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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

x is the sum of y consecutive integers. w is the sum of z co [#permalink]

Show Tags

18 Nov 2009, 20:37

1

This post received KUDOS

33

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

35% (02:13) correct
65% (01:37) wrong based on 735 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

Re: x is the sum of y consecutive integers. w is the sum of z co [#permalink]

Show Tags

18 Nov 2009, 22:37

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=5, TRUE

Case 2: x > w if y = [2,3] z = [1] 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 = [2] w = 2 2/1 is an integer, TRUE

Case 5: x/z is an integer if x = 9, z = [2] 9/1 is an integer, TRUE

Re: x is the sum of y consecutive integers. w is the sum of z co [#permalink]

Show Tags

19 Nov 2009, 03:07

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=5, TRUE

Case 2: x > w if y = [2,3] z = [1] 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 = [2] w = 2 2/1 is an integer, TRUE

Case 5: x/z is an integer if x = 9, z = [2] 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...

Last edited by kp1811 on 19 Nov 2009, 04:28, edited 1 time in total.

Re: x is the sum of y consecutive integers. w is the sum of z co [#permalink]

Show Tags

19 Nov 2009, 03:53

23

This post received KUDOS

15

This post was BOOKMARKED

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.

Answer : C _________________

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

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

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

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|

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.
_________________

x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 02:08

1

This post was BOOKMARKED

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

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 02:19

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?
_________________

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 02:29

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.
_________________

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 02:55

1

This post received KUDOS

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.

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 03:12

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.
_________________

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 04:17

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!!
_________________

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

21 Apr 2011, 05:09

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!!

Re: x is the sum of y consecutive integers. w is the sum of z consecutive [#permalink]

Show Tags

22 Apr 2011, 05:34

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.

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...