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hardikrs · 2009 November 2nd, 03:21 AM

Last month 15 homes were sold in town X. The average sale price of the homes was $150,000 and the median price was $130,000. Which of the following statements must be true.

1. At least one of the homes was sold for more than $165,000
2. At least one of the homes was sold for more than $130,000 and less than $150,000
3. At least one of the homes was sold for less than $130,000

A. I only
B. II only
C. III Only
D. I and II only
E. I and III only.

Please explain your answer.

thanks

touche · 2009 November 2nd, 04:43 AM

1. for sure.... diff between avg and median is 2k, then atleast one house will go upto 15+2=17k.
2. maybe... or all could be below 13k.
3. maybe... or all could satisfy range at stat 2.

IMO A

Attack · 2009 November 3rd, 04:15 PM

i also go with A.
We have avg=150k and median = 130k, Also total number of values= 15.
Therefore sum of values= 150k* 15 = 2250k.
Now, to find the Maximum value, under the constraint of given median, Consider the following set of values.
130,130,130,130,130,130,130,130,130,x,y,z,a,b,c,d.
the sum of the values is 2250.
hence sum of x,y,z,a,b,c,d= 2250-130*8= 1210.
if each of xyzabcd is equal then each is 1210/7 ~ 173.

Hence there is at least one value > 172.
Condition number 1. is satisfied.
(note that we can definitely have values less than 130 which satisfy the median criteria for the given values. But each value <130 will only add to the maximum value possilbe)
Condition 2. As we can see from the above set of values, it is not a necessary condition.
Condition 3. Again not a necessary condition as per the above set of values.
Hence A.

hardikrs · 2009 November 6th, 04:33 PM

since median is 130K, doesn't that mean house #8 = 130K, so there are 7 house less than 130K and 7 house greater than 130K, so shouldn;t it be I and III?

touche · 2009 November 7th, 01:32 PM

Quote:

Originally Posted by hardikrs

since median is 130K, doesn't that mean house #8 = 130K, so there are 7 house less than 130K and 7 house greater than 130K, so shouldn;t it be I and III?

Median 130k implies that #1 to #7=<130k, not necessarily less than 130k.

arindambanerji · 2009 November 12th, 08:36 AM

IMO A

(2250000-1040000)/7

2009 November 2nd, 03:21 AM	#1 (permalink)
hardikrs TestMagic Guru-in-Training Join Date: Apr 2008 Posts: 518	GPREP PS #23 Last month 15 homes were sold in town X. The average sale price of the homes was $150,000 and the median price was $130,000. Which of the following statements must be true. 1. At least one of the homes was sold for more than $165,000 2. At least one of the homes was sold for more than $130,000 and less than $150,000 3. At least one of the homes was sold for less than $130,000 A. I only B. II only C. III Only D. I and II only E. I and III only. Please explain your answer. thanks

2009 November 2nd, 04:43 AM	#2 (permalink)
touche Within my grasp! Join Date: Jun 2009 Location: mumbai Posts: 289	1. for sure.... diff between avg and median is 2k, then atleast one house will go upto 15+2=17k. 2. maybe... or all could be below 13k. 3. maybe... or all could satisfy range at stat 2. IMO A _ _ _ _ SIG _ _ _ _ Looking high and Low

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2009 November 3rd, 04:15 PM	#3 (permalink)
Attack Eager! Join Date: Apr 2009 Location: Chicago Posts: 31	i also go with A. We have avg=150k and median = 130k, Also total number of values= 15. Therefore sum of values= 150k* 15 = 2250k. Now, to find the Maximum value, under the constraint of given median, Consider the following set of values. 130,130,130,130,130,130,130,130,130,x,y,z,a,b,c,d. the sum of the values is 2250. hence sum of x,y,z,a,b,c,d= 2250-130*8= 1210. if each of xyzabcd is equal then each is 1210/7 ~ 173. Hence there is at least one value > 172. Condition number 1. is satisfied. (note that we can definitely have values less than 130 which satisfy the median criteria for the given values. But each value <130 will only add to the maximum value possilbe) Condition 2. As we can see from the above set of values, it is not a necessary condition. Condition 3. Again not a necessary condition as per the above set of values. Hence A.

2009 November 6th, 04:33 PM	#4 (permalink)
hardikrs TestMagic Guru-in-Training Join Date: Apr 2008 Posts: 518	since median is 130K, doesn't that mean house #8 = 130K, so there are 7 house less than 130K and 7 house greater than 130K, so shouldn;t it be I and III?

2009 November 12th, 08:36 AM	#6 (permalink)
arindambanerji TestMagic Guru-in-Training Join Date: Feb 2008 Posts: 741	IMO A (2250000-1040000)/7

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