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

It is currently 18 Oct 2019, 12:08

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

If a⊙b=(a+b)^2-2ab, which of the following is(are) true?

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
If a⊙b=(a+b)^2-2ab, which of the following is(are) true?  [#permalink]

Show Tags

New post 31 Jan 2018, 02:52
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:59) correct 38% (01:41) wrong based on 89 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(a⊙b=(a+b)^2-2ab\), which of the following is(are) true?

\(Ⅰ. a⊙b=b⊙a\)
\(Ⅱ. (a⊙b)⊙c=a⊙(b⊙c)\)
\(Ⅲ. a⊙1=a^2+1\)

A. Ⅰ only
B. Ⅱonly
C. Ⅲonly
D. Ⅰand Ⅲ
E. Ⅰ,Ⅱand Ⅲ

_________________
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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Senior Manager
Senior Manager
User avatar
G
Joined: 17 Oct 2016
Posts: 313
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
GMAT ToolKit User
Re: If a⊙b=(a+b)^2-2ab, which of the following is(are) true?  [#permalink]

Show Tags

New post 31 Jan 2018, 03:04
D. I and III only.

a⊙b=(a+b)²−2ab
=a²+b²+2ab-2ab
=a²+b²

Now lets test the conditions.

Ⅰ.a⊙b=b⊙a
a⊙b = a² + b²
b⊙a = b² + a²

Hence I is true

Ⅱ.(a⊙b)⊙c=a⊙(b⊙c)

(a⊙b)⊙c = (a² + b²)² + c²
a⊙(b⊙c) = a² + (b² + c²)²
clearly,
(a⊙b)⊙c≠a⊙(b⊙c)

II is false

Ⅲ.a⊙1=a²+1²
=a² + 1

III is true

Hence option D
_________________
Help with kudos if u found the post useful. Thanks
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a⊙b=(a+b)^2-2ab, which of the following is(are) true?  [#permalink]

Show Tags

New post 02 Feb 2018, 02:01
=>

\(a⊙b=(a+b)^2-2ab=a^2+2ab+b^2-2ab = a^2 + b^2\)

Statement I
\(b⊙a = b^2+a^2 = a^2 + b^2 = a⊙b\)
Therefore, statement I is true.

Statement II
\((a⊙b)⊙c = (a^2+b^2) ⊙c = (a^2+b^2)^2 +c^2 = a^4 + 2a^2b^2 + b^4 + c^2\)
\(a⊙(b⊙c) = a⊙ (b^2+c^2) = a^2+ (b^2+c^2)^2 = a^2 + b^4 + 2b^2c^2 + c^4\)
We can easily find a counterexample.
If \(a = 1\), \(b = 2\) and \(c = 3\), then
\((a⊙b)⊙c = (1⊙2)⊙3 = (1^2+2^2) ⊙3 = 5⊙3 = 5^2 + 3^2 = 25 + 9 = 34\) and
\(a⊙(b⊙c) = 1⊙(2⊙3) = 1⊙(2^2+3^2) = 1⊙13 = 1^2+13^2 = 1 + 169 = 170.\)
Thus, statement II is false.

Statement III
\(a⊙1 = a^2 + 1^2 = a^2 + 1\)
Therefore, statement III is true.

Therefore, the answer is D.

Answer: 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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: If a⊙b=(a+b)^2-2ab, which of the following is(are) true?   [#permalink] 02 Feb 2018, 02:01
Display posts from previous: Sort by

If a⊙b=(a+b)^2-2ab, which of the following is(are) true?

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





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