient that clear.... Archit



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
25 Feb 2013, 05:05
Archit143 wrote: VeritasPrepKarishma wrote: Archit143 wrote: Hi bunuel can you help with this question.....the book has given statement 1 is sufficient...it says that since b^2 is always positive so "a" must also be positive......but i think a can be negative also......
regards Archit Responding to a pm: A response above clarifies that this is an errata. The correct statement 1 is a = b^2 instead of a^2 = b^2. In that case If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) a = b^2 (2) a^2 = b^4 Is\(\frac{1}{a} > \frac{a}{(b^4 + 3)}\) ? Is \(\frac{(b^4 + 3)}{a} > a\) ? Is \(\frac{(b^4 + 3)}{a}  a > 0\) ? Is \(\frac{(b^4 + 3  a^2)}{a} > 0\) ? (1) a = b^2 This tells us that 'a' must be positive. Further, squaring, we get a^2 = b^4 Hence, the question becomes: Is 3/a > 0. It must be since a is positive. Sufficient (2) a^2 = b^4 Doesn't tell us anything about the sign of a. The question becomes: Is 3/a > 0? We cannot say. Not Sufficient Answer (A) Hi karishma Statement 1 is a^2 = b^2 and not a = b^2 Can you clear something that i am missing here... by the way thanks for explaining and statement is insufficient that clear.... Archit It's an error in the MGMAT book. They have given it in their errata. The link of their errata is given in this post (on the previous page): ifaisnotequaltozerois1aab122266.html#p989860
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1083
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
25 Feb 2013, 05:34
Thanks Karishma for clearing the doubts...Can you pls explain what does IaI = IbI mean....in simpler terms....



Intern
Joined: 03 Sep 2012
Posts: 1

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
13 Mar 2013, 18:01
If b^4 + 3 > a^2 => a^2  b^4 < 3
Now
2. a^2 = b^4 => a^2 b^4 = 0 It tells a^2  b^4 < 3 is sufficient
Wondering what wrong assumption I am making with above.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
13 Mar 2013, 21:56
Archit143 wrote: Thanks Karishma for clearing the doubts...Can you pls explain what does IaI = IbI mean....in simpler terms.... a = b means that the distance of a from 0 is equal to the distance of b from 0. This means, if a = 5, b = 5 or 5 Similarly, if a = 5, b = 5 or 5 So, imagine the number line. There are two points at a distance of 5 from 0. a and b could lie on any one of these points.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
13 Mar 2013, 22:01
kaushalsp wrote: If b^4 + 3 > a^2 => a^2  b^4 < 3
Now
2. a^2 = b^4 => a^2 b^4 = 0 It tells a^2  b^4 < 3 is sufficient
Wondering what wrong assumption I am making with above. 'Is \(\frac{1}{a} > \frac{a}{(b^4 + 3)}\)' is NOT the same as 'Is\(b^4 + 3 > a^2\)?' Mind you, it is not given that 'a' is positive. You cannot cross multiply in an inequality if you do not know the sign of the varaible. e.g. a < b/c is not the same as ac < b If we know that c is positive, then it is ok. Then a < b/c is same as ac < b If instead, c is negative, then a < b/c is the same as ac > b (Note that the inequality sign has flipped) Hence, statement (2) is not sufficient alone. Statement (1) tells us the sign of a and we see that it is sufficient alone (check my solution above)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194

If a NOT=0, is 1/a>a/(b^4+3) ? [#permalink]
Show Tags
31 Jul 2013, 08:19
Last edited by Zarrolou on 31 Jul 2013, 08:29, edited 1 time in total.
Edited the question.



Director
Joined: 14 Dec 2012
Posts: 832
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: If a NOT=0, is 1/a>a/(b^4+3) ? [#permalink]
Show Tags
31 Jul 2013, 08:52
bagdbmba wrote: 1. If a NOT=0, is \(\frac{1}{a}>\frac{a}{b^4+3}\)
i. \(a^2=b^2\) ii. \(a^2=b^4\) IMO E LET a = 1 according to statement 1==> \(b^4=1\) now putting in equation \(\frac{1}{1}>\frac{1}{1+3}\)==>satisfies if \(a = 1 b^4 =1\) \(\frac{1}{1}>\frac{1}{1+3}\)==>doesnt satisfies. statement 2:\(a^2 = b^2\) let \(a=1 b^4 = 1\) \(\frac{1}{1}>\frac{1}{1+3}\)==>satisfies let \(a=1 b^4 = 1\) \(\frac{1}{1}>\frac{1}{1+3}\)===>doesnt satisfies. combining both \(a,b= 1 or 1\) same cases will not satisfy hence E
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: If a NOT=0, is 1/a>a/(b^4+3) ? [#permalink]
Show Tags
31 Jul 2013, 10:53
bagdbmba wrote: 1. If a NOT=0, is \(\frac{1}{a}>\frac{a}{b^4+3}\)
i. \(a^2=b^2\) ii. \(a^2=b^4\) The question asks IS \(\frac{(b^4+3)}{a}>a \to\) Multiply both sides by\(a^2 \to a(b^4+3)>a^3 \to\) Is \(a(b^4+3a^2)>0\). From F.S 1, the question becomes: Is \(a(a^4a^2+3)>0\). Note that \((a^4a^2+3)\) will always be positive as because it can be represented as sum of 2 squares : \((a^42a^2+1)+a^2+2 = (a^21)^2+(a^2+2)\) Thus, the question now simply becomes : Is a>0 We clearly don't know that. Hence, Insufficient. From F.S 2, the question becomes : Is \(a(b^4+3a^2)>0 \to a(a^2+3a^2)>0 \to\) Is \(3a>0\). Again, Insufficient. Taking both together, we know that\(b^2 = b^4 \to b^2(b^21) = 0 \to b^2=a^2 = 1 [b^2 \neq{0}\) as\(a\neq{0}]\) Thus, a could be\(\pm1\). Insufficient. E. Sidenote: The actual question is from Manhattan Gmat and they had published an errata for this question , which modifies the first fact statement to \(a = b^2\). Now, if that would have been the case,the answer would have been A. However, with the given condition, the answer is E.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Math Expert
Joined: 02 Sep 2009
Posts: 39756

