GMAT Changed on April 16th - Read about the latest changes here

It is currently 25 May 2018, 00:06

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 integers and abc ≠ 0, is a^2 – b^2

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

Hide Tags

2 KUDOS received
Manager
Manager
User avatar
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 177
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 26 Mar 2013, 01:52
2
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:23) correct 30% (01:09) wrong based on 246 sessions

HideShow timer Statistics

If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2

(2) b = c^2 – 1

Need explanation
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45381
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 26 Mar 2013, 02:03
1
This post received
KUDOS
Expert's post
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2 --> a=c^2-2c+1. Not sufficient, since no info about b.

(2) b = c^2 – 1. Not sufficient, since no info about a.

(1)+(2) \(a^2-b^2 = (a-b)(a+b)=(c^2-2c+1-c^2+1)(c^2-2c+1+c^2-1)=(2-2c)(2c^2-2c)=4(1-c)(c^2-c)\) --> a^2-b^2 is a multiple of 4. Sufficient.

Answer: C.

Hope it's clear.
_________________

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

Senior Manager
Senior Manager
User avatar
Status: Final Lap
Joined: 25 Oct 2012
Posts: 270
Concentration: General Management, Entrepreneurship
GPA: 3.54
WE: Project Management (Retail Banking)
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 26 Mar 2013, 02:15
mun23 wrote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2

(2) b = c^2 – 1

Need explanation


Hi mun23

(1) a = (c – 1)^2 ALONE

(1) is INSUFFICIENT because this statement do not give any information about b

(2) b = c^2 – 1 ALONE

(2) is INSUFFICIENT because this statement do not give any information about a

(1) + (2) a = (c – 1)^2 AND b = c^2 – 1

After combining (1) and (2) -->
a + b = (c-1)^2 + c^2 - 1 = c^2 - 2c + 1 + c^2 - 1 = 2c(c-1)
a - b = (c-1)^2 - c^2 + 1 = c^2 - 2c + 1 - c^2 +1 = -2c + 2 = 2(1-c)

a^2 - b^2 = (a+b)(a-b) = 4c(c-1)(1-c) = -4c (c-1)^2

Hence , a^2 - b^2 = 4 * Integer , So the answer is Yes --> (1) + (2) SUFFICIENT

Answer : C
_________________

KUDOS is the good manner to help the entire community.

"If you don't change your life, your life will change you"

Manager
Manager
User avatar
Joined: 14 Oct 2014
Posts: 66
Location: United States
GMAT 1: 500 Q36 V23
If a, b, and c are integers and abc ≠ 0, is a2 – b2 a multiple of 4? [#permalink]

Show Tags

New post 11 Dec 2014, 16:27
1
This post was
BOOKMARKED
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2

(2) b = c^2 – 1
Director
Director
User avatar
S
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 604
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If a, b, and c are integers and abc ≠ 0, is a2 – b2 a multiple of 4? [#permalink]

Show Tags

New post 11 Dec 2014, 22:03
Question can be written as a^2 - b^2 or (a-b)*(a+b) is a multiple of 4
STAT1 alone is not sufficient as we don't know anything about b
STAT2 alone is not sufficient as we don't know anything about a
Taking both together

a = (c-1)^2 and b = c^2 - 1 or b = (c-1)*(c+1)

a+b = (c-1)^2 + (c-1)*(c+1) = (c-1)* (c-1 + c+1) = c*(c-1)
a-b = (c-1)^2 - (c-1)*(c+1) = (c-1)*(c-1 - (c+1)) = (c-1)*(-2) = -2*c*(c-1)
So, a^2 - b^2 = (a-b)*(a+b) = c*(c-1) * (-2*c*(c-1))
= -2*(c^2)*((c-1)^2)

If c is odd then c-1 will be even and c*c-1 will be a multiple of 2
else if c i even then again c*c-1) will be a multiple of 2

So, in both the cases c*(c-1) is a multiple of 2. So, -2*(c^2)*((c-1)^2) will be a multiple of 4 (Actually will be a multiple of 8 too)
So, Answer will be C

Hope it helps!


viktorija wrote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2

(2) b = c^2 – 1

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 277
Premium Member
Re: If a, b, and c are integers and abc ≠ 0, is a2 – b2 a multiple of 4? [#permalink]

