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If the average speed is (50-x) when climbing up the mountain, but (50+x) when climbing down the same mountain. Which of the following value of x could ensure that the average speed of the entire journey up and down the mountain is the greatest?
Mark drives from home to work. The total distance of the drive is 150 miles. During the first half of the drive, Mark drives at a speed of 30miles/hour. During the second half of the drive, Mark drives at a speed of 50miles/hour. Which of the following statements must be true?

Indicate all such statements.
How many ounces of 20% grape juice needs to be added to a bottle of 20-ounce 12% grape juice so that the mixture is 15% grape?
At A cornfield, super seed accounts for 17 percent of all seed, while at B cornfield, super seed accounts for 11 percent of all seed. Between cornfield A and B, there are more seed, in total, in cornfield B than in cornfield A .

Quantity A

The percentage of super seed among all seed in cornfield A and B

Quantity B

14%


The sales commission at Company X is 15 percent of the first $500 sales plus 20 percent of the sales in excess of the first $500. If a salesperson gets a final commission of $320,what is his/her sales?

_____dollars
If we put 92000 into a bank, the interest will be 920 after a month, what is the annual interest?

Give your answer as a percent.
Larry has 14000 dollars to make two one-year investments, one of which has a simple annual interest rate of 6%, and the other has 3%. The interest of the two investment is the same. How much money is invested in the 6% investment?

Give your answer to the nearest 0.01.
$10000 is divided into 2 parts, the first part and the second part are invested with the simple annual interest rate of 4% and 6% respectively. The total interest after one year is between 450 and 550 dollars, inclusive.

Which of the following statements must be true?

Indicate all such items.
A person used a part of $100,000 to buy a house, and put 1/3 of the remaining part into bank A with the annual interest rate of 4%. Then he put the remaining part into bank B with the annual interest rate of 6%. After a year, he got a total interest of $360. How many dollars did he use to buy a house?
Each person at a party shook hands exactly once with each of the other people at the party.

There was a total of exact 21 handshakes exchanged at the party.

Quantity A: The number of people at the party

Quantity B: 8
There are 10 blue balls, 8 green ones and 6 yellow ones, if one person pick up one by one without replacement, what is the minimum number of balls that he must pick up in order to ensure that two balls of the same color have been picked up?
There are 100 purple balls, 100 red balls and 100 blue balls, how many balls at least should be drawn to ensure four balls of a same color are selected?
N=113*123*135*261*293. In other words, 113, 123, 135, 261, 293 are five factors of N. 20 is added to which of the above factor of N such that N increases the most?
w(x+y+z)=wx+wy+z

Quantity A

z

Quantity B

0


1 < r < s < t, which of the following is closest to r*s*t ?
x > 0,y < 0

Quantity A

$$(x-y)^{2}$$

Quantity B

$$x^{2}+y^{2}$$


a≠ 0

Quantity A

$$(a+\frac{1}{a})^{2}$$

Quantity B

2


x and y are positive numbers.

Quantity A

$$\sqrt{x}$$+$$\sqrt{y}$$

Quantity B

$$\sqrt{x+y}$$


x+y > 1

Quantity A: $$x^{2}$$+$$y^{2}$$

Quantity B: 1
x and y are integers and $$x^{2}$$-$$y^{2}$$=27

Quantity A

x

Quantity B

10


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