GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Aug 2020, 03:10 ### 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

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.  # If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65829
If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
14 00:00

Difficulty:   95% (hard)

Question Stats: 34% (02:01) correct 66% (02:04) wrong based on 116 sessions

### HideShow timer Statistics

Competition Mode Question

If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

_________________
Director  P
Joined: 24 Oct 2015
Posts: 530
Location: India
Schools: Sloan '22, ISB'21, IIM
GMAT 1: 650 Q48 V31 GPA: 4
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
1
Quote:
If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

ab - 2b = 4b -ab
2ab - 6b = 0
2b (a - 3) = 0

statement 1: |a^2 - 9| ≤ 0
a^2 - 9 = 0
a can be +3 or -3
when a = 3, b can be anything.
when a= -3, b has to be 0.
not sufficient

statement 2: a < 0
a $$\ne 0$$
b has to be 0.
ans: B
Manager  G
Status: Done with one MBA, now aiming for something bigger!
Joined: 03 May 2020
Posts: 240
Location: India
Concentration: Marketing, Strategy
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
ab - 2b = (4 - a)b
6b = 2ab
3b = ab
b(3-a) = 0

St. 1:
|a^2 - 9| <= 0
a^2 - 9 <= 0; when a^2 - 9 <= 0 i.e; a -> [-3,3]..........(i)
a^2 - 9 >=0; when a^2 - 9 >= 0 i.e; a -> (-infinity, - 3] U [3, inifnity)..........(ii)

From (i):
if a = 3, b = any value
if a = 2, b = 0
if a = 1, b = 0

St. 1 is insufficient

St. 2:
a < 0
=> a != 3
=> a - 3 != 0
=> b = 0
St. 2 is sufficient

_________________
MBA - IB, IIFT | Class of 2018 - 20
Majors - Marketing | Minors - Finance, Strategy, and Trade
NMAT '17 - 99.xx percentile | IIFT '17 - 94.95 percentile | CAT '17 - 93.81 percentile
GMATWhiz Representative P
Joined: 07 May 2019
Posts: 989
Location: India
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1

Solution

Step 1: Analyse Question Stem

• We have, $$ab-2b = (4-a)b$$

• We need to find the value of b.

• Now, $$ab-2b = (4-a)b$$
$$⟹ b(a-2) – b(4-a) = 0$$
$$⟹ b( a- 2 – 4 + a)= 0$$
$$⟹ b(2a – 6)= 0$$
$$⟹ 2b(a-3)= 0 …….Eq.(i)$$
 So, if $$a ≠ 3$$, in that case b must be 0.
 And, if $$a = 3$$, in that case b can take any real number value.
• So, if we can determine that $$a ≠ 3$$, we can find the unique value of b.
Now, let’s analyse the statements.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: $$|a^2 – 9| ≤ 0$$
• We know that absolute values cannot be less than 0
o This, means, $$|a^2 – 9| = 0$$ $$⟹ a = -3,$$ or $$3$$
 If a = 3, in that case b = 0, unique solution
 However, if a = -3, in that cases b can take any real number value.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2: $$a< 0$$
• From this statement, we can be sure that $$a ≠ 3$$.
o Therefore, $$b = 0$$
Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
_________________

GMAT Prep truly Personalized using Technology

Prepare from an application driven course that serves real-time improvement modules along with a well-defined adaptive study plan. Start a free trial to experience it yourself and get access to 25 videos and 300 GMAT styled questions.

Countdown to Round 1 - Free Webinar Series: Registration Link | Watch Recordings of Webinars
Score Improvement Strategy: How to score Q50+ on GMAT | 5 steps to Improve your Verbal score
Study Plan Articles: 3 mistakes to avoid while preparing | How to create a study plan? | The Right Order of Learning | Importance of Error Log
Helpful Quant Strategies: Filling Spaces Method | Avoid Double Counting in P&C | The Art of Not Assuming anything in DS | Number Line Method
Key Verbal Techniques: Plan-Goal Framework in CR | Quantifiers the tiny Game-changers | Countable vs Uncountable Nouns | Tackling Confusing Words in Main Point
Intern  B
Joined: 31 Jul 2018
Posts: 5
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

from question:
ab-2b=4b-ab
2ab=6b

statement 1: tells us either a=<3, -3 or -3, 3<=a, nothing about B, hence Insuff
statement 2: tells us nothing about b, hence insuff
together: nothing about b.. hence IMO ans: E
Sloan MIT School Moderator V
Joined: 07 Mar 2019
Posts: 1347
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

ab - 2b = 4b - ab
2ab = 6b
2ab - 6b = 0
b(a - 3) = 0

So, either b = 0 and a - 3 ≠ 0
OR
b ≠ 0 and a - 3 = 0
OR
b = 0 and a - 3 = 0

(1) |a^2 - 9| ≤ 0
Since |mod| ≥ 0
|a^2 - 9| = 0 only
a^2 - 9 = 0
a = 3 => b can take any value
OR -3 => b = 0
However, b can take any value.

INSUFFICIENT.

(2) a < 0
Here, since a < 3 so b can take only one value i.e.
b = 0, so that b(a - 3) = 0

SUFFICIENT.

_________________

Originally posted by unraveled on 03 Jul 2020, 04:11.
Last edited by unraveled on 06 Jul 2020, 04:54, edited 1 time in total.
Intern  B
Joined: 09 Aug 2019
Posts: 2
Location: India
Concentration: Strategy, Operations
GPA: 3.07
WE: Consulting (Consulting)
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
Given: ab - 2b = (4 - a)b which upon simplification becomes b(3-a)=0. Thus, either b = 0 or a = 3 or both.

