Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 27 Sep 2010
Posts: 27

If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 Jan 2011, 01:11
1
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
37% (01:26) correct 63% (01:34) wrong based on 185 sessions
HideShow timer Statistics
If \(a^2*b^2*c^3 = 4500\). Is \(b+c = 7\) ? (1) a, b and c are positive integers (2) a > b
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 31 Aug 2009
Posts: 26

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 Jan 2011, 01:34
1
This post received KUDOS
Hi, The answer to this question should be C. 4500=2^2*3^2*5^3
This will yield C=5. Now possible values of 'a' are 2,2,3,3 and possible values of b are 3,3,2,2
Statement 1 tells a,b,c are positive integers. Hence possible values of 'b' reduces to 2,3. Not sufficient to answer the value of b+c. Statement 2 tells a>b. Hence possible values of b are 3, when a=2 and 2,2 when a=3. Hence not sufficient. Now statement 1 and 2 together will yield 'b' as 2 Hence sufficient.Hope this helps . Thank You.



Intern
Joined: 27 Sep 2010
Posts: 27

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 Jan 2011, 01:53
sashikanth wrote: Hi, The answer to this question should be C. 4500=2^2*3^2*5^3
This will yield C=5. Now possible values of 'a' are 2,2,3,3 and possible values of b are 3,3,2,2
Statement 1 tells a,b,c are positive integers. Hence possible values of 'b' reduces to 2,3. Not sufficient to answer the value of b+c. Statement 2 tells a>b. Hence possible values of b are 3, when a=2 and 2,2 when a=3. Hence not sufficient. Now statement 1 and 2 together will yield 'b' as 2 Hence sufficient.Hope this helps . Thank You. hey... thanks this is what i answered... but the correct answer is E... i need an explanation....... if it is E, then y so....



Intern
Joined: 13 Oct 2010
Posts: 21
Location: Milpitas, CA

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 Jan 2011, 02:12
4
This post received KUDOS
MichelleSavina wrote: If a^2.b^2.c^3 = 4500. Is b+c = 7 ? (1) a, b and c are positive integers (2) a > b 4500 = (2²)(3²)(5³) = (a²)(b²)(c³) Comparing the terms we see that, c = 5 But a and b can have different sets of values. 1. a = ±2, b = ±3 2. a = ±3, b = ±2 3. a = ±1, b = ±6 4. a = ±6, b = ±1 Statement 1: a, b and c are positive integers Hence, we should discard the negative values of a and b. Still we have four possible sets of values for a and b, 1. a = 2, b = 3 2. a = 3, b = 2 3. a = 1, b = 6 4. a = 6, b = 1 Thus (b + c) can have different possible values. Not sufficient Statement 1: a > b Hence, we should discard the values of a and b such that a < b. Still we have different sets of values for a and b, 1. a = ±2, b = 3 2. a = 3, b = ±2 3. a = ±1, b = 6 4. a = 6, b = ±1 Thus (b + c) can have different possible values. Not sufficient 1 & 2 Together : Still we can have two different sets of values for a and b, 1. a = 3, b = 2 2. a = 6, b = 1 Thus (b + c) can be equal to either 6 or 7. Not sufficient
_________________
Anurag Mairal, Ph.D., MBA GMAT Expert, Admissions and Career Guidance Gurome, Inc. 18005664043 (USA) +9199201 32411 (India) http://www.facebook.com/Gurome



Math Expert
Joined: 02 Sep 2009
Posts: 44351

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 Jan 2011, 03:50
6
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
MichelleSavina wrote: Q) If a^2.b^2.c^3 = 4500. Is b+c = 7 ? (1) a, b and c are positive integers (2) a > b
please explain... Given: \(a^2*b^2*c^3 = 4500=2^2*3^2*5^3\). Question: is \(b+c=7\) (1) a, b and c are positive integers > sure it's possible that \(a=3\), \(b=2\) and \(c=5\) and in this case the answer will be YES but it's also possible that \(a=2\), \(b=3\) and \(c=5\) and in this case the answer will be NO. Not sufficient. (2) a > b. Clearly insufficient. (1)+(2) Note that we are not told that a, b and c are prime numbers, so again it's possible that \(a=3>2=b\) and \(c=5\) and in this case the answer will be YES but for example it's also possible that \(a=2^2*3^2=6^2\), \(b=1\) and \(c=5\) (\(a^2*b^2*c^3 =6^2*1^2*5^3=4500\)) and in this case the answer will be NO. Not sufficient. Answer: E.
_________________
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



Intern
Joined: 04 Mar 2012
Posts: 48

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
19 May 2012, 09:01
If a^2b^2c^3 = 4500. Is b+c = 7 ? (1) a, b and c are positive integers (2) a > b
2^23^25^3 = 4500 and from statement 1 and 2, it can be deduced that b=2, c=5 and b+c =7, why the answer is E, shouldn't it be C?



