Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 May 2010
Posts: 37

What is the value of ab^2 ?
[#permalink]
Show Tags
09 Jun 2010, 06:22
Question Stats:
61% (01:29) correct 39% (01:24) wrong based on 462 sessions
HideShow timer Statistics
What is the value of ab^2? (1) a = b  1 (2) a = b^2  1
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
09 Jun 2010, 06:44
BigBrad wrote: The following question is located in the Equations, Inequalities & VICs Manhattan Guide book on page 135. I just need some clarification on the last part of their working out of the answer. I'll post this below in a spoiler section, so please click to find where I am a bit stuck. What is the value of \(ab^2\)? (1) \(a=b1\) (2) \(a=b^21\) Answer is C. MGMAT provides the following working out: "if we combine statements (1) and (2), we find that a and b can still have 2 different values. \(b1=b^21\) \(b=b^2\) \(0=b^2b\) \(0=b(b1)\) b= 0 or 1 a= 1 or 0 So \(b=0\) when \(a=1\), and \(b=1\) when \(a=0\). However, in either case \(ab^2=0\). Therefore statements (1) and (2) combined are sufficient. Please explain how b can equal 0 or 1?Could I deduce b=1 using this equation from above: \(0=b(b1)\). Take out the b on the outside of the brackets and solve the remaining \(0=(b1)\) equation, therefore \(b=1\)? Likewise, how do I deduce that b=0 also? Is it from this equation \(0=b^2b\)? What I seem to find difficult is how would you know that b has two answers. THANKS IN ADVANCE! What is the value of \(ab^2\)? (1) \(a=b1\). Clearly insufficient. (2) \(a=b^21\). Clearly insufficient. (1)+(2) \(b1=b^21\) > \(b^2=b\) > \(b^2b=0\) > \(b(b1)=0\). For the product of two numbers (\(b\) and \(b1\)) to be zero one of them (or both) must be zero. So either: \(b=0\) > \(a=b1=1\) > \(ab^2=0\); or \(b1=0\), \(b=1\) > \(a=b1=0\) > \(ab^2=0\). The same answer for both cases. Sufficient. Answer: C. Hope it helps.
_________________




Intern
Joined: 05 May 2010
Posts: 37

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
09 Jun 2010, 13:12
Thanks for the quick reply Bunuel, kudos for the explanation.
What I am slightly concerned about is that if a similar question appears on the GMAT, I may fail to spot the fact that b can have two answers. If \(b^2b=0\) then surely b must equal 0. Why do we then go and factorise to produce a new expression: \(b(b1)=0\)? And when solving for b using this latter expression, why do we drop the first b and do \(b1=0\) therefore \(b=1\) instead of \(b(b1)=0\) and solve?
Sorry if this sounds convoluted but I'm probably overlooking a rule somewhere, which essentially needs clarification.



Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
09 Jun 2010, 13:45
BigBrad wrote: Thanks for the quick reply Bunuel, kudos for the explanation.
What I am slightly concerned about is that if a similar question appears on the GMAT, I may fail to spot the fact that b can have two answers. If \(b^2b=0\) then surely b must equal 0. Why do we then go and factorise to produce a new expression: \(b(b1)=0\)? And when solving for b using this latter expression, why do we drop the first b and do \(b1=0\) therefore \(b=1\) instead of \(b(b1)=0\) and solve?
Sorry if this sounds convoluted but I'm probably overlooking a rule somewhere, which essentially needs clarification. First of all \(b^2b=0\) is a quadratic equation and it can have 2 solutions. Next: \(b^2b=0\) means that either \(b=0\) (0^20=0) or \(b=1\) (1^21=0) (so it's not necessary \(b\) to be zero). We did not drop \(b=0\) we just found the second solution \(b=1\). You might need to revise basics of algebra. Hope it helps.
_________________



Intern
Joined: 05 May 2010
Posts: 37

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
10 Jun 2010, 10:42
Ah got it now , silly mistake really. As it's been so long since I've touched algebra that I thought all quadratics looked like \(Ax^2+ Bx  C= 0\) so the \(b(b1)=0\) threw me a little. I realize now that \(b(b1)=0\) is the same as saying \((b) . (b1)=0\) which follows the concept of what a quadratic looks like after its been factorised ie \((x+1) . (x1)=0\). Thus, we can solve the two values for b by taking each expression individually (b & (b1)) and equating them each to zero. Thanks for your help Bunuel, very kind!



