For each of 6 online retailers, the table shows the percentage of all

Question

For each of 6 online retailers, the table shows the percentage of all orders placed with that retailer last year that were returned within certain time periods after purchase, together with the total percentage of orders that were returned. Each returned order is included in exactly one time period, and no order was returned on the day of purchase.

For example, “1–7 days” includes returns made at least 1 day but no more than 7 days after purchase, while “8–14 days” includes returns made more than 7 days but no more than 14 days after purchase, and so on.

All six retailers had different total numbers of orders. The retailers are numbered from greatest total number of orders placed last year, Retailer 1, to least, Retailer 6. The rows in the table are arranged from the lowest to the highest total-return percentage.

Retailer 
 1–7 days 
 8–14 days 
 15–21 days 
 22–30 days 
 More than 30 days 
 Total returns 
 
  6 
 5.0% 
 3.5% 
 2.8% 
 1.8% 
 2.1% 
 15.2% 
 
  4 
 6.0% 
 4.5% 
 3.5% 
 2.5% 
 2.0% 
 18.5% 
 
  3 
 7.0% 
 4.0% 
 3.0% 
 4.0% 
 3.8% 
 21.8% 
 
  2 
 8.0% 
 5.5% 
 4.5% 
 2.5% 
 3.1% 
 23.6% 
 
  1 
 9.5% 
 6.0% 
 4.0% 
 3.0% 
 2.6% 
 25.1% 
 
  5 
 8.8% 
 7.0% 
 5.5% 
 3.0% 
 2.5% 
 26.8%

For each statement, select  Must be true  if the statement must be true based on the information provided. Otherwise, select  Need not be true .

Bunuel · Accepted Answer

Official Solution:

• Retailer 4 had fewer orders returned no more than 21 days after purchase than Retailer 3.

Returns made no more than 21 days after purchase include the 1–7 day, 8–14 day, and 15–21 day categories.

For Retailer 4:

6.0% + 4.5% + 3.5% = 14.0%

For Retailer 3:

7.0% + 4.0% + 3.0% = 14.0%

Thus, the same percentage of each retailer’s orders was returned no more than 21 days after purchase.

However, Retailer 3 had more total orders than Retailer 4. Therefore, the same percentage must represent a greater number of orders for Retailer 3.

Thus, Retailer 4 must have had fewer such returned orders.

Answer:  Must be true .

• Retailer 2 had fewer orders returned more than 7 days but no more than 30 days after purchase than Retailer 5.

This period includes the 8–14 day, 15–21 day, and 22–30 day categories.

For Retailer 2:

5.5% + 4.5% + 2.5% = 12.5%

For Retailer 5:

7.0% + 5.5% + 3.0% = 15.5%

Retailer 2 had the smaller percentage, but Retailer 2 had more total orders than Retailer 5.

Thus, one retailer had the greater total number of orders, while the other had the greater percentage returned during this period. Without knowing the actual total numbers of orders, we cannot determine which had fewer returned orders.

Answer:  Need not be true .

• More than one-third of Retailer 3’s returned orders were returned more than 21 days after purchase.

For Retailer 3, orders returned more than 21 days after purchase include the 22–30 day and more-than-30-day categories:

4.0% + 3.8% = 7.8%

The total percentage of Retailer 3’s orders that were returned was 21.8%.

Therefore, the proportion of Retailer 3’s returned orders that were returned more than 21 days after purchase was:

7.8/21.8 ≈ 0.358

Since 0.358 is greater than 1/3, more than one-third of Retailer 3’s returned orders were returned more than 21 days after purchase.

Answer:  Must be true .

Correct answer:

Statement 1: "Must be true"
Statement 2: "Need not be true"
Statement 3: "Must be true"

officiisnobis · Answer

Must Be True
Need Not Be True
Must Be True

SwiftMonk · Answer

N
M
M

ML5 · Answer

1- M (Reason - Both are 14%, and retailer no. are arranged based on total orders)
2- N (Reason - Retain 2: 15.6% < Retailer 5: 18%; may be or may not depend on total orders)
3- M (Reason - 1/3 is 7.26 < Return after 21 days is 7.8% > 7.26 that is 1/3rd)

FerociousStorm · Answer

First-
Retailer 3: 7+4+3=14
Retailer 4: 6+4.5+3.5=14%

both have same percentage but 3 ranks higher, which means they had more total orders received so it MUST BE TRUE

Second - While it is true that 2 has fewer percentage of orders returned than 5, it is also true that 2 had more orders so two things can counter each other but we don't know how much. NEED NOT BE TRUE

Third - Returns after 21 days is 7.8% which is obviously greater than 1/3 of 21.8%. MUST BE TRUE

For each of 6 online retailers, the table shows the percentage of all

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Retailer	1–7 days	8–14 days	15–21 days	22–30 days	More than 30 days	Total returns
6	5.0%	3.5%	2.8%	1.8%	2.1%	15.2%
4	6.0%	4.5%	3.5%	2.5%	2.0%	18.5%
3	7.0%	4.0%	3.0%	4.0%	3.8%	21.8%
2	8.0%	5.5%	4.5%	2.5%	3.1%	23.6%
1	9.5%	6.0%	4.0%	3.0%	2.6%	25.1%
5	8.8%	7.0%	5.5%	3.0%	2.5%	26.8%

Must be true	Need not be true
		Retailer 4 had fewer orders returned no more than 21 days after purchase than Retailer 3.
		Retailer 2 had fewer orders returned more than 7 days but no more than 30 days after purchase than Retailer 5.
		More than one-third of Retailer 3’s returned orders were returned more than 21 days after purchase.

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For each of 6 online retailers, the table shows the percentage of all

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