A retailer sells 5 shirts. The first two he sells for $64...

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

A retailer sells 5 shirts. The first two he sells for $64...

by AAPL » Sat Feb 24, 2018 5:08 am

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A retailer sells 5 shirts. The first two he sells for $64 and $39. If the retailer wishes to sell the 5 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 3 shirts?

A. $49.00
B. $49.67
C. $50.00
D. $51.33
E. $55.50

The OA is A.

We know that the price for the first two is
$$64+39=103$$
Then, he wishes to sell the 5 shirts for an overall average price of over $50, then
$$Price_{total}=5\cdot50=250$$
Also, we know that the price for the remaining 3 is
$$250-103=147\ \Rightarrow A_{Remaining\ 3}=\frac{147}{3}=49$$
Is there a strategic approach to this PS question? Can any experts help me, please? Thanks!

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Source: Beat The GMAT — Problem Solving | Sat Feb 24, 2018 5:08 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sat Feb 24, 2018 2:00 pm

Hi AAPL,

We're told that a retailer sells 5 shirts. The first two sell for $64 and $39 and the retailer wishes to sell the 5 shirts for an overall average price of over $50. We're asked for the minimum average price of the remaining 3 shirts.

To start, there's a minor issue with how this question is worded - the 'intent' of this prompt is to have us find a result that leads to an average price of all 5 shirts that is AT LEAST $50 (not "over $50"). In these types of straight-forward 'Average' questions, the fastest approach is almost always to set up the Average Formula and just do the necessary math steps. That having been said, on tougher Average questions, alternative ways to get to the correct answer can be a lot faster (and easier to implement) IF you know what those alternatives are. Here is an alternative to the the Average Formula:

As a simple example, if we have two numbers: 17 and 19, then the average would be 18. The number 17 is "one BELOW" and the number 19 is "one ABOVE" That "-1" and "+1" cancel out and we have the average.

In this question, we already have two of the values and the overall average:
The number 64 is "14 above" 50
The number 39 is "11 below" 50

So far, we are "+14" and "-11" --> so we are "3 above" what the average is supposed to be. To 'offset' that "+3", we need each of the 3 remaining shirts to be "-1" from the average.

Average price of the 3 remaining shirts = $50 - $1 = $49

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jun 10, 2019 6:32 pm

AAPL wrote:A retailer sells 5 shirts. The first two he sells for $64 and $39. If the retailer wishes to sell the 5 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 3 shirts?

A. $49.00
B. $49.67
C. $50.00
D. $51.33
E. $55.50