Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 Jul 2015, 13:45

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Three straight metal rods have an average (arithmetic mean)

Author Message
TAGS:
Manager
Joined: 25 Jul 2012
Posts: 81
Location: United States
Followers: 0

Kudos [?]: 38 [0], given: 137

Three straight metal rods have an average (arithmetic mean) [#permalink]  27 Feb 2013, 21:23
3
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:55) correct 24% (00:52) wrong based on 161 sessions
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A. 71
B. 77
C. 80
D. 83
E. 89

Source: GMAT Prep Question Pack 1
Rated: Medium

If you know of any similar problems, please post.
[Reveal] Spoiler: OA

_________________

If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

 Kaplan Promo Code Knewton GMAT Discount Codes Veritas Prep GMAT Discount Codes
Manager
Joined: 24 Sep 2012
Posts: 90
Location: United States
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Followers: 4

Kudos [?]: 86 [0], given: 3

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  27 Feb 2013, 22:32
We know that there are 3 metal rods with an average length of 77 inches.
Total length=77*3=231 inches
Shortest rod length=65 inches
the sum of lengths of the two longer rods=231-65=166
Since, the longer rods have to be longer than 65, the smallest value one of these longer values could have is 66.

Now the question asks us for the longest median value. The median value is the middle value when the three rods are arranged in ascending order of lengths.

There are two ways of finding these values
1. Since we need to find the largest middle value, the two longer rods need to be of equal length. If both values are equal in length the middle value will be the largest possible value and the longest rod will be of the same length as the rod of median length. Hence, 2x =166 implies x=83.

Maximum length of the median rod=83

2. Testing the values given
Let us test the values from the bottom

e=89
166-89=77. Since 77 is less than 89, it cannot be the median value. WRONG

d=83
166-83=83. Both the rods are of the same length. Hence, this is the largest possible middle value.

DelSingh wrote:
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A.71
B.77
C.80
D.83
E.89

Source: GMAT Prep Question Pack 1
Rated: Medium

If you know of any similar problems, please post.

_________________

Thanks
Kris
Instructor at Aspire4GMAT

Visit us at http://www.aspire4gmat.com

New blog: How to get that 700+
New blog: Data Sufficiency Tricks

Press Kudos if this helps!

Math Expert
Joined: 02 Sep 2009
Posts: 28286
Followers: 4479

Kudos [?]: 45292 [1] , given: 6647

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  28 Feb 2013, 00:17
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
DelSingh wrote:
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A. 71
B. 77
C. 80
D. 83
E. 89

Source: GMAT Prep Question Pack 1
Rated: Medium

If you know of any similar problems, please post.

Say the lengths of the rods in ascending order are $$x_1$$, $$x_2$$, and $$x_3$$, where $$x_1\leq{x_2}\leq{x_3}$$.

The median of a set with odd number of terms is just the middle term, when arranged in ascending/descending order, hence the median is $$x_2$$.

Given that $$x_1+x_2+x_3=3*77$$ --> $$65+x_2+x_3=3*77$$ --> $$x_2+x_3=166$$. We need to maximize $$x_2=median$$, so we need to minimize $$x_3$$.

The minimum value of $$x_3$$ is $$x_2$$ --> $$x_2+x_2=166$$ --> $$x_2=median=83$$.

Similar topics:
gmat-diagnostic-test-question-79347.html
seven-pieces-of-rope-have-an-average-arithmetic-mean-lengt-144452.html
a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html
the-median-of-the-list-of-positive-integers-above-is-129639.html
in-a-certain-set-of-five-numbers-the-median-is-128514.html
given-distinct-positive-integers-1-11-3-x-2-and-9-whic-109801.html
set-s-contains-seven-distinct-integers-the-median-of-set-s-101331.html
three-boxes-have-an-average-weight-of-7kg-and-a-median-weigh-99642.html

Hope it helps.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629
Followers: 57

Kudos [?]: 726 [0], given: 135

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  28 Feb 2013, 03:55
Expert's post
DelSingh wrote:
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A. 71
B. 77
C. 80
D. 83
E. 89

If you know of any similar problems, please post.

Because it is mentioned that the average length of the three rods is 77 inches, we can assume there are three rods each of length 77 inches. Now we have been told that the shortest rod has a length of 65 inches. Thus, we can take 12 inches from one of the rods and will have to adjust it amongst the other two remaining rods. Now, if we divide 12 in any proportion other than 6 and 6, we will not have the maximum value for the median. Imagine, we redistribute 12 by giving 5 to one and 7 to another. This gives 65, 82 and 84.
Thus, giving 6 to both the rods, we have (77+6) = 83 inches for both the rods.