Statement 1: |a^2 - 9| ≤ 0, as absolute (modulus) values are either 0 or Positive Numbers. Therefore a^2 = 9.
We get a = 3 or a = -3. Thus we cannot be sure about the value of 'b'. Insufficient

Statement 2: a < 0, thus a≠3. Therefore, b = 0. Sufficient.

Choice B is the correct answer.
Senior Manager  D
Status: Student
Joined: 14 Jul 2019
Posts: 448
Location: United States
Concentration: Accounting, Finance
GPA: 3.9
WE: Education (Accounting)
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

Given, b (a-2) = b (4 -a), so, when b =0, a can assume any value. If b is not 0, a will be 3.

1) a^2 - 9 =0, as the absolute value cannot be less than 0. so, a is either -3 or +3. Both of the values will satisfy the equation given b is 0 or not. not sufficient.

2) no information about b. not sufficient.

Together, a can assume only the value -3. so b is 0. Sufficient.

Director  V
Joined: 30 Sep 2017
Posts: 991
GMAT 1: 720 Q49 V40 GPA: 3.8
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

(a - 2)b = (4 - a)b
Either a=3 or b=0

Q. what is the value of b?

(1) |a^2 - 9| ≤ 0
a=-3 --> b=0
a=3 --> b can be any
NOT SUFFICIENT

(2) a < 0
a=-3 --> b=0
Any other a --> b=0
SUFFICIENT

Ans (B)

Posted from my mobile device
Intern  B
Joined: 27 Jan 2017
Posts: 36
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

E - Neither sufficient

ab - 2b = (4 - a)b ==> ab - 2b = 4b - ab ==> 2ab = 6b. ==> a = 3

then 3b - 2b = (4-3)b ===> b=b

So whatever value we chose for B, will give us B and since neither statement 1 or 2 talk about option B we can conclude the answer is E
McCombs School Moderator G
Joined: 26 May 2019
Posts: 241
Location: India
GMAT 1: 690 Q50 V33
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

If ab - 2b = (4 - a)b, what is the value of b?

(1) |a^2 - 9| ≤ 0
(2) a < 0

This is a question in which the question stem gives more information than we usually give it credit for! ab - 2b = 4b - ab
=> 2ab - 6b = 0
=> (a-3)b = 0

So either a = 3 or b = 0

st1) From the inequality equation, it is clear that $$a\neq{3}$$, so b has to be equal to 0 (SUFFICIENT)

st2) clearly tells us that $$a\neq{3}$$ , so b = 0 (SUFFICIENT)

So, the answer should be D
Manager  S
Joined: 11 May 2019
Posts: 139
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
IMO B.

ab-2b = 4b-ab

2ab = 4b + 2b

2ab =6b

ab =3b

ab-3b = 0
b(a-3) = 0

either a=3 or b= 0 or both

Stmt 1
suggests that a^2 = 9
since it is absolute
a = 3

(a = -3 does not hold true after we simplify the question stem.)

3b = 3b

we get b = b
We dont get value so insuff.

Stmt 2 says a is negative.
Since this condition is false after we simplify the question stem.
so b has to be 0.
Suff.

B it is

Posted from my mobile device
Senior Manager  S
Joined: 18 Dec 2017
Posts: 308
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

1
From statement 1
a =3, so b can take up 0 or any other value
Not sufficient
From statement 2
a is less than 0 that means b can only be 0.
Sufficient

Posted from my mobile device
Intern  B
Joined: 01 Dec 2019
Posts: 2
If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

We have $$ab-2b=(4-a)b$$

$$(a-2)b=(4-a)b$$
$$ab-2b=4b-ab$$
$$2ab-6b=0$$
$$ab-3b=0$$
$$b(a-3)=0$$

From the above we can infer the following two cases -
(i) if $$a=3$$, $$b$$ can be any real number
(ii) if $$a\neq{3}$$, $$b$$ = 0

From Statement (1) we have,
$$|a^2 - 9|\leq{0}$$
We know that a modulus function always gives a positive number as it's output. Hence $$|a^2 - 9|$$ cannot be negative and can only be equal to 0 at the best.

$$a^2-9=0$$
$$a^2=9$$
$$a=3$$ or $$a=-3$$

Unique value of b cannot be arrived at by either value of a. Hence Options (A) and (D) may be eliminated.

From Statement (2) we have,
$$a<0$$

If $$a<0$$ then $$a\neq{3}$$. Then b should be equal to 0 as we have found in (ii) above. Since we have a unique value of b in this case, (B) is the answer.

Originally posted by Pran1990 on 04 Jul 2020, 05:05.
Last edited by Pran1990 on 09 Jul 2020, 03:39, edited 1 time in total.
Manager  G
Joined: 23 May 2020
Posts: 156
Location: India
GPA: 4
Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  [#permalink]

### Show Tags

And C

With statement A
You get two values of a= 3, -3
This is not sufficient to find b

With statement 2
A<0
We are not clear what A is and what can be possible value for b. So this is insufficient

1+2
it is clear that A= -3, as A<0, with this find B from given equation
-3B -2B = -5B = 7B
So B=0

Posted from my mobile device Re: If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)   [#permalink] 05 Jul 2020, 10:02

# If ab - 2b = (4 - a)b, what is the value of b? (1) |a^2 - 9| ≤ 0 (2)  