In any sequence of ~$n$~ nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence -2, 3,-4, 5 has three sign changes. Does the sequence of nonzero numbers ~$s_1,s_2,\ldots, s_n$~ have an even number of sign changes?

1. ~$s_k = (-1)^k$~ for all positive integers ~$k$~ from 1 to ~$n$~.

2. ~$n$~ is odd.

If ~$r$~ and ~$s$~ are positive numbers and \theta is one of the operations, ＋,－, ×, or ÷, which operation is \theta?

1. If ~$r = s$~, then ~$r \theta s$~ = 0.

2. If ~$r ≠ s$~, then ~$r \theta s ≠ s \theta r$~.

What is the remainder when the positive integer ~$n$~ is divided by 5?

1. When ~$n$~ is divided by 3, the quotient is 4 and the remainder is 1.

2. When ~$n$~ is divided by 4, the remainder is 1.

On a map, ~$\frac{1}{2}$~ inch represents 100 miles. According to this map, how many miles is City ~$X$~ from City ~$Y$~?

1. City ~$X$~ is 3 inches from City ~$Y$~ on the map.

2. Cities ~$X$~ and ~$Y$~ are each 300 miles from City ~$Z$~.

Is ~$n$~ equal to zero?

1. The product of ~$n$~ and some nonzero number is 0.

2. The sum of ~$n$~ and 0 is 0.

If ~$R, S$~, and ~$T$~ are points on a line, and if ~$R$~ is 5 meters from ~$T$~ and 2 meters from ~$S$~, how far is ~$S$~ from ~$T$~?

1. ~$R$~ is between ~$S$~ and ~$T$~.

2. ~$S$~ is to the left of ~$R$~, and ~$T$~ is to the right of ~$R$~.

In the figure above, ~$RST$~ is a triangle with angle measures as shown and ~$PRTQ$~ is a line segment. What is the value of ~$x+y$~?

1. ~$s = 40$~

2. ~$r = 70$~

If m and ~$n$~ are integers, what is the value of ~$m + n$~ ?

1. ~$(x +m)(x+n) = x^2 + 5x + mn$~ and ~$x ≠ 0$~

2. ~$mn$~ = 4 

The figure above represents a box that has the shape of a cube. What is the volume of the box?

1.PR=10cm

2.QT=5~$\sqrt{6}$~ cm

In the figure above, what is the area of region PQRST?

1.PQ=RS

2.PT=QT