D.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 23

Kudos [?]: 967 [0], given: 193

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  21 Aug 2013, 20:41
Smallest rod = 65
Average of all 3 rods = 77

Lets consider middle rod = 77, so the largest rod (x) calculation is:
65 + x = 77*2
x = 154 - 65 = 89.
Now, considering that middle rod = 77, the max lenght of the largest rod would be = 89.
So the max length of the middle rod possible = Avg of 89 & 77
= (89 +77)/2 = 83
_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Joined: 15 Aug 2013
Posts: 331
Followers: 0

Kudos [?]: 23 [0], given: 23

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  07 Dec 2014, 12:04
Bunuel wrote:
DelSingh wrote:
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A. 71
B. 77
C. 80
D. 83
E. 89

Source: GMAT Prep Question Pack 1
Rated: Medium

If you know of any similar problems, please post.

Say the lengths of the rods in ascending order are $$x_1$$, $$x_2$$, and $$x_3$$, where $$x_1\leq{x_2}\leq{x_3}$$.

The median of a set with odd number of terms is just the middle term, when arranged in ascending/descending order, hence the median is $$x_2$$.

Given that $$x_1+x_2+x_3=3*77$$ --> $$65+x_2+x_3=3*77$$ --> $$x_2+x_3=166$$. We need to maximize $$x_2=median$$, so we need to minimize $$x_3$$.

The minimum value of $$x_3$$ is $$x_2$$ --> $$x_2+x_2=166$$ --> $$x_2=median=83$$.

Similar topics:
gmat-diagnostic-test-question-79347.html
seven-pieces-of-rope-have-an-average-arithmetic-mean-lengt-144452.html
a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html
the-median-of-the-list-of-positive-integers-above-is-129639.html
in-a-certain-set-of-five-numbers-the-median-is-128514.html
given-distinct-positive-integers-1-11-3-x-2-and-9-whic-109801.html
set-s-contains-seven-distinct-integers-the-median-of-set-s-101331.html
three-boxes-have-an-average-weight-of-7kg-and-a-median-weigh-99642.html

Hope it helps.

Hi,

Is there a reason we cannot assume that the median is the mean in this case? Does that ONLY apply to evenly spaced sets?
Math Expert
Joined: 02 Sep 2009
Posts: 28286
Followers: 4479

Kudos [?]: 45292 [0], given: 6647

Re: Three straight metal rods have an average (arithmetic mean) [#permalink]  08 Dec 2014, 02:23
Expert's post
russ9 wrote:
Bunuel wrote:
DelSingh wrote:
Three straight metal rods have an average (arithmetic mean) length of 77 inches and the shortest rod has a length of 65 inches. What is the maximum possible value of the median length, in inches, of the three rods?

A. 71
B. 77
C. 80
D. 83
E. 89

Source: GMAT Prep Question Pack 1
Rated: Medium

If you know of any similar problems, please post.

Say the lengths of the rods in ascending order are $$x_1$$, $$x_2$$, and $$x_3$$, where $$x_1\leq{x_2}\leq{x_3}$$.

The median of a set with odd number of terms is just the middle term, when arranged in ascending/descending order, hence the median is $$x_2$$.

Given that $$x_1+x_2+x_3=3*77$$ --> $$65+x_2+x_3=3*77$$ --> $$x_2+x_3=166$$. We need to maximize $$x_2=median$$, so we need to minimize $$x_3$$.

The minimum value of $$x_3$$ is $$x_2$$ --> $$x_2+x_2=166$$ --> $$x_2=median=83$$.

Similar topics:
gmat-diagnostic-test-question-79347.html
seven-pieces-of-rope-have-an-average-arithmetic-mean-lengt-144452.html
a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html
the-median-of-the-list-of-positive-integers-above-is-129639.html
in-a-certain-set-of-five-numbers-the-median-is-128514.html
given-distinct-positive-integers-1-11-3-x-2-and-9-whic-109801.html
set-s-contains-seven-distinct-integers-the-median-of-set-s-101331.html
three-boxes-have-an-average-weight-of-7kg-and-a-median-weigh-99642.html

Hope it helps.

Hi,

Is there a reason we cannot assume that the median is the mean in this case? Does that ONLY apply to evenly spaced sets?

For an evenly spaced set (arithmetic progression), the median equals to the mean. Though the reverse is not necessarily true. Consider {0, 1, 1, 2} --> median = mean = 1 but the set is not evenly spaced.

So, for the original question we cannot assume that the mean and the median are the same.
_________________
Re: Three straight metal rods have an average (arithmetic mean)   [#permalink] 08 Dec 2014, 02:23
Similar topics Replies Last post
Similar
Topics:
Three sisters have an average (arithmetic mean) age of 25 ye 2 14 Jan 2013, 05:16
80 Seven pieces of rope have an average (arithmetic mean) lengt 23 20 Dec 2012, 06:46
21 Three boxes of supplies have an average (arithmetic mean) 7 05 Dec 2010, 13:17
2 The average (arithmetic mean) of a normal distribution of a 11 16 Aug 2010, 10:25
4 The average (arithmetic mean) of the multiples of 6 4 28 May 2010, 12:57
Display posts from previous: Sort by