The average height of the four Torres towers is 800 feet. If the four

Question

The average height of the four Torres towers is 800 feet. If the four Torres towers have a median height of 900 feet, what is the greatest possible height of the shortest building of the four?

A. 100 feet
B. 300 feet
C. 500 feet
D. 600 feet
E. 800 feet

Bunuel · Accepted Answer

a_1\leq{a_2}\leq{a_3}\leq{a_4} ; The average height of the four Torres towers is 800 feet: a_1+a_2+a_3+a_4=4*800 ; The median height of 900 feet: \frac{a_2+a_3}{2}=900 --> a_2+a_3=1800 ; Substitute a_2+a_3=1800 into a_1+a_2+a_3+a_4=4*80 : a_1+1800+a_4=4*800 ; a_1+a_4=1400 . To maximize a_1 we should minimize a_4 . Minimum value of a_4 is 900 (the median value), thus the maximum value of a_1 is 1400 - 900 = 500. Answer: C. a_1\leq{a_2}\leq{a_3}\leq{a_4} ; The average height of the four Torres towers is 800 feet: a_1+a_2+a_3+a_4=4*800 ; The median height of 900 feet: \frac{a_2+a_3}{2}=900 --> a_2+a_3=1800 ; Substitute a_2+a_3=1800 into a_1+a_2+a_3+a_4=4*80 : a_1+1800+a_4=4*800 --> a_1+a_4=1400 . To maximize a_1 we should minimize a_4 . Minimum value of a_4 is 900 (the median value), thus the maximum value of a_1 is 1400 - 900 = 500. Answer: C. Similar questions to practice: https://gmatclub.com/forum/five-peices-o ... 23513.html https://gmatclub.com/forum/company-c-sel ... 23415.html https://gmatclub.com/forum/the-guests-at ... 39648.html https://gmatclub.com/forum/686-000-in-bo ... 27503.html https://gmatclub.com/forum/a-certain-cit ... 76217.html https://gmatclub.com/forum/if-the-averag ... 27038.html https://gmatclub.com/forum/in-a-certain- ... 26030.html https://gmatclub.com/forum/the-average-a ... 07059.html https://gmatclub.com/forum/a-club-with-a ... 06123.html https://gmatclub.com/forum/three-boxes-o ... 05819.html https://gmatclub.com/forum/a-club-with-a ... 04850.html https://gmatclub.com/forum/three-boxes-h ... 99642.html Other Min/Max questions are HERE (DS) and HERE (PS).

Sunil2424 · Answer

Let us say the four towers are A, B, C & D.
The average height is 800 ft thus total height is 3200 ft.
The median height is 900 ft. Thus B+C/2 =900. 
Let us assume B and C have equal height of 900 ft and to get max height of A (which in this case is the shortest) 
then D height is also 900ft.
Then height of A is 500 ft.

C is the answer

Nidzo · Answer

Together their height is 800*4 = 3200

To make the smallest height the greatest it can be, minimize the greatest height. As the median is 900 the smallest size the biggest tower can be is 900. This makes the 3 largest towers have an equal height.
900*3 = 2700

3200-2700 = 500

Answer C

Showmeyaa · Answer

Let's assume these 4 boxes to be the heights of the buildings in ascending order:
  _1st_ _2nd_ _3rd_ _4th_

Total height = 800*4 = 3200
Given:  \frac{2nd + 3rd}{2} = 900 
 2nd + 3rd = 1800 
So, 1st + 4th have to sum to 1400.
So, to maximize 1st, we have to minimize 4th.
4th has to be at least 900, so, 1st has to be 500(C)

The average height of the four Torres towers is 800 feet. If the four

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The average height of the four Torres towers is 800 feet. If the four

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards