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Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1 [#permalink]
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The question is hard in part because it's difficult to understand, because they're not using verb tenses correctly. And it's also true that there is no unique correct answer here, because there's no requirement that the answer be an integer: the two packages could just as easily weigh 25.4 ounces or 24.8 ounces as 25 ounces.

The first 12 packages weigh 120 ounces, so cost $60 to ship. The insurance costs $5, so the total cost for these packages is $65. Shipping two additional packages with no insurance increases the total price by less than 20%, so by less than $13. So those two packages must weigh less than 26 ounces in total, since we pay $0.50 per ounce. Logically, the largest remaining answer choice must now be correct (assuming the question has only one correct answer), but if you didn't see that was true, you can do the calculation: when we add $1 of insurance to the cost of shipping the two packages, we must increase the total cost by more than $13, so we must be paying more than $12 because of the weight alone of those packages, and they must weigh more than 24 ounces.
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The mean weight of 12 packages a retailer needs to ship on Monday is 1 [#permalink]
Original Sum of the 12 packages weight = (10 oz average) * (12) = 120 oz

The Charge is .50 cents an ounce and 5 packages are insured for 1 dollar each

Thus, the Original cost of the 12 packages =

(.5) * (120 oz) + $5 =

$65

Info. 1:
2 additional packages are shipped. If neither are insured, the percent increase is Less Than < 20%

Let the combined weight of the 2 packages = X

New Cost of 14 packages if Neither is Insured = (.5) * (120 + X) + 5 =
65 + .5X

% Increase ——> [ (New - Initial) / (Initial) ] * 100%

[ (65 + .5X) - 65 ] / (65) * 100% < 20%

——Divide Each side of Inequality by 100%——-

(.5X) / (65) < (20/100)

(.5X) / (65) < (1/5)

2.5X < 65

X < 26 ounces


2nd piece of info:
If 1 of the new packages is insured, the percent increase is GREATER Than > 20%

New Cost of 14 total packages = (.5) * (120 + X) + 6 = 66 + .5X


%Increase:

[ ((66 + .5X) - 65) / (65) ] * 100% > 20%

(1 + .5X) / (65) > 1/5

5 + 2.5X > 65

2.5X > 65

X > 24



From info. 1———> X < 26
From info. 2 ———> X > 24

24 < X < 26

The combined weight must be 25 ounces

-C-

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Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1 [#permalink]
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LeenaSai wrote:
The mean weight of 12 packages a retailer needs to ship on Monday is 10 ounces. The retailer pays 50 cents per ounce on shipping, plus one dollar per package for insurance on five of the packages. If two additional packages must be shipped on Monday, the percent increase on the retailer’s shipping cost for that day is less than 20% if neither package is insured and greater than 20% if one package is insured. What is the combined weight of the two additional packages, in ounces ?

A) 23
B) 24
C) 25
D) 26
E) 27


Solution:

Currently, the total shipping and insurance cost of the 12 packages is:

12 x 10 x 0.5 + 5 x 1 = 60 + 5 = $65

Let’s let w be the combined weight of the two additional packages, and we can now create the inequalities:

65 + 0.5w < 65 x 1.2 → 65 + 0.5w < 78 → 0.5w < 13

and

65 + 0.5w + 1 > 65 x 1.2 → 66 + 0.5w > 78 → 0.5w > 12

Therefore, we have:

12 < 0.5w < 13

24 < w < 26

Assuming the combined weight of the two packages must be a whole number of ounces, we see that w must be 25.

Answer: C
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Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1 [#permalink]
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Re: The mean weight of 12 packages a retailer needs to ship on Monday is 1 [#permalink]
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