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

 It is currently 17 Oct 2019, 23:16

### 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

# The arithmetic mean of the even integers from 200 to 300

Author Message
TAGS:

### Hide Tags

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3335
Location: India
GPA: 3.12
The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

22 Dec 2017, 07:00
3
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:28) correct 29% (01:57) wrong based on 85 sessions

### HideShow timer Statistics

The arithmetic mean of the even integers from 200 to 300 (both inclusive) is greater by what number than the arithmetic mean of the odd integers in the same range?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Experts Global

_________________
You've got what it takes, but it will take everything you've got
Intern
Joined: 30 Aug 2017
Posts: 7
WE: Supply Chain Management (Other)
Re: The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

22 Dec 2017, 07:33

300-200 + 1 = 101
299-201 + 1 = 99
101 - 99 = 2
Current Student
Joined: 28 May 2014
Posts: 515
GMAT 1: 730 Q49 V41
Re: The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

22 Dec 2017, 07:56
2
pushpitkc wrote:
The arithmetic mean of the even integers from 200 to 300(both inclusive) is greater by what number
than the arithmetic mean of the odd integers in the same range?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Experts Global

Lets consider a smaller range:
(1) 200 to 204
even numbers: 200, 202, 204; Avg = 202
Odd numbers: 201, 203; Avg = (201+203)/2 = 202
Difference = 0

(1) 200 to 210
even numbers: 200, 202, 204, 206, 208, 210; Avg = (204+206)/2 = 205
Odd numbers: 201, 203, 205, 207, 209 Avg = (201+203+205+207+209)/5 = 205
Difference = 0

Ans: C.
_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 1140
Re: The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

22 Dec 2017, 07:57
Writing down the first few elements of the two sequences can help us understand what we're dealing with.
This is a Logical approach.

The even numbers between 200 to 300 are 200, 202, 204..... 296, 298, 300.
As usual for sequences on the GMAT, the difference between each two terms is constant.
So, the sum of the first and last terms (200+300) equals the sum of the second and second-last terms (202+298) and so on.
Then the average of this sequence is just (200+300)/2=250.

Similarly, the odd sequence is 201, 203, 205....295, 297, 299.
Once again, the sum of the first and last (201+299) is the same as the sum of the second and second-last (203 + 297) and so on.
Then the average of this sequence is (201+299)/2=250.

Therefore the difference between averages is 0.
_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3553
The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

22 Dec 2017, 09:54
1
pushpitkc wrote:
The arithmetic mean of the even integers from 200 to 300(both inclusive) is greater by what number
than the arithmetic mean of the odd integers in the same range?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: Experts Global

Evenly spaced sequence

The arithmetic mean of an arithmetic sequence is
$$\frac{FirstTerm + LastTerm}{2}$$

Even integers, arithmetic mean:
$$\frac{200+300}{2} = 250$$

Odd integers, arithmetic mean:
$$\frac{201 + 299}{2} = 250$$

Difference: 0

Small sample
As posters above demonstrate, to use a small sample is often shrewd.
Yet another way to take a small sample:

Replicate the pattern of the numbers in the prompt
• begin and end with even numbers
• if you're not sure, use integers that end in the same units digit (here, 0), and
• if you're going to do all the math, choose small numbers

The arithmetic mean of the even integers from 0 to 10, inclusive
$$0, 2, 4, 6, 8, 10$$, where $$A =\frac{S}{n} = \frac{30}{6} = 5$$

Arithmetic mean of odd integers from 0 to 10, inclusive
$$1, 3, 5, 7, 9$$, where $$A=\frac{S}{n} = \frac{25}{5} = 5$$
Difference: 0

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Non-Human User
Joined: 09 Sep 2013
Posts: 13239
Re: The arithmetic mean of the even integers from 200 to 300  [#permalink]

### Show Tags

04 Aug 2019, 07:02
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.
_________________
Re: The arithmetic mean of the even integers from 200 to 300   [#permalink] 04 Aug 2019, 07:02
Display posts from previous: Sort by