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Jack bought five mobiles at an average price of $150. The Timer 00:00 Your Answer A B C D E Global Stats Difficult 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.

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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!!

Cheers,
Brent

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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. Five mobiles @$150 average price means $750 spent The middle phone cost$200 and there are two phones that cost that amount or more and two that cost that amount or less.

Therefore, the minimum price that the most expensive phone could cost without constraint is then $200, so that eliminates A. Let's assume$200 is the most expensive phone and see if the constraint of most expensive being minimum 3x least cost phone can be met

If the most expensive phone cost $200, then so did the next most costly since the median also cost$200. So that's $600 of the$750 spent, leaving $150 for the last two phones. The least cost phone costs no more than$200/3 or $66 2/3, leaving$150 - $66 2/3 =$83 1/3 as the cost of the next phone.

So, given that the $83 1/3 is greater than$66 2/3, the proper order is preserved and the constraint is met, answer B, 200

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