## Saturday, October 9, 2010

### ME Board Reviewer: Math, Algebra, Computation (ANSWER and SOLUTION)

1. Which of the following is the solution set of the equation x2-2x-15 = 0
Solution:
Think of factors of the last digit that when subtracted gives the coefficient of the middle term
In this case, -15 can only be (3, -5), (-3, 5), (15, -1) or (-15, 1). Among these factors, (3, -5) is the only one whose sum will be equal to -3. So the solution set of the equation will be
X-5=0; x1 = 5
X+3=0; x2 = -3
Alternative Solution:
By trial and error (best when using your calculator), try each choices and see which among them when substituted to x will make the equation true, that is, x2-2x-15 equals zero.

B. (5, -3)

2. The next term in the progression 2, 8, 32, 128 is …
Solution:
The progression above is a Geometric progression since there is a common ratio (r). In this case, the common ratio is 4 and the next terms are obtained by multiplying the previous term by 4. So, next to 128 will be 128X 4 = 512

C. 512

3. Solve for x in the equation 3 lnx = 8
Solution:
Using properties of logarithm: nlna = lna^n
In this case, lnx^3=8
By making both sides an exponent of e (Euler’s number), we can cancel the ln.
e^(lnx^3)=e^8
x^ 3 = e^8
x= e^ (8/3)

A. e^ (8/3)

4. If x + y = 1 and x2+y2=2. Find x4+y4
Solution:
Squaring both sides of x+y =1 we get (x+y) ^2=1^2; x2+2xy+y2=1;
But x2+y2=2 so 2+ 2xy=1 or xy=-1/2;
Square both sides, 4x2y2=1; x2y2=1/4
Let’s square both sides of x2+y2=2; (X2+y2) ^2=2^2 then x4+2x2y2+y4 = 4;
But x2y2=1/4 so, x4+y4+2(1/4) =4
Solving the equation will give us X4 +y4 =7/2

D. 7/2

5. If lnx=5 and lny=2, lnx3/lnx4
Solution:
Using properties of logarithm; lnx3=3lnx and lny4=4lny
So lnx3/lny4 will be 3lnx/4lny = 3(5)/4(2) =15/8

B. 15/8

6. Joan can type the whole document in 3 hrs. On the other hand, James, being new to the job can type the same document in 5 hours. If they work together, how long can they finish 2 documents?
Solution:
rate of Joan 1/3; rate of James 1/5
Rate=no job/time time = no of job/rate
If they work together, their rate will be added
t= 2 jobs/ (1job/3hrs+1job/5hrs)
t=3.75 hours

D. 3.75 hrs

7. Three numbers are in the ratio 1: 2: 4. Find the numbers if their sum is 42.
Solution:
add the ratios 1+2+4 = 7
Divide the sum of the numbers by the sum of the ratio; 42/7=6
Multiply 6 by each ratio. The numbers will be 6, 12, and 24

A. 6, 12, 24

8. Find the sum of the coefficients in the expansion of (5x-4)^5
Solution:
To find the sum of the coefficients of an expansion, just replace the variable by 1 in the expression.
In this case, (5x-4) ^5; [(5(1)-3] ^5=32

D. 32

9. Evaluate the expression log 3+ log 2+ 4log7
Solution:
use your calculator
Note: When there’s no base mentioned, it is automatically considered to be 10.

D. 4.16

10. The sum of the infinite geometric progression is 3 and the common ratio is 1/3. What is the first term?
Solution:
For an infinite Geometric progression, the sum is given by the formula S=a1/r where S is the sum and r is the ratio.
In this case, the Sum and the ratio were given so using the formula we can get the first term.
a1=Sr; a1=9(1/3) =3

A. 3

Shortcut to questions.
Note: Writing solution to a math problem in a webpage like these is extremely difficult so I expect that some of you may be confused by the way I wrote the solution. If you have questions and clarifications, don't hesitate to send me a message at admin@tupmechanical.com or post a comment below.

#### 11 comments:

1. Your answer to #2 is incorrect since 32 times 4 is not 64 so the geometric ratio cannot be 4

2. @andrew: Thanks. Questions and answers are corrected accordingly.

3. @admin
answers to #8 and #10 is incorrect..
to #8:
since the coefficient has constant so the formula should be : (coef.X + K)^n - (K)^n
so the answer should be 1025
to #10:
the formula should be S=a1/1-r
so the answer should be 2..

1. tama ka dude..mali mali talaga toh,,,tsk2x

4. pakireview po ng #5,, mali kasi ang given,,Iny4 dapat...

5. mali mali naman.

6. For the admin, with all due respect, please kindly check first your review material before being published here. I thought it would be really helpful. It just confuses your visitors. :(

Thank you!

7. Dude hope you did some writing or explanation about this numbers. Thank you for sharing this very good math information.

8. In fact, this is too complicated for me! I think that a simple calculator will ease these calculations!

9. Thanks for the provided calculations! The problem was quite confused, but you were managed to resolve it finally!

10. Corrections
# 8: ans = 1025; (first coefficient + 2nd coef.)^exp. - (2nd coef.)^exp.
# 10: ans = 2; Sum Geo. seq. infinity = (1st no.)/1-ratio