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

It is currently 14 Oct 2019, 07:14

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 q, r, and s are consecutive even integers and q < r < s, which of t

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58310
If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 21 Oct 2014, 09:21
2
12
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

59% (02:39) correct 41% (02:27) wrong based on 182 sessions

HideShow timer Statistics

Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 21 Oct 2014, 19:00
3
2
s > r > q are consecutive even integers

Testing for \(s^2 - r^2 - q^2\)

I: For s = 0, r = -2, q = -4,

\(s^2 - r^2 - q^2 = -20\)

II: For s = 2, r = 0, q = -2

\(s^2 - r^2 - q^2 = 0\)

III: For s = 4, r = 2, q = 0

\(s^2 - r^2 - q^2 = 12\)

Step II & Step III have consecutive representation of values of s, r, q. No other combination is possible.

8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12

Answer = C
_________________
Kindly press "+1 Kudos" to appreciate :)
General Discussion
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 403
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 30 Dec 2014, 12:03
This is fine, but is there an approach that is not based on trial and error? Because, on first site, I don't see why 8 would be the value.. And I guess there should be, otherwise there is not much point in this question. Anyone can plug in numbers and test them.. Am I missing anything?
Manager
Manager
avatar
Joined: 13 Dec 2013
Posts: 59
Location: Iran (Islamic Republic of)
GMAT ToolKit User
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 31 Dec 2014, 03:45
2
If we changed the all 3 variables to one variable ( for example r ) we see that : s= r+2 and q= r-2 . so we should replace these equations in the

main equation and we get this equation: s^2 - r^2- q^2= (r+2)^2 - R^2- (r-2)^2 = 8r-r^2

so If we replaced any even integer in this new equation we see that ONLY 8 can not obtain.

If we replace 10 we get 8 (10) - (10)^2 = -20 so option A is ruled out

If we replace 4 we get 32- 16 = 16 etc So the only 8 can not the answer so option c..... :P
Manager
Manager
User avatar
G
Joined: 13 Oct 2013
Posts: 134
Concentration: Strategy, Entrepreneurship
GMAT ToolKit User
If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 31 Dec 2014, 14:25
my approach was:
take s=r-2 and q=r+2
=>s^2-r^2-q^2=(r-2)^2-r^2-(r+2)^2
by solving we will have -r(r+8)
when r =2, value is -20
when r= -2, value is 12
when r= 0, value is 0
when r=-4, value is 16

so remaining option is C:8
_________________
---------------------------------------------------------------------------------------------
Kindly press +1 Kudos if my post helped you in any way :)
Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 11
GMAT ToolKit User
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 08 Aug 2015, 02:29
4
Let the possible outcome of the equation be c.

Assuming the three numbers to be (r-2), r & (r+2), and substituting in the equation we get the equation as

8r-r^2 = c

Now multiplying by -1 we get

r^2-8r=-(c)

which becomes

r^2-8r+c=0

The determinant of this quadratic equation is thus:

64-4*c

now we compute the determinant for each of the options. The value of c which does not give a perfect square as the determinant will make the roots irrational and hence is not a valid answer:
a. c=-20 gives D=144 -> Rational roots
b. c=0 gives D=64 -> Rational roots
c. c=8 gives D=32 -> Irrational roots
d. c=12 gives D=16 -> Rational roots
e. c=16 gives D=0 -> Rational roots

Hence 8 cannot be the value of the expression.

Answer is C.
Intern
Intern
avatar
B
Joined: 13 Apr 2015
Posts: 30
GMAT ToolKit User
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 19 Aug 2016, 23:17
a more simple method would be using the quadratic equation.Since the numbers are consecutive

s=n+2
q=n
r=n-2

after substituting the values we get

n^2 +4+4n-n^2-n^2-4n+4n
which will be
8n-n^2

equate the values to this equation to get value of n.
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 359
GPA: 3.98
If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 01 Nov 2016, 06:03
2
Let’s denote consecutive even integers as follows: 2x, 2x+2, 2x+4
As to the question we have following:

\((2x+4)^2-(2x+2)^2-(2x)^2\) by simplifying this expression we’ll get:
\(-4x^2+8x+12\)

Now we need to put above polynomial into correspondence to our question choices and find out if resultant expression has integer solutions or, read it other way, can it be factorized or not.

a) \(-4x^2+8x+12=-20\)
\(-4x^2+8x+32=0\)
\(-4(x-4)(x+2)=0\) Yes.

b) \(-4x^2+8x+12=0\)
\(-4(x-3)(x+1)=0\) Yes.

c) \(-4x^2+8x+12=8\)
\(-4(x2-2x-1)=0\) This polynomial does not have integer roots.

d) \(-4x^2+8x+12=12\)
\(-4x(x+2)=0\) Yes.

e) \(-4x^2+8x+12=16\)
\(-4(x-1)^2=0\) Yes.

Answer C.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 08 Apr 2018, 11:12
Hi All,

We're told that Q, R and S are consecutive EVEN integers, so we're restricted there (notice that the prompt does NOT say anything about the 3 values being positive though). While this question might look a bit complex, you can "brute force" this question quickly by following the instructions and TESTing values. Using these values, here are the results (note that we're looking for what CANNOT be the value):

0, 2, 4 = 16 - 4 - 0 = 12 Eliminate D
2, 4, 6 = 36 - 16 - 4 = 16 Eliminate E
-2, 0, 2 = 4 - 0 - 4 = 0 Eliminate B
-4, -2, 0 = 0 - 4 - 16 = -20 Eliminate A

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13119
Re: If q, r, and s are consecutive even integers and q < r < s, which of t  [#permalink]

Show Tags

New post 05 Jun 2019, 13:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If q, r, and s are consecutive even integers and q < r < s, which of t   [#permalink] 05 Jun 2019, 13:48
Display posts from previous: Sort by

If q, r, and s are consecutive even integers and q < r < s, which of t

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





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