Problem Solving

AAPL wrote:e-GMAT

Jack bought five mobiles at an average price of $150. The median of all the prices is $200. What is the minimum possible price of the most expensive mobile that Jack has bought, if the price of the most expensive mobile is at least thrice that of the least expensive mobile?

A. $150
B. $200
C. $250
D. $300
E. $350

OA B.

Jack bought five mobiles at an average price of $150.
So, (sum of all 5 mobiles)/5 = $150
Multiply both sides by 5 to get: sum of all 5 mobiles = $750

The median of all the prices is $200.
Let a = smallest value
Let b = 2nd smallest value
Let d = largest value
Let c = 2nd largest value
So, when we arrange the values in ASCENDING order we get: a, b, $200, c, d

From here, a quick approach is to test each answer choice, starting from the smallest value

A) $150
This answer choice suggests that d = $150, which is impossible, since the greatest value cannot be less than the median ($200)
ELIMINATE A

B) $200
This answer choice suggests that d = $200
Let's add this to our list to get: a, b, $200, c, $200
This means c must also equal $200. So we have: a, b, $200, $200, $200

Is it possible to assign values to a and b so that all of the conditions are met?
YES!
We must satisfy the condition that sum of all 5 mobiles = $750 and it must be the case that the price of the most expensive mobile is at least thrice that of the least expensive mobile
Well, if we let a = $50, then the price of the most expensive mobile ($200) is at least thrice that of the least expensive mobile ($50)
Finally, if we let b = $100, we get: $50, $100, $200, $200, $200, which meets the condition that sum of all 5 mobiles = $750
PERFECT!!

Answer: B

Cheers,
Brent