# Challenging Logic Question!

• Aug 10th 2011, 02:55 AM
KayPee
Challenging Logic Question!
How best can I approach this logic question?

Six pairs of shoes cost as much as 1 coat, 2 pairs of jeans cost as much as 3 pairs of shoes, and 4 pairs of socks cost as much as one pair of jeans. How many coats could I exchange for 64 pairs of socks?
• Aug 10th 2011, 05:26 AM
red_dog
Re: Challenging Logic Question!
Let $\displaystyle x$=the cost of one pair of shoes
$\displaystyle y$=the cost of 1 coat
$\displaystyle z$=the cost of 1 pair of jeans
$\displaystyle t$=the cost of 1 pair of socks.

We have:
$\displaystyle 6x=y$
$\displaystyle 2z=3x$
$\displaystyle 4t=z$
Then
$\displaystyle y=6x=4z=16t\Rightarrow 4y=64t$
So we have to exchange 4 pairs of coats for 64 pairs of socks.
• Aug 10th 2011, 05:56 AM
Soroban
Re: Challenging Logic Question!
Hello, KayPee!

I avoided varaiables ... too confusing.
(I would have used initials, but we have Shoes and Socks.)

Quote:

Six pairs of shoes cost as much as 1 coat.
2 pairs of jeans cost as much as 3 pairs of shoes.
4 pairs of socks cost as much as one pair of jeans.
How many coats could I exchange for 64 pairs of socks?

We are told: .$\displaystyle \begin{Bmatrix}6\text{ shoes} &=& 1\text{ coat} & [1] \\ 2\text{ jeans} &=& 3\text{ shoes} & [2] \\ 4\text{ socks} &=& 1\text{ jean} & [3] \end{Bmatrix}$

$\displaystyle \begin{array}{cccccccc}\text{Multiply [3] by 4:} & 16\text{ socks} &=& 4\text{ jeans} & [4] \\ \text{Multiply [2] by 2:} & 4\text{ jeans} &=& 6\text{ shoes} & [5] \\ \text{And we have [1]:} & 6\text{ shoes} &=& 1\text{ coat} & [6] \end{array}$

Equate [4], [5] and [6]: .$\displaystyle 16\text{ socks} \:=\:1\text{ coat}$

. . . . . . . . . .Multiply 4: .$\displaystyle 64\text{ socks} \:=\:4\text{ coats}$

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An unfortunate choice of items of clothing.

Someone may feel obligated to mention the two shoes
. . and the two socks in each pair.

Yet "a pair of jeans" involves only one item of clothing.
(They are singular at the top, plural at the bottom.)

Our language has many pseudo-pairs: a pair of pants,
. . a pair of slacks, a pair of scissors, a pair of pliers.

One would think that brassiere would be referred to in pairs;
. . the concept of two is so strongly suggested.
(Okay, maybe it's because I'm a guy . . .)