Author 
Message 
TAGS:

Hide Tags

Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 91
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
08 Dec 2010, 08:39
6
This post received KUDOS
39
This post was BOOKMARKED
Question Stats:
27% (02:27) correct 73% (02:03) wrong based on 1871 sessions
HideShow timer Statistics
For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a? (1) a^2  a = 12 (2) b^2  b = 2
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 43804

For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
08 Dec 2010, 08:57
11
This post received KUDOS
Expert's post
18
This post was BOOKMARKED
aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
(1) a^2  a = 12
(2) b^2  b = 2 Given: \(a\) and \(b\) are integers, also \(\sqrt{a^3a^2b}=7\) > \(a^3a^2b=49\) (1) a^2  a = 12 > \(a=3\) or \(a=4\). Now, both values of \(a\) give an integer solution for \(b\) (\(b=85\) or \(b=1\)), so both values are valid. Not sufficient. (2) b^2  b = 2 > \(b=1\) or \(b=2\) > if \(b=1\) then \(a^3a^2=48\) > \(a^2(a1)=48\) > \(a=4=integer\) BUT if if \(b=2\) then \(a^3a^2=51\) > \(a^2(a1)=51=3*17\) > this equation has no integer solution for \(a\), hence only the first case is valid: \(b=1\) and \(a=4=integer\). Sufficient. Answer: B.
_________________
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



Manager
Status: Preparing Apps
Joined: 04 Mar 2009
Posts: 91
Concentration: Marketing, Strategy
GMAT 1: 650 Q48 V31 GMAT 2: 710 Q49 V38
WE: Information Technology (Consulting)

Re: DS question [#permalink]
Show Tags
08 Dec 2010, 09:13
can you elaborate on how you solved \(a^2(a1) = 48\) to \(a = 4\)?
Similarly how did you conclude that \(a^2(a1) = 51\) will not have an interger as a solution?



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: DS question [#permalink]
Show Tags
08 Dec 2010, 09:31
6
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
03 Jul 2013, 00:18



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
03 Jul 2013, 01:15
3
This post received KUDOS
aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
(1) a^2  a = 12
(2) b^2  b = 2 Given in the question stem that \((a^3a^2b) = 49\)\(\to a^2(a1) = 49+b\) From F.S 1, we know that a(a1) = 12, thus, \(a*12 = 49+b \to\) a is an integer for both b = 1 or b = 13. Thus, we get two different values of a, Insufficient. From F. S 2, we know upon solving for the quadratic \(b^2b2\), the integral roots are 1 or 2. Now,\(a^2(a1) = 49+b\) For b = 2, \(a^2(a1) = 51\). Assuming that a is odd/even, the given product is an arrangement like odd*odd*even = even, and 51 is not even. Similarly, for a is even, the arrangement will be like even*even*odd = even, and just as above 51 is not even. Thus, \(b\neq{2}\) For b = 1,\(a^2(a1)\) = 48. Now all the integral roots of this polynomial can only be factors of 48, including both negative and positive factors. However, any negative factor will never satisfy the given polynomial as because (a1) will become a negative expression, which can never equal 48.Hence, the given polynomial has no integral solutions in 48,24,12,8,6,4,3,2,1. By the same logic, we know that any integral solution,if present will be one of the positive factors of 48.It fails for 1,2,3 and we find that a=4 is a root.If for a=4, the expression equals 48, then for a value above 4, the expression \(a^2(a1)\)is bound to be greater than 48. Thus, the only solution possible for the given polynomial is a=4, a unique value,Sufficient. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Director
Joined: 25 Apr 2012
Posts: 721
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
03 Jul 2013, 08:54
1
This post received KUDOS
aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
(1) a^2  a = 12
(2) b^2  b = 2 Tough one...Took more than 3 min 50 sec and ended up getting it wrong... We can change the given equation to (a^3a^2b) = 49 (squaring both sides) From St 1 we have a^2a=12 > substituting in above given eqn we get {a(a^2a) b} =49 > 12ab=49 > a = (49+b)/12 Now a and b are integers therefore (49+b)/12 should be an integers Possible values b=11, a=5 b=23, a =6, b=1, a=4So St 1 alone is not sufficient St 2 says b^2b =2 > b(b1) =2 possible values of b are b=2 or b=1 Substituting in given expression we get (a^3a^2b) = 49 a^3a^2= 51 or> a^2(a1)= 51 (17*3) we see that 51 even after reducing to prime factors gives us no Integer value of a a^3a^2= 48 > a^2(a1)= 48 (4^2)*3 and hence we get value of a= 4 or 4 Substituting values of b=1 and a=4 or 4, we can see that only for a=4 the above given equation is proven. Hence a =4 I did highlight the value of b=1, a=4 from statement and can be taken as a hint without solving completely eqn 2 Ans B
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 625

