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

 It is currently 17 Oct 2019, 15:53 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.  x is the sum of y consecutive integers. w is the sum of z

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

Hide Tags

Manager  Joined: 11 Aug 2009
Posts: 79
x is the sum of y consecutive integers. w is the sum of z co  [#permalink]

Show Tags

9
83 00:00

Difficulty:   95% (hard)

Question Stats: 35% (02:23) correct 65% (02:27) wrong based on 632 sessions

HideShow timer Statistics

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

A. x = w
B. x > w
C. x/y is an integer
D. w/z is an integer
E. x/z is an integer
Math Expert V
Joined: 02 Sep 2009
Posts: 58402

Show Tags

11
17
nonameee wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

A. x = w
B. x > w
C. x/y is an integer
D. w/z is an integer
E. x/z is an integer

Can someone please prove?

Quote:
For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms.
But For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.

• If $$k$$ is odd, the sum of $$k$$ consecutive integers is always divisible by $$k$$. Given $$\{9,10,11\}$$, we have $$k=3$$ consecutive integers. The sum of 9+10+11=30, therefore, is divisible by 3.

• If $$k$$ is even, the sum of $$k$$ consecutive integers is never divisible by $$k$$. Given $$\{9,10,11,12\}$$, we have $$k=4$$ consecutive integers. The sum of 9+10+11+12=42, therefore, is not divisible by 4.

• The product of $$k$$ consecutive integers is always divisible by $$k!$$, so by $$k$$ too. Given $$k=4$$ consecutive integers: $$\{3,4,5,6\}$$. The product of 3*4*5*6 is 360, which is divisible by 4!=24.
_________________
Manager  Joined: 29 Oct 2009
Posts: 177
GMAT 1: 750 Q50 V42 Re: x is the sum of y consecutive integers. w is the sum of z co  [#permalink]

Show Tags

35
1
35
For a set of 'n' consecutive integers, the sum of integers is :
(a) always a multiple of 'n' when n is ODD
(b) never a multiple of 'n' when n is EVEN
(Note : Try it out!)

From y = 2z, we can conclude that x is the sum of consecutive integers for an EVEN number of terms since y will always be even.

Thus x/y can never be an integer.

_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders!
http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy!
1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html
2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html
3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html
General Discussion
Manager  Joined: 13 Aug 2009
Posts: 129
Schools: Sloan '14 (S)
Re: x is the sum of y consecutive integers. w is the sum of z co  [#permalink]

Show Tags

1
2
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

Case 1: x = w
if y = [2,3] z = 
5=5, TRUE

Case 2: x > w
if y = [2,3] z = 
5>1, TRUE

Case 3: x/y is an integer
if y = [2,3,4] x = 9
9/3 is an integer, TRUE

Case 4: w/z is an integer
if z =  w = 2
2/1 is an integer, TRUE

Case 5: x/z is an integer
if x = 9, z = 
9/1 is an integer, TRUE

Am I doing something wrong here?
Manager  Joined: 30 Aug 2009
Posts: 226
Location: India
Concentration: General Management
Re: x is the sum of y consecutive integers. w is the sum of z co  [#permalink]

Show Tags

h2polo wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

Case 1: x = w
if y = [2,3] z = 
5=5, TRUE

Case 2: x > w
if y = [2,3] z = 
5>1, TRUE

Case 3: x/y is an integer
if y = [2,3,4] x = 9
9/3 is an integer, TRUE

Case 4: w/z is an integer
if z =  w = 2
2/1 is an integer, TRUE

Case 5: x/z is an integer
if x = 9, z = 
9/1 is an integer, TRUE

Am I doing something wrong here?

well well well...I came to 3 taking y as a multiple of 2 (considering y=2z and y,z both are integers)
yet I may be wrong...

