It is currently 13 Dec 2017, 20:40

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper 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, b, and c are positive numbers, is a < b < c?

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 81

Kudos [?]: 389 [1], given: 37

If a, b, and c are positive numbers, is a < b < c? [#permalink]

Show Tags

New post 13 Apr 2012, 21:21
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

66% (00:46) correct 34% (00:55) wrong based on 107 sessions

HideShow timer Statistics

If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc
(2) ac = bc
[Reveal] Spoiler: OA

Kudos [?]: 389 [1], given: 37

Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2012
Posts: 351

Kudos [?]: 209 [0], given: 31

Concentration: Operations, Strategy
Re: Arithmetic [#permalink]

Show Tags

New post 13 Apr 2012, 23:14
Smita04 wrote:
If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc
(2) ac = bc


statement 1:

b(a-c)=0
i.e. either b=0 or a=c

given b>0
hence a=c

=> a IS NOT LESS THAN c.
sufficient

statement 2:

similarly by above reasoning a=b
so NO
hence SUfficient

hence D

HOPE THIS HELPS...!!
_________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS
If there's a loophole in my analysis--> suggest measures to make it airtight.

Kudos [?]: 209 [0], given: 31

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

Re: Arithmetic [#permalink]

Show Tags

New post 14 Apr 2012, 00:45
If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc --> since b>0 we can reduce given equation by b and we'll get a = c, so a < b < c is not true. Sufficient.
(2) ac = bc --> since c>0 we can reduce given equation by c and we'll get a = b, so a < b < c is not true. Sufficient.

Answer: D.
_________________

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 [?]: 135562 [0], given: 12699

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4467

Kudos [?]: 3146 [0], given: 0

GPA: 3.82
Premium Member
Re: If a, b, and c are positive numbers, is a < b < c? [#permalink]

Show Tags

New post 26 Nov 2017, 10:25
Smita04 wrote:
If a, b, and c are positive numbers, is a < b < c?

(1) ab = bc
(2) ac = bc


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables and 0 equation, we need to consider both conditions together first.

Condition 1) & 2)
Since b is positive, ab = bc ⇔ a = c.
Since c is positive, ac = bc ⇔ a = b.
Thus the answer to a < b < c is no.
They are sufficient by CMT (Common Mistake Type) 1, since the answer is no.

In addition, since this is an inequality question (one of the key question areas), we should also consider choices A and B by CMT 4(A).

Condition 1)
Since b is positive, ab = bc ⇔ a = c.
Thus the answer to a < b < c is no.
This is sufficient by CMT1.

Condition 2)
Since c is positive, ac = bc ⇔ a = b.
This is sufficient by CMT1.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3146 [0], given: 0

Re: If a, b, and c are positive numbers, is a < b < c?   [#permalink] 26 Nov 2017, 10:25
Display posts from previous: Sort by

If a, b, and c are positive numbers, is a < b < c?

  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®.