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Hi everyone :)

So we have a reasonable and tricky question here.
We need to understand what we have been asked here.
We have 2 scenarios: X , . / , X .
[?]: Cary shipped on the 1st day? ( X , )
X , . = YES Sufficient
, X . = No Sufficient
Both = Insufficient


(1) All X , = Standard shipping
[ltr]We don't know anything regard Cory shipment (yet) so Insufficient.
let's prove that:
Case 1: X , = YES
Case 2: , X = NO
Both = Insufficient

(2) Cory shipment = Standard
We don't know how standard is relating to 1st/2nd day (yet).
Clearly Insufficient.

(1)+(2) Cory=Standard , 1st Day=Standard
So, We know that every shipment on 1st day is standard
Case 1: X , = YES
Now, What about 2nd day? We don't know what shipments were that day.
it can be Rush/Standard shipments. if it is standard shipment it can be Cory shipment. So:
Case 2: , X = NO
Both = Insufficient

Answer E[/ltr]
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I would say answer E

Even when combining the two statements, we cannot definitively determine whether Cory purchased his item on the first day
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A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.
Ans: E

Statement 1) : on first day, standard shipping was the only method ==> only clearance items were sold on day 1, doesn't say anything about Cory [Not Suff]

Statement 2) Cory bought Clearance item, no way to identify if it was first day or second [Not Suff]

Together:
First day was clearance only and Cory bought Clearance item. both together doesn't specify if there was no clearance item sold on Day 2 so what if Cory bought the item on Day 2 and got the standard shipping on Day-2?? [Together Not Suff]

E: Not Suff
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IMO, C

clearance item => standard shipping
non-clearance => rush shipping

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
=> We can only infer that item bought on the first day is clearance. But we don't know if Cory purchased a clearance item or not =? Not sufficient.

(2) The item Cory purchased was a clearance item.
=> He could buy it on the first day, whose shipping method is standard shipping. But he could also buy it on the second day and we don't know full details about the shipping method of the second day => Not sufficient

(1) + (2) => sufficient.
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All clearance items were shipped with standard shipping. That means, if it is a clearance item, then it is shipped with standard shipping.
All rushed shipping items were non-clearance. That means, if an item is shipped in rushed shipping, then it is non-clearance.

We want to know if Cory purchased the item on the first day.

STATEMENT 1 -

Standard shipping was the only method of shipping on the first day.
On the second day, either both of the shipping method options could be available, or just the rushed shipping method.

This tells nothing about Cory and the items she purchased. INSUFFICIENT

STATEMENT 2 -

If Cory purchased a clearance item, this means it was shipped with standard shipping. But was it purchased on the first day or the second, we can't say.
INSUFFICIENT

STATEMENT 1 and 2 COMBINED -

We know from statement 2 that Cory purchased a clearance item and it was shipped with standard shipping.
We know from statement 1 that standard shipping was the only method of shipping on the first day.

But we still don't know whether standard shipping was available on the second day as well.

Therefore, INSUFFICIENT.

FINAL ANSWER - Option E
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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I'm never good at these but I think I know how to solve it. I would love if someone could correct me, improve my logic.

Let's take what we know: We have 2 consec days, say Mon and Tues, and on both of these days, lets assume that both clearance items and non-clearance items exists. Since they are shipped the same day they are sold, you can have Monday Clearance (Standard shipping), Monday NC (Rush), Tues Clearance (Standard), Tues NC (Rush). The question asks YES or NO: Did Cory buy his item on Monday?

1- Only standard items were sent out on Monday = ONLY CLEARANCE ITEMS. this tells us nothing about if Cory bought on Monday or not. Insufficient to answer the question. A and D are out.

2- Cory bought clearance = Cory got standard shipping. Cory could have gotten standard shipping on Monday or on Tuesday. B is out.

Take both statements together. Monday's shipping inventory was ONLY clearance (statement 1) but there is no guarantee that Cory bought on Monday. All we know from statement 2 is that he got clearance. Tuesday clearance is still an option. So C, both statements together are insufficient.

