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Answers to Statistics and Probability Part 1: Mechanical Engineer Board Exam Review

Here's the solution and answers to the ME board questions in Mathematics (Statistics and Probability)

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?
Solution:
The total number of persons to be seated is 8 and the number of chairs is only 7.
When words denoting “arrangement” are used, it most likely pertains to permutations.
So, the formula to be used is permutation of 8 taking 7 at a time.
n = 8, r = 7, nPr, then use your calculator or this formula
nPr = n!/(n-r)! = 8!(8-1)!=40320 permutations or arrangements
A. 40320

2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?
Solution:
Since the number varies as you rearrange the digits (example 1342 is different from 1423), then this problem is about permutation.
So, the formula is the permutation of 5 numbers taken 3 at a time.
n = 5, r = 3, nPr; use your calculator or this formula: nPr = n!/(n-r)!
nPr = 5!/(5-3)!=60 permutations
C. 60

3. There are 2 white, 3 red, …

Statistics and Probability Part 1: Mechanical Engineer Board Exam Review

Here are some review questions in Mathematics, Statistics and Probability.

Instruction: Choose the BEST answer.

Mechanical Engineering Board Exam Review: Statistics and Probability part 1

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?
a. 40320
b. 5040
c. 720
d. 8

2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?
a. 720
b. 10
c. 60
d. 120

3. There are 2 white, 3 red, and 4 blue balls inside a basket. If three balls are drawn randomly in succession without replacement, what is the probability that the first ball is white, and the next two balls are blue?
a. 32/729
b. 4/63
c. 8/243
d. 1/21

4. What is the mode of the following numbers: 54, 45, 75, 60, 65, 65, 60, and 57?
a. 65
b. 60
c. 62.5
d. 60 and 65

5. From the given numbers of question number 4, what is the median?
a. 65
b. 60
c. 62.5
d. 60 and 65

6. From the given numbers of question number 4, what is the variance?
a. 77.84
b. 60.125
c. 68.11
d. 8.82

7. Seve…

Professional Mechanical Engineer (PME) October 2010 Results

The Professional Regulation Commission (PRC) announces that 22 passed the Professional Mechanical Engineer Examination given by the Board of Mechanical Engineering in Manila this October 2010.

The following are the successful examinees.

1 AGOSTO, FLORENDO SABADO
2 AGTARAP, FERDINAND OLIVAR
3 ALCORIZA, RODOLFO SANTOS
4 AMTO, JOEL CELMAR
5 BALDONADO, BERNARDINO MAGUMUN
6 BOTE, RICARDO JR BAUTISTA
7 CABRERA, WILLIAM MATURAN
8 CANSINO, CECILIO JR LOPEZ
9 CHAVIT, CECILIO BOMEDIANO
10 DE LA ROSA, FERDINAND MANGAT
11 DIASANA, SERGIO SR BABA
12 DOROTAN, ELMER VILLANCA
13 GULMATICO, LLOYD CASTROBERDE
14 LORETO, JORGE JR DELOS REYES
15 MALOLES, ROBERT DICK TELYAEN
16 PEREZ, RIOLANDO VILLANUEVA
17 SIAPNO, JOSE II PADON
18 SO, ROLANDO CHING
19 TAPU, BENITO TABUT
20 TIGARONITA, BEN JR CORDERO
21 VILLAREAL, REYNAN MORATA
22 YU, LAWRENCE RUSSIANA
NOTHING FOLLOWS----------------------

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^…

Mechanical Engineering Board Exam Reviewer: Algebra, Mathematics, Computation Part 1

Here’s a set of question on the topic Mathematics, specifically on Algebra. These questions are similar to those coming out of the board exam.

Instruction: Choose the best answer.

1. Which of the following is the solution set of the equation x^2-2x-15 = 0
a. (3, -5)
b. (5, -3)
c. (15, -1)
d. (-15, 1)

2. The next term in the progression 2, 8, 32, 128 is …
a. 128
b. 256
c. 512
d. 1024

3. Solve for x in the equation 3 lnx = 8
a. e^ (8/3)
b. e^ (3/8)
c. e^ (4/3)
d. e^ (3/4)

4. If x + y = 1 and x^2+y^2=2. Find x^4+y^4
a. ½
b. 3/4
c. 15/4
d. 7/2

5. If lnx=5 and lny=2, lnx3/lnx4
a. 10/3
b. 15/8
c. 125/16
d. 5/2

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?
a. 3 hrs
b. 3.5 hrs
c. 2.75 hrs
d. 3.75 hrs

7. Three numbers are in the ratio 1: 2: 4. Find the numbers if their sum is 42.
a. 6, 12, 24
b. 4, 12, 36
c. 4, 16, 22
d. 3, 15, 24

8. Find the sum of…