Algebra

Problem
Solve for x from the following equations:

$xy = 12$ $yz = 20$ $zx = 15$
A.   2 C.   4
B.   3 D.   5

 

Problem
A germ population has a growth curve $Ae^{0.4t}$. At what value of $t$ does its original value doubled?

A.   t = 7.13 C.   t = 1.73
B.   t = 1.37 D.   t = 3.71

 

Problem
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

A.   1 C.   5
B.   9 D.   3

 

Problem
The first three terms of a geometric progression are 2x, 4x + 14 and 20x - 14. Find the sum of the first ten terms.

A.   413,633 C.   489,335
B.   498,533 D.   431,336

 

Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?

A.   0.5 C.   1.5
B.   1.0 D.   2.0

 

Problem
The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

A.   9 C.   15
B.   12 D.   18

 

Problem
There are 7 arithmetic means between 3 and 35. What is the sum of all the terms?

A.   133 C.   665
B.   608 D.   171

 

Problem
A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water.

A.   30 kph C.   40 kph
B.   50 kph D.   20 kph

 

Problem
When the polynomial $x^4 + bx^3 + 5x^2 + dx + 6$ is divided by $x - 2$ the remainder is 16. When it is divided by $x + 1$ the remainder is 10. Find the value of constant $d$.

A.   7 C.   -5
B.   -7 D.   5

 

Problem
Determine the percentage uncertainty in the area of a square that is 6.08 ± 0.01 m on a side.

A.   0.27% C.   0.26%
B.   0.25% D.   0.29%

 

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