Show Tags

New post 12 Dec 2014, 01:33
viktorija wrote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2

(2) b = c^2 – 1


st.1 alone is not sufficient as nothing is mentioned about b
st.2 alone is not sufficient as nothing is mentioned about a

st.1 and st.2

\(a= (c-1)^2\) and \(b= (c^2-1)\)

\(a^2-b^2= (a-b)(a+b)\)
put the value of a and b in the above expression, we have

\(a^2-b^2 = ((c-1)^2 - (c^2-1))((c-1)^2 + (c^2 - 1))\)

= \(((c^2+1-2c) - c^2 +1) ((c^2+1-2c) +c^2 - 1)\)

= \((2-2C)(2C^2-2c)\)

=\(4c(1-c)(c-1)\)

as can be seen, the above expression is a multiple of 4. hence answer is C.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45381
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 12 Dec 2014, 04:38
Intern
Intern
avatar
B
Joined: 31 Jan 2017
Posts: 41
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 03 Aug 2017, 08:55
Ans : C
a^2-b^2=-4c(c-1)^2

Sent from my SM-J210F using GMAT Club Forum mobile app
Study Buddy Forum Moderator
User avatar
P
Joined: 04 Sep 2016
Posts: 968
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 13 Apr 2018, 17:06
Bunuel niks18 chetan2u amanvermagmat


Quote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2 --> a=c^2-2c+1.

(2) b = c^2 – 1.


How about this approach?
If I simplify question stem to best possible, what am I asked?
Is a / b even?

Why?
a. A multiple pf 4 is always even
b. Squaring of odd / even is always odd /even
c. Even - Even = Even.
or Odd - Odd = Even

I did above in my head.
Essentially, either of statements is clearly insuff
since I need to know both a and b.

What happens when I combine and simplify \(a^2\) - \(b^2\)
I get -2c + 1.

Even if I do not know value of c, I know -2 will always be even
Even + Odd = Odd. So, we do get an unique ans: NO
_________________

It's the journey that brings us happiness not the destination.

DS Forum Moderator
avatar
G
Joined: 22 Aug 2013
Posts: 1145
Location: India
Premium Member CAT Tests
Re: If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 14 Apr 2018, 11:07
adkikani wrote:
Bunuel niks18 chetan2u amanvermagmat


Quote:
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 a multiple of 4?

(1) a = (c – 1)^2 --> a=c^2-2c+1.

(2) b = c^2 – 1.


How about this approach?
If I simplify question stem to best possible, what am I asked?
Is a / b even?

Why?
a. A multiple pf 4 is always even
b. Squaring of odd / even is always odd /even
c. Even - Even = Even.
or Odd - Odd = Even

I did above in my head.
Essentially, either of statements is clearly insuff
since I need to know both a and b.

What happens when I combine and simplify \(a^2\) - \(b^2\)
I get -2c + 1.

Even if I do not know value of c, I know -2 will always be even
Even + Odd = Odd. So, we do get an unique ans: NO


Hello

Its NOT necessary for a & b to be even for this to be true. a & b could be both odd also. Eg, a=5, b=3, here a^2 - b^2 = 25-9 = 16, which is a multiple of 4.
Manager
Manager
avatar
B
Joined: 21 Aug 2017
Posts: 84
CAT Tests
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2 [#permalink]

Show Tags

New post 22 Apr 2018, 09:54
The math on the previous posts is clear, so I can't add anything to that. That's a surefire way of getting the problem correct.

I took a different approach in plugging in numbers to the prompts. It was obvious right away that 1 and 2 alone are insufficient because they don't give full details about the variables.

After combining, start picking smart numbers for C and work out what A and B would be. I made C = 2, 3, and 4, and then worked out what that would make A and B equal to. This gave me a good enough sample size to test divisibility of 4 and to feel comfortable enough in picking answer choice C.

Is this a perfect approach? No, but I got to the right answer in well under 2 minutes with a high probability of being correct.
If a, b, and c are integers and abc ≠ 0, is a^2 – b^2   [#permalink] 22 Apr 2018, 09:54
Display posts from previous: Sort by

If a, b, and c are integers and abc ≠ 0, is a^2 – b^2

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.