Question

1. If the product of the integers a,b, and c is 1, then what is the difference between the largest and the smallest possible values of a^2*b^3*c^4?

a. -2 b. -1 c. 1 d. 2

2. Hats are purchased at the rate of $33 per dozen. If they are sold at a closeout sale for $2.50 each, the percent loss on the cost price is:
a. 3 b. 3 1/3 c. 9 1/11 d. 10

Answer 1

Problem 1

The largest value would be 1 and the smallest would be -1.

To get a product of 1, either all are 1 or two of the variables are -1 and the other one is 1.

Largest value = (1)^2 * (1)^3 * (1)^4 =1

Smallest value = (- 1)^2 * (- 1)^3 * (1)^4 = -1

The difference is:

largest value – smallest value = 1 – (-1) = 2

Therefore the answer is letter D.

Problem 2

% loss = (final price – initial price) * 100%/ initial price

where, final price per dozen = ( $2.50 / piece) (12 piece / dozen) = $30

Therefore,

% loss = ($30 - $33) * 100 / $33

% loss = - 300/ 33 = 9 1/11

Therefore the answer is letter C.