It is currently 15 Dec 2017, 02:27

Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1 | UCLA R1


Close

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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If a^2b^2c^3 = 4500. Is b + c = 7?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Intern
Intern
User avatar
Joined: 27 Sep 2010
Posts: 27

Kudos [?]: 94 [2], given: 3

If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 Jan 2011, 00:11
2
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

37% (01:29) correct 63% (01:33) wrong based on 173 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
[Reveal] Spoiler: OA

Kudos [?]: 94 [2], given: 3

1 KUDOS received
Intern
Intern
avatar
Joined: 31 Aug 2009
Posts: 27

Kudos [?]: 30 [1], given: 45

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 Jan 2011, 00:34
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.

Kudos [?]: 30 [1], given: 45

Intern
Intern
User avatar
Joined: 27 Sep 2010
Posts: 27

Kudos [?]: 94 [0], given: 3

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 Jan 2011, 00:53
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....

Kudos [?]: 94 [0], given: 3

4 KUDOS received
Intern
Intern
User avatar
Joined: 13 Oct 2010
Posts: 21

Kudos [?]: 10 [4], given: 0

Location: Milpitas, CA
Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 Jan 2011, 01:12
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

[Reveal] Spoiler:
The correct answer is E.

_________________

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
+91-99201 32411 (India)
http://www.facebook.com/Gurome

Kudos [?]: 10 [4], given: 0

Expert Post
6 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42620

Kudos [?]: 135696 [6], given: 12706

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 Jan 2011, 02:50
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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135696 [6], given: 12706

Manager
Manager
avatar
Joined: 04 Mar 2012
Posts: 50

Kudos [?]: 298 [0], given: 10

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 19 May 2012, 08:01
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?

Kudos [?]: 298 [0], given: 10

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 281

Kudos [?]: 194 [0], given: 5

Location: India
Concentration: General Management
Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 19 May 2012, 15:42
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

Kudos [?]: 194 [0], given: 5

Manager
Manager
avatar
Joined: 16 May 2011
Posts: 71

Kudos [?]: 18 [0], given: 2

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 20 May 2012, 09:32
Good question....But is GMAC really expecting us to figure that out in a span of 2 min???

Kudos [?]: 18 [0], given: 2

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 281

Kudos [?]: 194 [0], given: 5

Location: India
Concentration: General Management
Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 20 May 2012, 10:48
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

Kudos [?]: 194 [0], given: 5

Intern
Intern
avatar
Joined: 28 Feb 2012
Posts: 25

Kudos [?]: 52 [0], given: 1

Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 May 2012, 08:00
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.

Kudos [?]: 52 [0], given: 1

Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 222

Kudos [?]: 65 [0], given: 16

Schools: Johnson '15
Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 22 May 2012, 08:41
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

Kudos [?]: 65 [0], given: 16

Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 120

Kudos [?]: 41 [0], given: 15

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

New post 10 Feb 2014, 23:19
Great question! Fell in to the trap and picked C. E makes perfect sense.

Kudos [?]: 41 [0], given: 15

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10401

Kudos [?]: 3693 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If a^2b^2c^3 = 4500. Is b + c = 7? [#permalink]

Show Tags

New post 23 Nov 2017, 14:56
1
This post received
KUDOS
Expert's post
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:
[Reveal] Spoiler:
E


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

Co-Founder & 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!***********************

Kudos [?]: 3693 [1], given: 173

Re: If a^2b^2c^3 = 4500. Is b + c = 7?   [#permalink] 23 Nov 2017, 14:56
Display posts from previous: Sort by

If a^2b^2c^3 = 4500. Is b + c = 7?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.