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 350,000 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:

If a is the sum of x consecutive positive integers. b is the [#permalink]
05 Mar 2012, 23:36

1

This post received KUDOS

15

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

32% (03:24) correct
68% (02:10) wrong based on 252 sessions

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

Re: sum of x consecutive positive integers [#permalink]
06 Mar 2012, 02:48

10

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b? A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

The sum n consecutive integers is give by: \(Sum=\frac{(2a_1+n-1)*n}{2}\) (check Number Theory chapter of Math Book for more: math-number-theory-88376.html);

Notice that: If \(n=even=2*odd\), so when \(n\) (# of consecutive integers) is even but not a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*odd)}{2}=odd*odd=odd\);

If \(n=even=2*even\), so when \(n\) is a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*even)}{2}=odd*even=even\);

That's because a set of even number of consecutive integers has half even and half odd terms. The sum of even terms is obviously even. As for odd terms: their sum is even if their number is even (so total # of terms is multiple of 4) and their sum is odd if their number is odd (so total number of terms is even but not a multiple of 4);

So, the sum of 10 (not a multiple of 4) consecutive integers will be odd (the sum of 5 even and 5 odd integers) and the sum of 4 (multiple of 4) consecutive integers will be even (the sum of 2 even and 2 odd integers), so option D is not possible.

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
06 Mar 2012, 22:48

Hi, I am struggling with the explanation.Here is what I had done. but was unable to eliminate answers the premise was that for x and y to be equal both should be either even or odd Please take a look and let me know

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
07 Mar 2012, 00:46

Expert's post

devinawilliam83 wrote:

Hi, I am struggling with the explanation.Here is what I had done. but was unable to eliminate answers the premise was that for x and y to be equal both should be either even or odd Please take a look and let me know

I'm not sure what you are trying to say there with the diagram but the 4th row is not correct: if the # of terms is multiple of 4 then the sum is even, regardless of the first term. _________________

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
27 Oct 2012, 20:25

3

This post received KUDOS

For consecutive terms , Sum = median * number of terms. So if m1 and m2 are two medians..

a= m1*x and b = 2*y

as per given condition. a=b => m1*x = m2*y if you put x=10 and y =4

10m1 = 4m2 => 5m1 = 2m2.....

When number of terms are even, the median is always a fraction. I.e 3.5 or 4.5 but when number of terms is odd then median is always an integer. Now in above case. m1 and m2 both are fractions but m2's fraction can be nullified by 2 which is multiplied by m2. But for m1 it is not the case.

So all combinations are possible but if number of terms are multiple of 4, then the other can not be of the form 4n+1 or 4n+2 or 4n+3.

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
02 Feb 2013, 10:05

Toooo good Bunuel... Instead of learning formula i am more comfortable with the conceptual approach. Do you think learning formula is integral for GMAT.

Re: sum of x consecutive positive integers [#permalink]
30 Nov 2013, 06:43

Bunuel wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b? A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

The sum n consecutive integers is give by: \(Sum=\frac{(2a_1+n-1)*n}{2}\) (check Number Theory chapter of Math Book for more: math-number-theory-88376.html);

Notice that: If \(n=even=2*odd\), so when \(n\) (# of consecutive integers) is even but not a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*odd)}{2}=odd*odd=odd\);

If \(n=even=2*even\), so when \(n\) is a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*even)}{2}=odd*even=even\);

That's because a set of even number of consecutive integers has half even and half odd terms. The sum of even terms is obviously even. As for odd terms: their sum is even if their number is even (so total # of terms is multiple of 4) and their sum is odd if their number is odd (so total number of terms is even but not a multiple of 4);

So, the sum of 10 (not a multiple of 4) consecutive integers will be odd (the sum of 5 even and 5 odd integers) and the sum of 4 (multiple of 4) consecutive integers will be even (the sum of 2 even and 2 odd integers), so option D is not possible.

Answer: D.

Hope it's clear.

Brunel ,

Sum = n/2( 2a +(n-1)d ).....i still not able to get ur sum formula . I guess for consecutive number you are taking d=1 ...

Re: sum of x consecutive positive integers [#permalink]
01 Dec 2013, 05:20

Expert's post

archit wrote:

Bunuel wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b? A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

The sum n consecutive integers is give by: \(Sum=\frac{(2a_1+n-1)*n}{2}\) (check Number Theory chapter of Math Book for more: math-number-theory-88376.html);

Notice that: If \(n=even=2*odd\), so when \(n\) (# of consecutive integers) is even but not a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*odd)}{2}=odd*odd=odd\);

If \(n=even=2*even\), so when \(n\) is a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*even)}{2}=odd*even=even\);

That's because a set of even number of consecutive integers has half even and half odd terms. The sum of even terms is obviously even. As for odd terms: their sum is even if their number is even (so total # of terms is multiple of 4) and their sum is odd if their number is odd (so total number of terms is even but not a multiple of 4);

So, the sum of 10 (not a multiple of 4) consecutive integers will be odd (the sum of 5 even and 5 odd integers) and the sum of 4 (multiple of 4) consecutive integers will be even (the sum of 2 even and 2 odd integers), so option D is not possible.

