The answer explanation ends up leading to the correct answer, but the explanation doesn't account for negative numbers. I provided examples of numbers less than 1/3, that have different tenths digits. 0: .01 < .33... 1: .10 < .33... 2: .23 < .33... 3: .30 < .33... 4: -.4 < .33... (-.5, -.6, -.7, -.8...

Statement 1: x can be any negative number, or x can be 0. |-1| = 1 = -(-1). -2, -3, -2.5 work: any negative number works. 0 works, because |-0| = 0 = -0. So statement 1 alone isn't sufficient. Statement 2: x can't be a negative number. For example, |-1|^2 = 1 is not = - ((-1)^2) = -1. x can't be a p...

"If I choose N as 2, then when I do N-2, the result is 0 which is not a multiple of 4. "

As I mentioned in the first reply, 0 is a multiple of 4.

Make a list of prices, and see if it adds to 91. Consider the constraints: the price of the highest main or lowest side, and that all the prices must be integers. Start from the given price. If the price doesn't add to $91, make adjustments. 1: The main dishes are 16, 15, 14, and 13 dollars. The sid...

At least two means visiting 2 or 3 or 4 cities. The order matters, because going to New York then Los Angeles, for example, is a different itinerary than going to Los Angeles then New York. Since order matters, use permutations. Visiting 2 cities out of 4, when order matters, is 4P2. Visiting 3 out ...

This problem isn't about solving equations. It's about determining if a statement or statements are sufficient for answering the question. "Generally, when I test for range I do so to make sure the inequality is valid. For example, in (1) I tested for where x is negative and got x>-1. The probl...

This is a number line, magnitude problem. Remember: On a yes/no DS question, you don't need a yes answer. You only need a definitive yes or no. It looks like the diagram doesn't provide any information. But it provides a lot of information: q>r>s>t and all the numbers are real numbers. If they weren...

Here's an even faster answer:

"OnlyEworks"

Seriously, though, plugging in is often faster than working the algebra. But if you remember how to rationalize the denominator, as Ashke showed, the algebra on this one takes about 10 seconds.