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# On Days 1 through 4 of a recent week, Product X was out of stock at

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Re: On Days 1 through 4 of a recent week, Product X was out of stock at [#permalink]
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Official Explanation

According to the graph and the accompanying text, 25% of the Day 1 shoppers returned on Day 2, and 19% of those shoppers subsequently returned on Day 3. Thus, on Day 3, 100(.25)(.19) = 4.75% of Day 1 shoppers returned to the store.

The correct answer is Between 1 and 10.

Day 1 shoppers who purchased an item in place of Product X paid, on average, 130% of the amount that they would have paid for Product X. According to the graph, 60% of Day 1 shoppers chose to buy an alternative product on Day 1. The total spent by these shoppers, as a fraction of the total all Day 1 shoppers would have spent had each instead bought Product X, is $$\frac{(60)(130)}{(100)(100)} = \frac{7,800}{10,000}$$, or 78%.

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On Days 1 through 4 of a recent week, Product X was out of stock at [#permalink]
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parkhydel wrote:
Attachment:
3.jpg

On Days 1 through 4 of a recent week, Product X was out of stock at Retailer R. Day 1 shoppers are those shoppers who came to Retailer R on Day 1 of that week seeking Product X. For each of the first 3 days of that week, the graph shows the subsequent behavior of all the Day 1 shoppers who came to Retailer R seeking Product X on that day. Shoppers at Retailer R who purchased a different item in lieu of Product X paid an average of 30% more for the item.

From each drop-down menu, select the option that creates the most accurate statement based on the information provided.

1. ____________% of Day 1 shoppers returned to the store on Day 3.

A. Fewer than 1
B. Between 1 and 10
C. More than 10

B

2. Shoppers at Retailer R who purchased substitute items from other manufacturers on Day 1 paid a total amount that was approximately______________% of the total all Day 1 shoppers would have paid had each of them been able to purchase Product X on Day 1.

A. 60
B. 78
C. 100
D. 130

B

Dear experts, AndrewN KarishmaB

For the question 1, 1. ____________% of Day 1 shoppers returned to the store on Day 3.

A. Fewer than 1
B. Between 1 and 10
C. More than 10

I understand that on Day 1 there are 25% of the shoppers who return the Day 2 = 25% of 100 = 25.
But we don't how many people in 25% decide to return on Day 3. All of them may not return to Day 3 (0%) or Most of them may return to Day3 (thus, it is possible that No. of Day1 shoppers may be still 25 or greater than 10)­
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Re: On Days 1 through 4 of a recent week, Product X was out of stock at [#permalink]
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­Tougher one!

If we read with precision and stay organized, then the calculations are pretty quick.

Video solution here:

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Re: On Days 1 through 4 of a recent week, Product X was out of stock at [#permalink]
For blank 1, the question is asking what percentage of the people on Day1, who did not make a purchase, returned the next day, retuned on day 2 but still did not make a purchase, retuned the next day.
Let s be the total number of shoppers on Day 1.
25% did not make a purchase, retuned the next day- 0.25x
On day 2,
19% still did not make a purchase and returned the next day ie out of 0.25x 19% retuned on day 3. 0.25x * 0.19 ~0.05x. Since the answer is a percentage, it will be ~5% so between 1 and 10.

For blank 2, the question is asking the percentage of the amount spent by 60% of the people in Day 1 in comparison to the amount that all the people on day1 would have spent had product X been available.
The cost of different item is 1.3 times product X.
Let the cost of product X be c and the total number of shoppers on day 1 be s.
The percentage = 0.6*1.3*cs/cs = 0.78*100= 78%
Re: On Days 1 through 4 of a recent week, Product X was out of stock at [#permalink]
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