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:

The sum of four consecutive odd numbers is equal to the sum [#permalink]
21 Sep 2011, 10:52

6

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

27% (03:46) correct
73% (11:27) wrong based on 240 sessions

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed?

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed? (A) 12 (B) 17 (C) 25 (D) 33 (E) 50

Four consecutive odd numbers: k-2, k, k+2, k+4 Three consecutive even numbers: n-2, n, n+2

Yeah!!! So I see. I'll wait for few others to point out the error. I can't think where I may be going wrong. BTW, what's the source of the problem? _________________

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed? (A) 12 (B) 17 (C) 25 (D) 33 (E) 50

Four consecutive odd numbers: k-2, k, k+2, k+4 Three consecutive even numbers: n-2, n, n+2

All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:

We know, 101<n<200 104<=n<=196

Count=(196-104)/4+1=92/4+1=23+1=24

Ans: 24.

k-2, k, k+2, k+4 n-2, n, n+2

Why did you take the minus??? Why not : Four consecutive odd numbers: O, O+2, O+4, O+6 Three consecutive even numbers: E, E+2, E+4 O+O+2+ O+4+ O+6 = E+ E+2+E+4 4O + 12 = 3E + 6 4O + 6 = 3E 4O = 3(E-2) O = 3(E-2)/4

1+3+5+7 = 16 3+5+7+9 = 24 5+7+9+11=32 ... so you can see the sum of 4 odd numbers increment by 8.

Therefore all even number that are divisible by 8 between 101-200 will have a possible series that adds up to it.. therefore 200-101/8 gives you 12.75 = 12!

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed? (A) 12 (B) 17 (C) 25 (D) 33 (E) 50

Four consecutive odd numbers: k-2, k, k+2, k+4 Three consecutive even numbers: n-2, n, n+2

Why did I consider: n-2, n, n+2: For the sake of simplicity, because we are given that 101<n<200 (Middle term of the even number)

According to given condition: Sum of 4 consecutive integers=Sum of 3 even integers k-2+k+k+2+k+4=n-2+n+n+2 4k+4=3n 4(k+1)=3n k=(3/4)n-1;

Now, we know that n(middle term of the even sequence) is between 101 and 200, exclusive

So, 101<n<200

But, we should also conform to the fact that k is ODD.

How can we get k as odd Say n=102; k=(3/4)*102-1=76.5-1=75.5(It is NOT ODD); so n=102 IS not a possible/valid sequence Likewise n=103; will also not give k as odd; n=104; k=(3/4)*104-1=77(ODD)

We see that if n=A multiple of 8, then k becomes ODD. How so?

4*Even=4*2x=Even So, n must be in the form of 8x.

105,106,107,108,109,110,111(They are not divisible by 8), thus k can't be an ODD integer

112 is divisible by 8.

So, if we find all the values from 101 to 200 that are divisible by 8, we will have our count. The sequence will be.

1st: 102,104,106 2nd: 110,112,114 3rd: 118,120,122 ... 12th: 190,192,194 Note: we just have to care about the middle term. The first term and last term will be follow: +-2.

Also, so far k is ANY ODD integer, we are good. _________________

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed? (A) 12 (B) 17 (C) 25 (D) 33 (E) 50

Sum of four consecutive odd numbers: (2a - 3) + (2a - 1) + (2a + 1) + (2a + 3) = 8a

Sum of three consecutive even numbers: (2b - 2) + 2b + (2b + 2) = 6b

Given 8a = 6b or a/b = 3/4, a and b can be any integers. So, 'a' has to be a multiple of 3 and 'b' has to be a multiple of 4. Possible solutions are: a = 3, b = 4; a = 6, b = 8; a = 9, b = 12 etc Since 101 < 2b < 200 i.e. 51 <= b < 100 Since b also has to be a multiple of 4, the values that b can take are 52, 56, 60, 64 ... 96 Number of values b can take = (Last term - First term)/Common Difference + 1 = (96 - 52)/4 + 1 = 12 _________________

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. _________________

Re: The sum of four consecutive odd numbers is equal to the sum [#permalink]
13 Nov 2013, 01:48

bindiyajoisher wrote:

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 200, how many such sequences can be formed?

(A) 12 (B) 17 (C) 25 (D) 33 (E) 50

We need to choose n : 101 < n < 200 and n is even, and (n-2) + n + (n+2) = sum of 4 consecutive odd numbers.

I am assuming the 4 consecutive odd numbers to be e-3, e-1, e+1, e+3 where e could be an even integer > 3.

Hence: (n-2) + n + (n+2) = e-3 + e-1 + e+1 + e+3

3n = 4e

Let us analyse the above equation. For the above equation to hold true, e should be a multiple of 6 (as it should have a 3 in it and is an even) and n should be a multiple of 8 (because n should have factors 4 and 2 as 3 is a prime already and 4e has these factors in RHS). This is the least requirement.

So every multiple of 8 will satisfy the above equation if I do not restrict e.

So possible values of n(for no restriction on e) = all multiples of 8 between 101 and 200 = 12.

Re: The sum of four consecutive odd numbers is equal to the sum [#permalink]
12 Apr 2015, 03:03

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. _________________

we have to find number which is both multiple of 6 and 8.

lets looks at the minimum sum 102+104+106 = 312 = 75+77+79+81

lets looks at maximum sum = 198+200 +202 = 600=197+ 199 + 201 + 203

so 312<=6(b+1) <= 600 and 6(b+1) should be divisible by 6 and 8 . 51<=b<=99, off these values whenever b+1 is multiple of 4 , 6(b+1) will be divisible by 8 and 6 too .

52 is first term and 96 is last , N= 12 . hope it helps . _________________

Thanks, Lucky

_______________________________________________________ Kindly press the to appreciate my post !!

gmatclubot

The sum of four consecutive odd numbers is equal to the sum
[#permalink]
12 Apr 2015, 08:37

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

There is one comment that stands out; one conversation having made a great impression on me in these first two weeks. My Field professor told a story about a...

Our Admissions Committee is busy reviewing Round 1 applications. We will begin sending out interview invitations in mid-October and continue until the week of November 9th, at which point...