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
31 Jul 2013, 10:56



BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
14 Aug 2013, 11:11
VeritasPrepKarishma wrote: Archit143 wrote: Hi bunuel can you help with this question.....the book has given statement 1 is sufficient...it says that since b^2 is always positive so "a" must also be positive......but i think a can be negative also......
regards Archit Responding to a pm: A response above clarifies that this is an errata. The correct statement 1 is a = b^2 instead of a^2 = b^2. In that case If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) a = b^2 (2) a^2 = b^4 Is\(\frac{1}{a} > \frac{a}{(b^4 + 3)}\) ? Is \(\frac{(b^4 + 3)}{a} > a\) ? Is \(\frac{(b^4 + 3)}{a}  a > 0\) ? Is \(\frac{(b^4 + 3  a^2)}{a} > 0\) ? (1) a = b^2 This tells us that 'a' must be positive. Further, squaring, we get a^2 = b^4 Hence, the question becomes: Is 3/a > 0. It must be since a is positive. Sufficient (2) a^2 = b^4 Doesn't tell us anything about the sign of a.The question becomes: Is 3/a > 0? We cannot say. Not Sufficient Answer (A) Hi Karishma, As per the above highlighted part, if \(a\) is 've' then \(a=b^2\), so \(\sqrt{a}\) will be \(\sqrt{b^2}\). Hence \(a\) becomes imaginary as \(b^2\) is always positive.So here also \(a\) must be '+ve'. But, we've considered \(a\) as 've' also! Could you please explain this? Much appreciate your feedback.
_________________
UPDATED : eGMAT SC ResourcesConsolidated  ALL RC ResourcesConsolidated  ALL SC ResourcesConsolidated  UPDATED : AWA compilations109 Analysis of Argument Essays  GMAC's IR Prep Tool
Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!
GMAT Club guide  OG 111213  Veritas Blog  Manhattan GMAT Blog
KUDOS please, if you like the post or if it helps



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7452
Location: Pune, India

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
15 Aug 2013, 23:14
bagdbmba wrote: VeritasPrepKarishma wrote: Archit143 wrote: Hi bunuel can you help with this question.....the book has given statement 1 is sufficient...it says that since b^2 is always positive so "a" must also be positive......but i think a can be negative also......
regards Archit Responding to a pm: A response above clarifies that this is an errata. The correct statement 1 is a = b^2 instead of a^2 = b^2. In that case If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) a = b^2 (2) a^2 = b^4 Is\(\frac{1}{a} > \frac{a}{(b^4 + 3)}\) ? Is \(\frac{(b^4 + 3)}{a} > a\) ? Is \(\frac{(b^4 + 3)}{a}  a > 0\) ? Is \(\frac{(b^4 + 3  a^2)}{a} > 0\) ? (1) a = b^2 This tells us that 'a' must be positive. Further, squaring, we get a^2 = b^4 Hence, the question becomes: Is 3/a > 0. It must be since a is positive. Sufficient (2) a^2 = b^4 Doesn't tell us anything about the sign of a.The question becomes: Is 3/a > 0? We cannot say. Not Sufficient Answer (A) Hi Karishma, As per the above highlighted part, if \(a\) is 've' then \(a=b^2\), so \(\sqrt{a}\) will be \(\sqrt{b^2}\). Hence \(a\) becomes imaginary as \(b^2\) is always positive.So here also \(a\) must be '+ve'. But, we've considered \(a\) as 've' also! Could you please explain this? Much appreciate your feedback. \(a^2 = b^4\) When you take the square root of both sides here, you get \(a = b^2 = b^2\) You do not get a = b^2. Note that when you take square root of \(x^2 = y^2\), you get x = y, not x = y So a can still be negative. Say a = 9, b = 3 In this case, \(a^2 = b^4 = (9)^2 = 3^4\)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



BSchool Forum Moderator
Joined: 27 Aug 2012
Posts: 1194

Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1) [#permalink]
Show Tags
09 Sep 2013, 04:27




Re: If a is not equal to zero, is 1/a > a / (b^4 + 3) ? (1)
[#permalink]
09 Sep 2013, 04:27



Go to page
Previous
1 2
[ 34 posts ]




