Possible car configurations

Seven cars of seven different models are going to park in a row of seven side-by-side parking spots for an advertisement. Model P and Model Q must park next to each other, and Model S must be somewhere to the right of Models P & Q. How many possible configurations are there for the cars? A.) 600...

Square root of x^2

What is the value of x?

1.) √x^4 = 9
2.) √x^2 = -x

Ratios problem

The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?

A.) 1
B.) 13
C.) 14
D.) 18
E.) 21

Algebraic expression problem

It takes 1 pound of flour to make y cakes. The price of flour is w dollars for x pounds. In terms of w, x and y, what is the dollar cost of the flour required to make 1 cake?

A.) xy/w
B.) y/wx
C.) w/xy
D.) wx/y
E.) wxy

How can this be solved algebraically?

|xy| > x²y² only if x and y are NONZERO, with the result that both sides of the inequality are POSITIVE. Since |xy| > x²y² only if both sides are positive, we can safely square the inequality: (|xy|)² > (x²y²)² x²y² > x�y�. I may be understanding this incorrectly. I understand the ine...

Thanks Mitch - really like the approach. Do you know if this approach can be used in general for most of these problem types? As one other example, could it be applied when the data sufficiency statements provide inequalities? Example: If y = |x + 7| + |2 - x|, is y = 9? 1.) x < 2 2.) x > -7

Remainder problem

What is the remainder when (2^16)*(3^16)*(7^16) is divided by 10?

A.) 0
B.) 2
C.) 4
D.) 6
E.) 8

Hypothetical change on OG 2015 #102

What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2,304 cubic inches.
(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

If Statement (1) stated that the carton was shaped as a cube, would the answer then be C?