Originally posted by kp1811 on 19 Nov 2009, 04:07.
Last edited by kp1811 on 19 Nov 2009, 05:28, edited 1 time in total.
Manager  Joined: 30 Aug 2009
Posts: 226
Location: India
Concentration: General Management

Show Tags

3
delta09 wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d. w/z is an integer
e) x/z is an integer

C

a) x= w if x = (1+2+3+4+5+6) = 21 and w = (6+ 7+8)=21.
b) x>w if x= (1+2+3+4+5+6) = 21 and w = (4+5+6)= 15
c) x/y => x = (1+2+3+4+5+6) = 21 and y = 6 then x/y is NOT an integer
=> x = (1+2+3+4) and y = 4 then x/y is NOT an integer
d) w/z =>w = (6+ 7+8)=21 and z=3 then w/z = 3
e) x/z => x = (1+2+3+4+5+6) = 21 and z = 3 then x/z = 7
Manager  Joined: 09 May 2009
Posts: 162

Show Tags

1
delta09 wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d. w/z is an integer
e) x/z is an integer

IMO (C).

y will always be even since y=2z

assume 6 numbers
n-2 n-1 n n+1 n+2 n+3
x=6n+3, y=6, z=3

x/z = 2n+1

x/y = n+1/2 ==> cannot be integer
_________________
GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME
Intern  Joined: 18 Jul 2009
Posts: 27
Re: Intresting problem  [#permalink]

Show Tags

3
3
OA is C

sum of even no is not always odd.

consider 1+2+3+4=10 which is even

For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms.

consider above example 10 is not multiple of 4.

But For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.

1+2+3=6 multiple of 3
Senior Manager  Joined: 22 Dec 2009
Posts: 253

Show Tags

2
2
delta09 wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d. w/z is an integer
e) x/z is an integer

since y = 2z... it is even...

x is the sum of y (even no) of integers....

Hence x/y would never be an integer....

Therefore C....

Note
For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms.
But For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.

_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! |Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~
Manager  Joined: 26 Mar 2007
Posts: 61
Concentration: General Management, Leadership
Schools: Thunderbird '15
x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

1
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d) w/z is an integer
e) x/z is an integer
Manager  Joined: 15 Apr 2011
Posts: 54
Location: Bangalore India
Schools: LBS, HBS, ISB, Kelloggs, INSEAD
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

kannn wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d) w/z is an integer
e) x/z is an integer

Why the answer is not A for this one, as if y consecutive integers are 1 2 3 4 5 and z consecutive integers are 1 2 3 4 5 6 7 8 9 10 then x(sum of y ints) not equal to y(sum of z ints).

please someone explain, whats the flaw in my opinion?
_________________
Thanks,
AM
Retired Moderator Joined: 20 Dec 2010
Posts: 1579
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

atulmogha wrote:
kannn wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d) w/z is an integer
e) x/z is an integer

Why the answer is not A for this one, as if y consecutive integers are 1 2 3 4 5 and z consecutive integers are 1 2 3 4 5 6 7 8 9 10 then x(sum of y ints) not equal to y(sum of z ints).

please someone explain, whats the flaw in my opinion?

You should try and find a case where the statement (a) will hold true or try and find the option which must not be true. Question asks: "each of the following could be true EXCEPT".

c) x/y -- integer. or x/even -- integer; thus x will have to be even to make the statement true but as we know "x" is the sum of equal numbers of odds and evens and will always be odd. This statement "Must not" be true or always be false.
_________________
Manager  Joined: 26 Mar 2007
Posts: 61
Concentration: General Management, Leadership
Schools: Thunderbird '15
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

1
fluke wrote:
atulmogha wrote:
kannn wrote:
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

a) x = w
b) x > w
c) x/y is an integer
d) w/z is an integer
e) x/z is an integer

Why the answer is not A for this one, as if y consecutive integers are 1 2 3 4 5 and z consecutive integers are 1 2 3 4 5 6 7 8 9 10 then x(sum of y ints) not equal to y(sum of z ints).

please someone explain, whats the flaw in my opinion?

You should try and find a case where the statement (a) will hold true or try and find the option which must not be true. Question asks: "each of the following could be true EXCEPT".

c) x/y -- integer. or x/even -- integer; thus x will have to be even to make the statement true but
as we know "x" is the sum of equal numbers of odds and evens and will always be odd
. This statement "Must not" be true or always be false.