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
03 Jul 2013, 09:00
mridulparashar1 wrote: aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
a^3a^2= 48 > a^2(a1)= 48 (4^2)*3 and hence we get value of a= 4 or 4
Substituting values of b=1 and a=4 or 4, we can see that only for a=4 the above given equation is proven.
Hence a =4
I did highlight the value of b=1, a=4 from statement and can be taken as a hint without solving completely eqn 2 Ans B Minor mistake. The given polynomial will not yield a = 4 as a root.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 26 Sep 2013
Posts: 216
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
10 Nov 2013, 08:31
Bunuel wrote: aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
(1) a^2  a = 12
(2) b^2  b = 2 Given: \(a\) and \(b\) are integers, also \(\sqrt{a^3a^2b}=7\) > \(a^3a^2b=49\) (1) a^2  a = 12 > \(a=3\) or \(a=4\). Now, both values of \(a\) give an integer solution for \(b\) (\(b=85\) or \(b=1\)), so both values are valid. Not sufficient. (2) b^2  b = 2 > \(b=1\) or \(b=2\) > if \(b=1\) then \(a^3a^2=48\) > \(a^2(a1)=48\) > \(a=4=integer\) BUT if if \(b=2\) then \(a^3a^2=51\) > \(a^2(a1)=51=3*17\) > this equation has no integer solution for \(a\), hence only the first case is valid: \(b=1\) and \(a=4=integer\). Sufficient. Answer: B. if \(b=1\) then \(a^3a^2=48\) > \(a^2(a1)=48\) > \(a=4=integer\) how do you solve something like that, is it just quick trial & error since you know a & b have to be integers and there's only a few values of a that would give results somewhat near 48?



Math Expert
Joined: 02 Sep 2009
Posts: 43804

For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
10 Nov 2013, 11:10
AccipiterQ wrote: Bunuel wrote: aalriy wrote: For integers a and b, if (a^3 – a^2 – b)^1/2 = 7, what is the value of a?
(1) a^2  a = 12
(2) b^2  b = 2 Given: \(a\) and \(b\) are integers, also \(\sqrt{a^3a^2b}=7\) > \(a^3a^2b=49\) (1) a^2  a = 12 > \(a=3\) or \(a=4\). Now, both values of \(a\) give an integer solution for \(b\) (\(b=85\) or \(b=1\)), so both values are valid. Not sufficient. (2) b^2  b = 2 > \(b=1\) or \(b=2\) > if \(b=1\) then \(a^3a^2=48\) > \(a^2(a1)=48\) > \(a=4=integer\) BUT if if \(b=2\) then \(a^3a^2=51\) > \(a^2(a1)=51=3*17\) > this equation has no integer solution for \(a\), hence only the first case is valid: \(b=1\) and \(a=4=integer\). Sufficient. Answer: B. if \(b=1\) then \(a^3a^2=48\) > \(a^2(a1)=48\) > \(a=4=integer\) how do you solve something like that, is it just quick trial & error since you know a & b have to be integers and there's only a few values of a that would give results somewhat near 48? Yes, that's correct. We know that \(a\) is an integer, thus \(a^2(a1)=(perfect \ square)*(positive \ integer)=48\). From here you can use trial and error and find that \(a=4\).
_________________
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



Manager
Joined: 05 Jun 2014
Posts: 69

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
08 Sep 2014, 00:03
I have just one question, why isnt the absolute value used after the expression is squared?



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
08 Sep 2014, 03:10



NonHuman User
Joined: 09 Sep 2013
Posts: 13832

Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the [#permalink]
Show Tags
22 Oct 2017, 04:10
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: For integers a and b, if (a^3 a^2 b)^1/2 = 7, what is the
[#permalink]
22 Oct 2017, 04:10






