GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Dec 2018, 11:44

### 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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Happy Christmas 20% Sale! Math Revolution All-In-One Products!

December 20, 2018

December 20, 2018

10:00 PM PST

11:00 PM PST

This is the most inexpensive and attractive price in the market. Get the course now!
• ### Key Strategies to Master GMAT SC

December 22, 2018

December 22, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# For real numbers a, b, and c, is ab = bc + 3?

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51280
For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

23 Aug 2016, 08:10
2
1
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:33) correct 43% (02:56) wrong based on 146 sessions

### HideShow timer Statistics

For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b
(2) b + 3 = c

_________________
Intern
Joined: 18 Aug 2013
Posts: 12
Re: For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

23 Aug 2016, 09:47
1
(1) ab = 3b => It gives no information about 'c' --> Insufficient

(2) b + 3 = c => It gives no information about 'a' --> Insufficient

Both (1) and (2) together .. Lets substitute these two conditions (1) and (2) in the main eqn (to be proved)

ab = b.(b+3) + 3 = b^2 + 3b + 3

3b = b^2 + 3b + 3 => b^2 = -3 --> For this eqn to be equal, 'b' should be imaginary.

But, we are given that a, b and c are real numbers => These numbers cannot be imaginary ..

Hence, b^ 2 = -3 CANNOT be true for any values of a,b and c.. Option (C)
Senior Manager
Joined: 23 Apr 2015
Posts: 303
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

23 Aug 2016, 09:55
2
Bunuel wrote:
For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b
(2) b + 3 = c

Consider 1) $$ab = 3b$$
there are 2 possibilities, $$b = 0$$ or $$b\neq{0}$$ which means $$a = 3$$ or $$a\neq{3}$$ and also $$c$$ is not known.
Not Sufficient , Eliminate A and D

Consider 2) $$b + 3 = c$$
Substituting on the given equation: $$ab = b(b+3) + 3 = b^2 + 3b + 3$$ . Still $$a$$ and $$b$$ are not known.
Not Sufficient , Eliminate B

Consider 1) and 2) together (include that 1) has 2 possibilities based on $$b = 0$$ and $$b\neq{0}$$)
when $$b = 0$$, then $$c=3$$and $$ab = bc +3$$ becomes $$0 = 0 + 3$$ and Hence FAILS
when $$b\neq{0}$$, then $$a = 3$$ and $$ab = bc + 3$$ becomes $$3b = b(b+3) + 3=> b^2 = -3$$
giving values for b which are not real and the Hence Fails,

so answer is C, since when 1) and 2) considered together, the equality FAILS.

PS: this took more than 2 mins, anyone with faster approach please.

+1 for kudos.
Intern
Joined: 27 Apr 2016
Posts: 4
GPA: 3.5
WE: Information Technology (Computer Software)
Re: For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

03 Sep 2016, 06:35
C is the correct option: Below is the solution

Statement 1: ab=3b i.e b(a-3)=0 . Either b=0 or a=3 : We leave this, as no solution we get
Statement 2: b+3=c No info about anything else, so leave this too

Combining both 1 & 2

If we take b=0 , then c=3 according to statement 2 .
Try inputting this in ab= bc+3 . 0 is not equal to 3 Therefore ruled out

Now take a=3 and b+3 =c
Input these in ab=bc+3 ; b(a-c)=3 ; (c-3)(3-b-3) =3 ; -bc+3b =3 ; b(3-c)=3 : This matches the required where 3=a.

Hence combining the statements gave the answer .

Therefore Option C :D
Senior Manager
Joined: 02 Apr 2014
Posts: 473
GMAT 1: 700 Q50 V34
For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

16 Jan 2018, 09:56
ab = bc + 3?
ab - bc = 3 ?
b(a-c) = 3?

Statement 1:
ab - 3b = 0
=> b = 0 OR a = 3
if b = 0 => b(a-c) not equals to 3
if a = 3 => we dont know the value of c to say if b(a-c) equals to 3

Statement 2:
b + 3 = c
b(a-c) = 3? => (c-3)(a-3)= 3 ? => don't know about a to conclude => insuff

1 + 2
if b = 0, we saw from statement 1, b(a-c) is not equal to 3
if a = 3 and b + 3 = c, b(a-c) = 3 ? => (c-3)(3-c) = 3? => (3-c)(3-c) = -3? => (3-c)^2 = -3? definitely not equal to -3, as squared values are >= 0
sufficient to answer the question as NO => (C)
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6661
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: For real numbers a, b, and c, is ab = bc + 3?  [#permalink]

### Show Tags

20 Jan 2018, 21:13
Bunuel wrote:
For real numbers a, b, and c, is ab = bc + 3?

(1) ab = 3b
(2) b + 3 = c

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 equations, E is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):
ab = 3b
⇔ ab - 3b = 0
⇔ (a-3)b = 0
⇔ a = 3 or b = 0

Case 1: $$a = 3$$
$$ab = 3b$$ and $$bc + 3 = b(b+3)+3$$
$$ab = bc + 3$$
$$⇔ 3b = b(b+3)+3$$
$$⇔ 3b = b^2 + 3b + 3$$
$$⇔ 0 = b^2 + 3$$, which is false.
The answer is "No".

Case 2: $$b = 0$$
$$ab = bc + 3$$
$$⇔ 0a = 0c + 3$$
$$⇔ 0 = 0 + 3$$, which is false.
The answer is "No".

The answer is always "No".

They are sufficient by CMT (Common Mistake Type) 1, since the answer "no" also means the condition is sufficient.

The answer is C.

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.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: For real numbers a, b, and c, is ab = bc + 3? &nbs [#permalink] 20 Jan 2018, 21:13
Display posts from previous: Sort by

# For real numbers a, b, and c, is ab = bc + 3?

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

 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®.