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Jack bought five mobiles at an average price of $152. The median of al

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Jack bought five mobiles at an average price of $152. The median of al  [#permalink]

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New post Updated on: 13 Aug 2018, 00:48
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Question Stats:

51% (02:40) correct 49% (02:51) wrong based on 150 sessions

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Solve any Median and Range question in a minute- Exercise Question #1

1- 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.

Options

    a) $150
    b) $200
    c) $250
    d) $300
    e) $350

To solve question 2: Question 2

To read the article: Solve any Median and Range question in a minute

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Originally posted by EgmatQuantExpert on 11 Jul 2018, 08:00.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:48, edited 4 times in total.
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Re: Jack bought five mobiles at an average price of $152. The median of al  [#permalink]

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New post 11 Jul 2018, 08:51
1
The answer is B.
My explanation:
a) cannot be the answer as the median itself is $200.
b) correct
c) Let's assume the 5th phone (in terms of ascending prices) is of $250. Then the two extreme cases are possible for the value of x4 (x1, x2, $200, x4, $250) - it can either be $200 or $250. If it is $250, then in the eq. 152 = (x1+x2+200+250+250)/5, x1+x2 = 60 but according to the question, 3*x1 = 250 => x1 ~ 89. NOT POSSIBLE. If x4 is $200, then in the eq. 152 = (x1+x2+200+200+250)/5, x1+x2 = 110 and ideally x1 should be greater than 89, but if it is the case then x2<x1. NOT POSSIBLE.
d) Solving similarly as option c. No solution possible.
e) Solving similarly as option c. No solution possible.

Hence the correct answer is B.
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Re: Jack bought five mobiles at an average price of $152. The median of al  [#permalink]

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New post 13 Sep 2018, 07:23
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EgmatQuantExpert wrote:
1- 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.

Options

    a) $150
    b) $200
    c) $250
    d) $300
    e) $350


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

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Re: Jack bought five mobiles at an average price of $152. The median of al  [#permalink]

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New post 29 Mar 2019, 11:41
EgmatQuantExpert

Can you please explain how to solve this question using the below approach mentioned in the article
o To find the maximum value of a variable, we minimize the value of all the other unknown variables present in set.
o To find the minimum value of a variable, we maximize the value of all the other unknown variables present in set.
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Re: Jack bought five mobiles at an average price of $152. The median of al  [#permalink]

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New post 10 Apr 2019, 17:59
EgmatQuantExpert wrote:
Solve any Median and Range question in a minute- Exercise Question #1

1- 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.

Options

    a) $150
    b) $200
    c) $250
    d) $300
    e) $350


We are looking for the minimum possible price of the most expensive mobile. Notice that the total price of the 5 mobiles is 150 x 5 = $750, and the median price is $200, Let’s now analyze the given answer choices.

Since the price of the most expensive mobile must be at least the median price, we can eliminate choice A. So let’s start with choice B.

B. $200

If the price of the most expensive mobile is $200, then each of 3 most expensive mobiles is $200. So the total price of the 2 least expensive mobile is 750 - 3 x 200 = $150. We can have the least expensive mobile as $50 and the second least expensive mobile as $100. So the price of the most expensive mobile is 4 times (which is at least 3 times) the price of the least expensive mobile. This satisfies the given parameters of the problem. So the correct answer is B.

Answer: B
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Re: Jack bought five mobiles at an average price of $152. The median of al   [#permalink] 10 Apr 2019, 17:59
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