So E is the correct answer (fingers crossed)

Ans E
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(1)

Cory could have purchased his item on the first or the second day.

Condition (1) is insufficient

(2)

Cory's item was shipped with standard shipping because it was a clearance item.
But Cory could have purchased his clearance item on the first or the second day.

Condition (2) is insufficient

(1)+(2)

Maybe in the second day there were items shipped with standard shipping, so Cory's item could be sold on the first or the second day.

Conditions (1)+(2) are insufficient

Answer E
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Statement 1 is confirming that first day is standard shipping and we do not have any other info so not sufficient, eliminate A and D
Statement 2 Cory has purchased a clearance item and we do know that it has used standard shipping but we do not know the days when it was shipped hence not sufficient
Eliminate B
Combining both statements:
we know the first day is of Standard shipping but we do not know about the second day as Second day could only be of Rush shipping or of both Rush as well as of Standard shipping so we are not sure when Cory has purcahsed the item.
hence E is the answer.
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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i) Standard shipping was the only method of shipping used for items purchased on the first day.

This implies that on D1 no non-clearance items were sold. But neither do we know the type of item bought by Cory nor if on the second day, both shipments were used or only one type. Hence, INSUFFICIENT

ii) The item Cory purchased was a clearance item.

Here, we know the item purchased by Cory but we don't know whether she purchased it on D1 or D2. INSUFFICIENT

i) + ii)

We know that only standard shipping was used on D1 which implies only clearance items were sold & also that, Cory purchased clearance item but we don't know the items sold on D2 i.e. no where it is written that on D2 no clearance items were sold. Hence, Cory could've purchased on D1 or D2

INSUFFICIENT

IMO E
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

Statement (1):
Standard shipping was the only method of shipping used for items purchased on the first day.
  • If only standard shipping was used on the first day, it implies that all items sold on the first day were shipped using standard shipping.
  • Clearance items are always shipped with standard shipping. Thus, all clearance items could have been purchased on the first day.
  • However, non-clearance items can also be shipped with standard shipping. Therefore, non-clearance items purchased on the first day would also have been shipped with standard shipping.
  • This statement does not provide any information about Cory’s specific item, so we cannot determine whether he purchased his item on the first day.
Statement (1) is not sufficient.

Statement (2):
The item Cory purchased was a clearance item.
  • Clearance items are always shipped with standard shipping. However, this does not tell us when Cory purchased his item.
  • Since both days could have included clearance items shipped with standard shipping, this statement alone does not determine whether Cory purchased his item on the first day.
Statement (2) is not sufficient.

Combine Statements (1) and (2):
From Statement (1), we know that only standard shipping was used for items purchased on the first day. From Statement (2), we know that Cory’s item was a clearance item, which is always shipped with standard shipping.
  • Since all clearance items are shipped with standard shipping, and all items purchased on the first day were shipped with standard shipping, it is possible that Cory purchased his item on the first day.
  • However, clearance items can also be purchased on the second day and still be shipped with standard shipping. There is no direct evidence tying Cory’s purchase specifically to the first day.
Even when combined, the statements are not sufficient.
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Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 


2 consecutive days: shipped the item on the day it was sold
Standard Shipping: Clearance item
Rush Shipping: Non-Clearance item

Did Cory purchase his items on the first day?

Statement 1: Standard shipping was the only method of shipping used for items purchased on the first day.

This means that on the first day, only clearance items were being purchased.

We still do not know what Cory purchased, so this is not enough.
Statement 1 is not sufficient.

Statement 2: The item Cory purchased was a clearance item.

We know what type of item Cory has purchased but we do not know when it was sold nor the mode of shipping.

Statement 2 is not sufficient.

Statement (1) + (2)

Cory purchased a clearance item, which means it was on standard shipping. Standard shipping was used only on the first day.

So, the answer is Yes and the information is sufficient.

[C] is the correct answer.
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To find : Did cory purchase on first day?
Given a
Non clearance - Standard shipping
Clearance - Rush shipping

Statement 1 : Only standard shipping for day 1.