Sume of 1,2,3, 4 (even number of integers) = 10, which is even. Am I missing something? Help please.
Though I agree that it is not divisible by 4 i.e.m 2y.
Retired Moderator Joined: 20 Dec 2010
Posts: 1579
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

kannn wrote:
fluke wrote:

Sume of 1,2,3, 4 (even number of integers) = 10, which is even. Am I missing something? Help please.
Though I agree that it is not divisible by 4 i.e.m 2y.

No, you are right. Thanks for correcting me. Rule is as follows:

1. If n is odd, the sum of "n" consecutive integers is always divisible by n.
2. If n is even, the sum of "n" consecutive integers is never divisible by n.
_________________
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

This is heavily cloaked problem masking the issue that -
The average of even number of integers is never an integer.

Here x = sum of even number of consecutive integers ( y).
y = 2z (even)
x / y = fraction. Answer C
Manager  Joined: 25 Aug 2008
Posts: 139
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

Yup.. Even i got C.. But I'm still confused as to y E is not the OA.. E states: x/z is an integer. Same logic for could be true works here?? HELP!!  _________________
Cheers,
Varun

If you like my post, give me KUDOS!!
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

Lets assume that x is the sum of first y consecutive integers
x = y(y+1)/2 ----------(1)
y = 2z
Substituting the value of y in (1)
x = 2z(2z+1)/2 = z(2z+1)
x/z = 2z+1. We know that z is an integer.

Hence x/z can be an integer.

varunmaheshwari wrote:
Yup.. Even i got C.. But I'm still confused as to y E is not the OA.. E states: x/z is an integer. Same logic for could be true works here?? HELP!!  Manager  Status: It's "Go" Time.......
Affiliations: N.C.C.
Joined: 22 Feb 2011
Posts: 135
Location: India
Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

The answer must be "C" because if there are n consecutive integers & n is even then mean of those integer will never be an integer..
say 2,3,4,5 -> (2+3+4+5)/4 = 14/4 = 3.5

Easy one got it in 57 sec.
_________________
We are twice armed if we fight with faith.

He who knows when he can fight & when He can't will be victorious.
Senior Manager  Status: Up again.
Joined: 31 Oct 2010
Posts: 464
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Re: x is the sum of y consecutive integers. w is the sum of z consecutive  [#permalink]

Show Tags

y= even number.
x= sum of y numbers

Rule is that average of even number of consecutive integers is never even. Therefore, x/y will never be an integer.

Do we need "w" here? or its just there to confuse? Because anyways its given z is a positive integer.
_________________
My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Originally posted by gmatpapa on 22 Apr 2011, 09:37.
Last edited by gmatpapa on 22 Apr 2011, 11:06, edited 1 time in total.
SVP  P
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1883
GMAT 1: 780 Q51 V48 GRE 1: Q800 V740 Re: Someone please explain this one  [#permalink]

Show Tags

The question can be restated as:
If x is the sum of y consecutive integers, and w is the sum of y/2 consecutive integers, and neither of y or z is 0, then which of the following can NEVER be true?

Note that since y>0 and z=y/2 and z>0 and both y and z are integers, y will always be an even integer.

(a) x=w. This is certainly possible. Take x=-2,-1,0,1,2,3 and w=0,1,2
(b) x>w. This is certainly possible. Take x=-2,-1,0,1,2,3 and w=-2,-1,0
(c) Correct answer. You can never make a case that satisfies this. Why?
Sum of the AP = (y/2) [2a+(y-1)*1]
If y = 2k as y is always even, Sum = x = k [2a+ (2k-1)]
If we divide this by y, i.e. 2k, we get x/y = k[2a+2k-1]/2k. This is an odd number divided by an even number, and so can never be an integer.
(d) This is certainly possible. Evaluates to [2a+(z-1)]/2, which can be true if z is odd.
(e) This is certainly possible. Take x=-2,-1,0,1 and then z=2, and x/z=-1, which is an integer.
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services Re: Someone please explain this one   [#permalink] 11 May 2012, 03:36

Go to page    1   2    Next  [ 34 posts ]

Display posts from previous: Sort by

x is the sum of y consecutive integers. w is the sum of z

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

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