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

It is currently 21 Sep 2018, 19:15

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

Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d

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

Hide Tags

Intern
Intern
avatar
Joined: 30 Nov 2010
Posts: 39
Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post Updated on: 22 May 2018, 06:22
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:47) correct 27% (00:42) wrong based on 83 sessions

HideShow timer Statistics

Is the product abcd even?

(1) \(a^2+ b^2 + c^2 + d^2 = 0\)
(2) a = b = c = d


I dont understand the answer. If you ask me it's (E) --> "Statements (1) and (2) TOGETHER are NOT sufficient"

The question does not insist on "integers" so I was thinking more in terms of negative roots. here's the explanation:
If a= [square_root]5, b=[square_root](-5), c=[square_root](7), d=[square_root]-(7) , it still satisfies Eqn#1 and the product of abcd is not even(abcd= 1225).

When do you decide you can assume the problem involves integers and does not involve integers?


M03-35

Originally posted by chethanjs on 05 Apr 2011, 19:44.
Last edited by pikolo2510 on 22 May 2018, 06:22, edited 2 times in total.
Renamed the topic and edited the question.
Intern
Intern
avatar
Joined: 05 Apr 2011
Posts: 10
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 05 Apr 2011, 21:38
is the first equation equal zero? Something is missing in the first equation i guess.
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1451
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 05 Apr 2011, 22:27
Yes, the first option has a^2+ b^2 + c^2 + d^2 = 0, which automatically makes A as correct answer. GMAT does not deal with complex numbers, and only real numbers are in consideration here. so square of any real number is non-negative and hence a = b = c = d = 0.

@chethanjs, please revisit the question.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 30 Nov 2010
Posts: 39
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 06 Apr 2011, 04:04
Sorry, yea, 1st eqn is a^2+ b^2 + c^2 + d^2 = 0 .

@subash: oh ok. Thanks.
Intern
Intern
avatar
Joined: 30 Mar 2011
Posts: 8
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 07 Apr 2011, 04:33
Wouldn't statement 2 be sufficient as well?

If a = b = c = d, then abcd = a^4.

If a is positive then, a^4 is positive.

If a is negative, a^4 is still positive.

Only remaining case is a = 0, but I assume we can think of 0 as positive.
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 07 Apr 2011, 04:38
1
oster wrote:
Wouldn't statement 2 be sufficient as well?

If a = b = c = d, then abcd = a^4.

If a is positive then, a^4 is positive.

If a is negative, a^4 is still positive.

Only remaining case is a = 0, but I assume we can think of 0 as positive.


Question asks whether a.b.c.d is EVEN.

a=1,
a.b.c.d=a^4=1; odd

a=2,
a.b.c.d=a^4=16; even

a=0,
a.b.c.d=a^4=0; even

By the way; "0" is neither +ve nor -ve.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 30 Mar 2011
Posts: 8
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 07 Apr 2011, 12:04
fluke wrote:
oster wrote:
Wouldn't statement 2 be sufficient as well?

If a = b = c = d, then abcd = a^4.

If a is positive then, a^4 is positive.

If a is negative, a^4 is still positive.

Only remaining case is a = 0, but I assume we can think of 0 as positive.


Question asks whether a.b.c.d is EVEN.

a=1,
a.b.c.d=a^4=1; odd

a=2,
a.b.c.d=a^4=16; even

a=0,
a.b.c.d=a^4=0; even

By the way; "0" is neither +ve nor -ve.


Ah yes, d'oh!

Thanks!
Intern
Intern
avatar
Joined: 05 Oct 2010
Posts: 13
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 07 Apr 2011, 14:20
I am still confused. Wouldn't it be correct to presume that the statement 1)a^2+ b^2 + c^2 + d^2 = 0 would be true only if a, b, c, d equal zero??

As follows, abcd would equal zero and thus answer A) would be correct
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 07 Apr 2011, 14:28
katealpha wrote:
I am still confused. Wouldn't it be correct to presume that the statement 1)a^2+ b^2 + c^2 + d^2 = 0 would be true only if a, b, c, d equal zero??

As follows, abcd would equal zero and thus answer A) would be correct


katealpha, you scored a bull's eye. No need to be confused.
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 508
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 08 Apr 2011, 12:47
katealpha wrote:
I am still confused. Wouldn't it be correct to presume that the statement 1)a^2+ b^2 + c^2 + d^2 = 0 would be true only if a, b, c, d equal zero??

As follows, abcd would equal zero and thus answer A) would be correct


You're correct. any square is always \(>= 0\). The only case when a bunch of squares will add to zero is when all squares are themselves zero and this will only happen when each number is zero.
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49300
Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d  [#permalink]

Show Tags

New post 22 May 2018, 05:48
chethanjs wrote:
Is the product abcd even?

(1) a^2+ b^2 + c^2 + d^2
(2) a = b = c = d


I dont understand the answer. If you ask me it's (E) --> "Statements (1) and (2) TOGETHER are NOT sufficient"

The question does not insist on "integers" so I was thinking more in terms of negative roots. here's the explanation:
If a= [square_root]5, b=[square_root](-5), c=[square_root](7), d=[square_root]-(7) , it still satisfies Eqn#1 and the product of abcd is not even(abcd= 1225).

When do you decide you can assume the problem involves integers and does not involve integers?


M03-35


Is the product abcd even?

(1) a^2+b^2+c^2+d^2=0 --> number squared is always non-negative (zero or positive), so the sum of 4 non-negative values to be 0 then each must be zero, so abcd=0=even. Sufficient.

(2) a=b=c=d. Clearly insufficient.

Answer: A.

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

Re: Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d &nbs [#permalink] 22 May 2018, 05:48
Display posts from previous: Sort by

Is the product abcd even? (1) a^2+ b^2 + c^2 + d^2 (2) a = b = c = d

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

Events & Promotions

PREV
NEXT


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®.