Not sufficient as we don't know whether cory purchased first day

Statement 2 : Cory purchased a clearance item

Not sufficient alone - as we don't know if he purchased it on day 1

Together - We know clearance was only shipped for day 2 - sufficient

OPTION C

Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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The correct answer is E

Given:
Items were sole for 2 consecutive days.
Standard shipping --> Clearance item
Rush shipping --> Non-clearance item

Question: Did Cory purchase his item on the first day?

Statement 1:
Standard shipping was the only method of shipping used for items purchased on the first day. - This is not sufficient

Statement 2:
The item Cory purchased was a clearance item - We don't have any idea about the day - Not Sufficient

Combining 1 and 2:
We know that Corry purchased a clearance item and only standard shipping method was used on the first day.
But what about the second day?
Nothing is mentioned about the second day - it might be only clearance or only non-clearance or a mix of both clearance and non-clearance

Hence, both statements together are not sufficient.


Bunuel
Quote:
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.


 


This question was provided by Manhattan Prep
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.



Given that,

every clearance item was shipped with standard shipping, and
every item that was shipped with rush shipping was non-clearance.



(1) Standard shipping was the only method of shipping used for items purchased on the first day.


No mention about Cory's purchase; hence, can't be determined whether Cory purchased his item on first day or second day

INSUFFICIENT


(2) The item Cory purchased was a clearance item.

No mention about method of shipping for 1st day , or 2nd day


so, can't be determined whether Cory purchased his item on first day or second day

INSUFFICIENT


(1) & (2) combined


1st day, only Standard Shipping ---> so, clearance item
However, it is not known whether any clearance item was sold on 2nd day..

hence, can't be determined whether Cory purchased his item on first day or second day

INSUFFICIENT



(E) is the CORRECT answer
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A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.
------------------------

Statement (1):
As only standard shipping was used on the first day, all items purchased on that day must be clearance items. However, it is not clear whether Cory[color=#0f0f0f] purchased clearance or non clearance item. In addition, standard shipping option was also available[/color] on the second day.

Insufficient

Statement (2):
Cory's item is a clearance item, meaning it was shipped with standard shipping. However, it is not clear if Cory bought it on the first or second day, as standard shipping could be used on both days.

Insufficient

Statement (1) + Statement (2):

As only standard shipping was used on the first day, all items purchased on that day must be clearance items. And Cory[color=#0f0f0f] purchased clearance item. However, standard shipping option was also available on the second day. Cory could have purchased on second day as well.[/color]

Insufficient

Answer is E
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Quote:
A certain online store sold a number of items over the course of two consecutive days and shipped each item on the day it was sold. During those two days, every clearance item was shipped with standard shipping, and every item that was shipped with rush shipping was non-clearance. Did Cory purchase his item on the first day?

(1) Standard shipping was the only method of shipping used for items purchased on the first day.
(2) The item Cory purchased was a clearance item.

1) every clearance was shipped with standard shipping, doesn't mean that if standard shipping was the only method, then every items bought on day 1 was clearance (if x is y, doesn't mean y is x)
No info on what Cory may have bought, not sufficient
2) No info on types of items sold on either day, not sufficient

1 and 2 together: We don't know if all items on day 1 was clearance, or if there are clearance items sold on day 2 as well. Not sufficient

Choose E
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We know that,

Clearance items are always shipped with standard shipping
Rush shipping option only applies to non-clearance items.

We need to find out if Cory purchased his item on the first day

1=> Standard shipping was the only method of shipping used for items purchased on the first day

All items purchased on the first day were shipped with standard shipping.
But it does not provide any specific information about whether Cory purchased his item on the first day, as it does not link Cory or his item to the timing of the purchase

2=> The item Cory purchased was a clearance item

Since clearance items are always shipped with standard shipping, we know Cory’s item was shipped with standard shipping.
However, this alone does not indicate whether Cory purchased his item on the first day, as standard shipping could apply to clearance items purchased on either day

Now lets combine both statements,
We see that two statements together still do not definitively tell us whether Cory purchased his clearance item on the first day or the second day, as clearance items with standard shipping could apply to either day.

E. Statements (1) and (2) TOGETHER are NOT sufficient.
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