Manager
Joined: 17 Mar 2010
Posts: 130

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
12 Jun 2010, 23:50
Bunuel, Please can you explain my confusion? If I place the equation as b1 = b^21 and solve it by thinking b1 = (b1) (b+1) ==> b = 1..... which is only one solution... is this method wrong?? or it is ok? Please kindly tell me if i am making some mistake.



Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
13 Jun 2010, 04:55
amitjash wrote: Bunuel, Please can you explain my confusion? If I place the equation as b1 = b^21 and solve it by thinking b1 = (b1) (b+1) ==> b = 1..... which is only one solution... is this method wrong?? or it is ok? Please kindly tell me if i am making some mistake. First of all the roots of the equation \(b1 = b^21\) are \(b=0\) and \(b=1\) (see the solution in my post), if you got these roots you solved the equation correctly and if you got different roots you solved incorrectly. Next, I don't understand why aren't you cancelling (1) from \(b1=b^21\) > \(b=b^2\). But anyway if you don't and we proceed the way you are doing: \(b1=b^21\) > \(b1=(b1)(b+1)\). Now how is \(b=1\) the root of this equation? \(b1=2\neq{(b1)(b+1)}=0\).
_________________



Manager
Joined: 17 Mar 2010
Posts: 130

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
13 Jun 2010, 07:29
Sorry, it was an error from my side. I mean to say if I arrive with only one solution ==> b=0, accroding to the method i mentioned. Then why it is considered wrong? b1 = b^2  1 b1 = (b1) (b+1) 1 = b+1 ==> b=0
Why I am not cancelling 1 on each side? I dont know... That is the first thought when i looked at the equation. I want to make a note in my mind why it is wrong so that i dont make these mistakes on the test day. Thanks for your ever woderful support.



Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: Data sufficiency question on equations from MGMAT
[#permalink]
Show Tags
13 Jun 2010, 07:43
amitjash wrote: Sorry, it was an error from my side. I mean to say if I arrive with only one solution ==> b=0, accroding to the method i mentioned. Then why it is considered wrong? b1 = b^2  1 b1 = (b1) (b+1) 1 = b+1 ==> b=0
Why I am not cancelling 1 on each side? I dont know... That is the first thought when i looked at the equation. I want to make a note in my mind why it is wrong so that i dont make these mistakes on the test day. Thanks for your ever woderful support. I see. When you write \(1 = b+1\) after \(b1 = (b1) (b+1)\) what you are actually doing is reducing (dividing) the equation by \(b1\) but we can not do that as it can equal to zero. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.So basically when you divide by \(b1\) you assume that it doesn't equal to zero, thus missing the second valid solution for \(b1 = (b1) (b+1)\) which is \(b1=0\) > \(b=1\). Again if we proceed the way you are doing \(b1 = (b1) (b+1)\) > \((b1)(b1) (b+1)=0\) > factor out \(b1\) > \((b1)(1b1)=0\) > \((b1)b=0\) (the type of equation you'd receive right away if you'd cancel out \(1\)) > \(b=0\) or \(b=1\). Hope it's clear.
_________________



Intern
Joined: 26 Mar 2010
Posts: 11

Re: Ineqaulity question
[#permalink]
Show Tags
06 Jul 2010, 23:22
Jinglander wrote: Can some one talk me through the logic on this one. What is the value of AB^2
a=b1 a=b^21 Here, we are asked to find the value of ab^2. 1. a = b1. Clearly insufficient coz with this info it is impossible to find the value of ab^2. 2. a = b^21. Clearly insufficient due to reason stated above. With equations 1 and 2, we could equate the value for a b1 = b^21 b^2 = b b^2  b = 0 (cannot divide by b on both sides since we don't know the value of b which could be 0) b(b1) = 0 Thus, b = 0 , or b = 1 If b = 0 , a = b1 = 0 1 = 1 and ab^2 = 0 If b = 1, a = b1 = 1  0 = 0 and ab^2 = 0 Thus with 1 and 2 we get ab^2 as 0. Hence C hope it helps, meshtrap



Kaplan GMAT Instructor
Joined: 21 Jun 2010
Posts: 67
Location: Toronto

Re: Ineqaulity question
[#permalink]
Show Tags
07 Jul 2010, 20:19
Hi Jinglander,
individually, the statements are insufficient, as meshtrap points out.
Notice that (2) gives us a difference of squares (commonly tested pattern on the GMAT):
a = b^2  1
can be rewritten as:
a = (b1)*(b+1)
We know from (1) that a = b  1. Thus, b + 1 must be equal to 1. Thus, we can compute b's value. Thus, we can compute a's value. Thus, we can compute a*b^2.
Choose C.