Answer: D.

Hope it's clear.

Brunel ,

Sum = n/2( 2a +(n-1)d ).....i still not able to get ur sum formula . I guess for consecutive number you are taking d=1 ...

Yes, the common difference between the numbers in a set of consecutive numbers is 1. _________________

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
01 Dec 2013, 07:09

devinawilliam83 wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

this is a very bad question ... no way a GMAT question... very time consuming ...

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
11 Apr 2014, 03:53

6

This post received KUDOS

devinawilliam83 wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

Sum of 2 consecutive integers = Odd Sum of 4 consecutive integers = Even Sum of 6 consecutive integers = Odd Sum of 8 consecutive integer = Even and so on is the pattern.

If we look at answer option D. Sum of 10 consecutive integer = Odd, Sum of 4 consecutive integers = Even.

Odd cannot be equal to Even.

Hence the answer is D. _________________

Perfect Scores

If you think our post was valuable then please encourage us with Kudos

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
05 Jan 2015, 23:15

1

This post received KUDOS

Expert's post

mdcash wrote:

devinawilliam83 wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

this is a very bad question ... no way a GMAT question... very time consuming ...

Actually, it isn't that bad. There is the logical approach of number properties that you can use but even if that doesn't work out in the limited time, go with brute force!

A. x = 2; y = 6

Sum of first 6 numbers is 6*7/2 = 21 Can the sum of two consecutive numbers be 21? Sure 10 and 11. Out

B. x = 3; y = 6 Sum of first 6 numbers is 21. Can sum of three consecutive numbers be 21? Divide 21 by 3 to get 7. The three numbers will be 6, 7, 8. Out

C. x = 7; y = 9 Sum of first 9 numbers is 9*10/2 = 45. Can sum of 7 consecutive numbers be 45? 45 is not divisible by 7 so this will not work. Try another method: Sum1 = Sum2 7*Mean1 = 9*Mean2 If Mean1 = 9 and Mean2 = 7, it will satisfy. i.e. 6, 7, 8, 9, 10, 11, 12 and 3, 4, 5, 6, 7, 8, 9, 10, 11 Out

D. x = 10; y = 4 10*Mean1 = 4*Mean2 Mean1/Mean2 = 2/5 Both Mean1 and Mean2 must be fractions "something.5" (Even consecutive numbers) Also, Mean1 = 2x and Mean2 = 5x Hard. Hold it.

E. x = 10; y = 7 10*Mean1 = 7*Mean2 Mean1/Mean2 = 7/10 Mean1 must be a fraction "something.5" (10 consecutive numbers) and Mean2 must be an integer (7 consecutive numbers) Such as 3.5/5 but you don't have 10 positive integers around 3.5 So perhaps 10.5/15 The numbers are 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 12, 13, 14, 15, 16, 17, 18 Out

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
16 Jun 2015, 22:17

devinawilliam83 wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?

A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

Ok, I did it simply in the head...here it is

x = 10 : (sum of 5 even no.+ sum of 5 odd no.)=(even+odd)=odd number over all. y = 4 : (sum of 2 even no.+sum of 2 odd no.)=(even+even)=even number over all.

Re: If a is the sum of x consecutive positive integers. b is the [#permalink]
27 Jun 2015, 07:05

Bunuel wrote:

If a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b? A. x = 2; y = 6 B. x = 3; y = 6 C. x = 7; y = 9 D. x = 10; y = 4 E. x = 10; y = 7

The sum n consecutive integers is give by: \(Sum=\frac{(2a_1+n-1)*n}{2}\) (check Number Theory chapter of Math Book for more: math-number-theory-88376.html);

Notice that: If \(n=even=2*odd\), so when \(n\) (# of consecutive integers) is even but not a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*odd)}{2}=odd*odd=odd\);

If \(n=even=2*even\), so when \(n\) is a multiple 4 then \(Sum=\frac{(2a_1+n-1)*n}{2}=\frac{(even+even-odd)*(2*even)}{2}=odd*even=even\);

That's because a set of even number of consecutive integers has half even and half odd terms. The sum of even terms is obviously even. As for odd terms: their sum is even if their number is even (so total # of terms is multiple of 4) and their sum is odd if their number is odd (so total number of terms is even but not a multiple of 4);

So, the sum of 10 (not a multiple of 4) consecutive integers will be odd (the sum of 5 even and 5 odd integers) and the sum of 4 (multiple of 4) consecutive integers will be even (the sum of 2 even and 2 odd integers), so option D is not possible.

Answer: D.

Hope it's clear.

Hi Bunuel, Could you please explain why we're only dealing with n=even here? Also I'm unable to understand the part "As for odd terms: their sum is even if their number is even (so total # of terms is multiple of 4) and their sum is odd if their number is odd (so total number of terms is even but not a multiple of 4);". Can you please clarify? Thanks

gmatclubot

Re: If a is the sum of x consecutive positive integers. b is the
[#permalink]
27 Jun 2015, 07:05

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...