Senior Manager
Joined: 30 Aug 2009
Posts: 279
Location: India
Concentration: General Management

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
19 May 2012, 16:42
gmihir wrote: If a^2b^2c^3 = 4500. Is b+c = 7 ? (1) a, b and c are positive integers (2) a > b
2^23^25^3 = 4500 and from statement 1 and 2, it can be deduced that b=2, c=5 and b+c =7, why the answer is E, shouldn't it be C? a,b and c don't have to be prime. a=6 and b=1 will also satisfy the 2 statements alone and b+c=1+5 = 6. insuff together. hence E



Manager
Joined: 16 May 2011
Posts: 70

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
20 May 2012, 10:32
Good question....But is GMAC really expecting us to figure that out in a span of 2 min???



Senior Manager
Joined: 30 Aug 2009
Posts: 279
Location: India
Concentration: General Management

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
20 May 2012, 11:48
dchow23 wrote: Good question....But is GMAC really expecting us to figure that out in a span of 2 min??? yes...such questions may very well appear in the actual GMAT



Intern
Joined: 28 Feb 2012
Posts: 25

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 May 2012, 09:00
Seriouslly very good question. Even after looking at the anwer I was not able to figure out how this can be possible. I thought about this and realised how our mind works in one direction. As it has been so well trained to do the prime factors as soon as you see any problem like this. It can not think any other situation.
Thanks for posting such question which can break the mindset.



Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 218

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
22 May 2012, 09:41
MichelleSavina wrote: If a^2*b^2*c^3 = 4500. Is b+c = 7 ?
(1) a, b and c are positive integers (2) a > b fantastic problem, but i got stumped.. i selected C as the answer and now i understand why the answer is E
_________________
Regards, Harsha
Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat
Satyameva Jayate  Truth alone triumphs



Manager
Joined: 04 Jan 2014
Posts: 120
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
11 Feb 2014, 00:19
Great question! Fell in to the trap and picked C. E makes perfect sense.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11292
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]
Show Tags
23 Nov 2017, 15:56
Hi All, We're told that (A^2)(B^2)(C^3) = 4500. We're asked if B+C = 7. This is a YES/NO question. This question really tests the 'thoroughness' of your thinking  and it's likely that many Test Takers would get this question wrong because they wouldn't consider all of the possible options. To start, it would help to 'break down' 4500 into pieces... 4500 = (9)(500) = (3^2)(5)(100) = (3^2)(5)(2^2)(5^2) = (2^2)(3^2)(5^3) Based on the starting equation, we know that C MUST be +5. However, there are more than just these two possible values for A and B. Since we're SQUARING terms, A and B could be (2 or 2) and (3 or 3). In addition, this question is NOT forcing us to deal with Prime Numbers, so there is another option besides "2 and 3" to consider.... "1 and 6" is another possible pairing of values for A and B.... (1^2)(6^2)(5^3) ...meaning that we would have to also consider that the values could be (1 or 1) and (6 or 6): (1) A, B and C are POSITIVE integers IF.... A=2, B=3, C=5 then the answer to the question is NO A=3, B=2, C=5 then the answer to the question is YES Fact 1 is INSUFFICIENT 2) A > B A=3, B=2, C=5 then the answer to the question is YES A=6, B=1, C=5 then the answer to the question is NO Fact 2 is INSUFFICIENT Combined, we already have two groups of values that fit both Facts and produce different answers to the given question: A=3, B=2, C=5 then the answer to the question is YES A=6, B=1, C=5 then the answer to the question is NO Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************




Re: If a^2b^2c^3 = 4500. Is b + c = 7?
[#permalink]
23 Nov 2017, 15:56






