# At Southgate Mall, mattresses are sold only at Mattress Madness. Every mattress at Mattress Madness is on sale at a 2...

Minh on July 15, 2015

Help!

Can you explain this question? Thank you!

Replies

Melody on July 16, 2015

Okay let's diagram this argument:

"At Southgate Mall, mattresses are sold only at Mattress Madness."

So: If a mattress is sold at Southgate Mall, it is from Mattress Madness.

P1: MSGM ==> MM
not MM ==> not MSGM

"Every mattress at Mattress Madness is on sale at a 20 percent discount."

So: If it is a mattress from Mattress Madness, then it is on sale at a 20 percent discount.

P2: MM ==> 20%D
not 20% D ==> not MM

"So every mattress for sale at Southgate Mall is on sale at a 20 percent discount."

C: MSGM ==> 20%D
not 20%D ==> not MSGM

Here we have a valid positive transitive argument. We can connect P1 to P2 like so: MSGM ==> MM ==> 20%D to conclude: MSGM ==> 20%D, which is exactly what our conclusion is.

Now, let's diagram answer choice (C):

"All the food in Diane's apartment is in her refrigerator."

So: If it is food in Diane's apartment, then it is in her refrigerator.

P1: FDA ==> R
not R ==> not FDA

"Diana purchased all the food in her refrigerator within the past week."

So: If it is food in Diane's refrigerator, then it was purchased within the past week.

P2: R ==> PPW
not PPW ==> not R

"Therefore, she purchased all the food in her apartment within the past week."

So: If it is food in Diane's apartment, it was purchased within the past week.

C: FDA ==> PPW
not PPW ==> not FDA

Answer choice (C), just like in the argument, is a valid positive transitive argument. We can connect P1 to P2 like so: FDA ==> R ==> PPW to conclude: FDA ==> PPW, which is exactly what our conclusion is.

Hope that clears things up! Please let us know if you have any other questions.

on November 7, 2017

I don't understand the difference between answers C and D they seem so similar

Mehran on November 13, 2017

Hi @franco, thanks for your post. This is a Parallel Reasoning question. Let's first look closely at the argument in the stimulus, so we can be sure that we parallel it correctly.

At Southgate Mall:
P: Mattresses are sold only at Mattress Madness.
M ==> MM
P: Every mattress at Mattress Madness is on sale at a 20% discount.
MM ==> 20%
C: So every mattress for sale at Southgate Mall is on sale at a 20% discount.
M ==> 20%
This is a valid transitive argument.

P: All the food in Diane's apartment is in her refrigerator.
F ==> R
P: Diane purchased all the food in her refrigerator within the past week.
R ==> past week
C: Therefore, she purchased all the food in her apartment within the past week.
F ==> past week
This is also a valid transitive argument.