Manager
Joined: 18 Oct 2013
Posts: 68
Location: India
Concentration: Technology, Finance
Schools: Duke '16, Johnson '16, Kelley '16, Tepper '16, Marshall '16, McDonough '16, Insead '14, HKUST '16, HSG '15, Schulich '15, Erasmus '16, IE April'15, Neeley '15
GMAT 1: 580 Q48 V21 GMAT 2: 530 Q49 V13 GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)

Re: what is the value of ab?
[#permalink]
Show Tags
20 Nov 2013, 12:06
1)Doesn't give anything about a and b.So not sufficient.Eliminate A and D 2)Doesn't give anything about a and b.So not sufficient. Eliminate B 1+2) (b1)=b^21 (b1)=(b1)(b+1) 1=b+1 b=0 So answer is C



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 591

Re: what is the value of ab?
[#permalink]
Show Tags
20 Nov 2013, 12:12
vikrantgulia wrote: 1)Doesn't give anything about a and b.So not sufficient.Eliminate A and D 2)Doesn't give anything about a and b.So not sufficient. Eliminate B 1+2) (b1)=b^21 (b1)=(b1)(b+1) 1=b+1 b=0 So answer is C Just a caveat:Note the part that is highlighted, You can't cancel out (b1) on both the sides, as you don't know whether b=1 or not. Thus, either b=1 or b=0. In either case, you get ab=0.
_________________



Intern
Joined: 17 Oct 2013
Posts: 49

Re: what is the value of ab?
[#permalink]
Show Tags
20 Nov 2013, 13:36
mau5 wrote: vikrantgulia wrote: 1)Doesn't give anything about a and b.So not sufficient.Eliminate A and D 2)Doesn't give anything about a and b.So not sufficient. Eliminate B 1+2) (b1)=b^21 (b1)=(b1)(b+1) 1=b+1 b=0 So answer is C Just a caveat:Note the part that is highlighted, You can't cancel out (b1) on both the sides, as you don't know whether b=1 or not. Thus, either b=1 or b=0. In either case, you get ab=0. Answer is C. Just to add for St 2 we have a = (b1)(b+1) => a=a(b+1) { from St 1 we have a=b1} a= a(b+1) 1=b+1 => b=0, so ab is 0, sufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: What is the value of ab?
[#permalink]
Show Tags
21 Nov 2013, 03:10
vikrantgulia wrote: What is the value of ab?
(1) a = b  1 (2) a = b^2  1 Merging similar topics. Please refer to the solutions above. Quote: What is the value of ab?
(1) a = b + 1 (2) a^2 = b + 1 Discussed here: whatisthevalueofab143841.html
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58335

Re: what is the value of ab?
[#permalink]
Show Tags
21 Nov 2013, 03:11
viksingh15 wrote: mau5 wrote: vikrantgulia wrote: 1)Doesn't give anything about a and b.So not sufficient.Eliminate A and D 2)Doesn't give anything about a and b.So not sufficient. Eliminate B 1+2) (b1)=b^21 (b1)=(b1)(b+1) 1=b+1 b=0 So answer is C Just a caveat:Note the part that is highlighted, You can't cancel out (b1) on both the sides, as you don't know whether b=1 or not. Thus, either b=1 or b=0. In either case, you get ab=0. Answer is C. Just to add for St 2 we have a = (b1)(b+1) => a=a(b+1) { from St 1 we have a=b1} a= a(b+1) 1=b+1 => b=0, so ab is 0, sufficient. You cannot reduce a=a(b+1) by a and write 1=b+1 because you exclude a possible solution a=0. Check here for more: whatisthevalueofab95543.html#p737359Hope this helps.
_________________



Director
Joined: 12 Nov 2016
Posts: 701
Location: United States
GPA: 2.66

Re: What is the value of ab^2 ?
[#permalink]
Show Tags
08 Sep 2017, 22:32
BigBrad wrote: What is the value of ab^2?
(1) a = b  1 (2) a = b^2  1 So actually this is a slightly tricky question St 1 two variables not enough info insuff St 2 two variables not enough info insuff St 1 & 2 b^21= b1= b^2= b b=, 0, 1 But since the question is what is the product of A(B)^2 In either scenario you would inevitably multiply by 0  if 1 then A becomes 0 or if A is 1 then B is 0 C



NonHuman User
Joined: 09 Sep 2013
Posts: 13077

Re: What is the value of ab^2 ?
[#permalink]
Show Tags
31 Oct 2018, 15:07
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: What is the value of ab^2 ?
[#permalink]
31 Oct 2018, 15:07






