How to Solve Word Problems by Working Backwards Part 1

Most of us would always take a pen and solve for x if we see word problems. But did you know that you can solve them by working backward or even mentally? In this post, I am going to teach you some techniques on solving problems by working backward.

Example 1: One number is three more than the other. Their sum is 45. What are the numbers?


In the given, one number is 3 more than the other. This means that if you subtract 3 from the larger number they will be equal. Note that if we subtract 3 from one of the numbers, then we should also subtract 3 from their sum. Therefore, their sum will be 45 – 3 = 42. Since the numbers are equal, we now divide the sum by 2. That is, 42/2 = 21.

So, the smaller number is 21 and the larger is 21 + 3 = 24.

Check: 21 + 24 = 45

Example 2: One number is 5 less than the other. Their sum is 43. What is the smaller number?


This is very similar to Example 1. Here, one number is 5 less than the other; so, if we add 5 to the smaller number, they will be equal. If we add 5 to the smaller number, we should also add 5 to their sum. Therefore, their sum will be 43 + 5 = 48. Since the two numbers are equal, we can divide the sum by 2. That is 48/2 = 24. Since we added 5, it means that 24 is the larger number. So, the smaller number is 24 – 5 = 19.

Check: 19 + 24 = 43

In the next post, we are going to discuss more examples.

Practice Exercises on Subtracting Decimals

We have already learned how to add and subtract numbers with decimals. In this post, we practice subtracting decimals. Recall that in subtracting decimals, the decimal points should be aligned.

Practice Exercises

1.) 2.32 – 1.82
2.) 6.71 – 3.9
3.) 6 – 0.52
4.) 5.03 – 4.25
5.) 0.53 – 0.33
6.) 4 – 1.26
7.) 7.28 – 2.4
8.) 7.08 – 0.29
9.) 3 – 0.305
10.) 40 – 12.5


1.) 0.5
2.) 2.81
3.) 5.48
4.) 0.78
5.) 0.2
6.) 2.74
7.) 4.88
8.) 6.79
9.) 2.695
10.) 27.5

Enjoy learning!

How to Explore PH Civil Service Exam Reviewer

The PH Civil Service Exam Reviewer website ( has already provided free reviewers for the past two years and so far many testimonials have already reached me that this website has been very useful in this review. Below are some of the useful links within the website that are often ignored or missed especially when browsing using mobile phones.

1.) Math – The math page contains basic concepts in numerical ability such as operations on fractions, decimals,  solving equations, as well as finding areas of geometric figures. This also includes topics like LCM, GCF, and addition of positive and negative integers. If you are not very good in math, I suggest that you start with this page.

2.) Word Problems – The Word Problems page contains detailed tutorials about word problems. This includes number problems, age problems, motion problems, work problems, mixture problems, coin problems, investment problems, ratio problems, digit problems, and more.

3.) English – The English page contains reviewers on vocabulary, grammar and correct usage, and paragaraph organization. It also contains basic grammar tutorials particularly the tenses of the verbs.

4.) Practice Tests – This contains practice tests and exercises on both English and Math topics discussed in the site.

5.) Post List – contains the complete of posts of this website. This includes list of Civil Service Exam Passers.

6.) Videos – Useful videos from Sipnayan for learning mathematics.

Another useful site is the Sipnayan Youtube Channel which contains more than 300 Tagalog Math Tutorial videos. 🙂

Lastly, as a bonus, if you already passed the Civil Service Exam, then you may want to explore our partner website, the Philippine Government Jobs, if you want to work for the Philippine Government.

How to Compare Decimal Numbers

We have already learned how to compare fractions and in this post, we are going to learn how to compare decimals. In comparing decimals it is important to understand place value. In the number 213.489, the following are their place values. For the whole numbers,

2 – hundred
1 – tens
3 – ones.

For the decimal numbers,

4 – tenths
8 – hundredths
9 – thousandths

In whole numbers, clearly, the larger the number of digits the larger the number. For example, 821 > 92 since 821 has three digits and 92 has only two digits. Since whole numbers are always greater than decimal numbers in comparing decimal numbers, look at the whole numbers first. Therefore, we have the following rule.

Rule 1: In comparing decimal numbers, look at the whole number first. The decimal numbers containing larger whole numbers have larger values.

Example 1: 84.23 > 82.345 since 84 is greater than 82.

Example 2: 12.56 < 15.001 since 12 is less than 15.

Example 3: 141.85 > 123.4 because 141 is greater than 123

Rule 2: If the whole numbers are equal, then compare the numbers by looking at the tenths place first. The number with the larger digit in tenths place is larger.

Example 1: 18.34 > 18.21 since 3 > 2.

Example 2: 12.95 > 12.15 since 9 > 1.

Example 3: 0. 9 > 0.873 since 9 > 8.

Notice that in Rule 2 Example 3, even if 0.873 has more digits, it is still less than 0.9 since 9 is greater than 8 and they are in the tenths place.

Rule 3: If the whole numbers and the tenths place are equal, then compare first the hundredths place. The number with the larger digits in the hundredths place is the larger number.

Rules 2 and 3 can be generalized. That means that you have to compare the digits from the tenths place first, then hundredths, then thousandths, and so on.

What about negative numbers?

Please take note however the rules of negative numbers.

  • Positive numbers are always greater than negative numbers.
  • If both numbers are negative, do the following:

1.) Make them positive
2.) Apply the rules above
3.) Reverse your answer.

Example: Compare -82.45 and -82.31

1.) Make them positive: 82.45 and 82.31
2.) Apply the rules above:

From the rules above, the whole numbers are both 82, so we look at the tenths place. 0.4 > 0.3, so 82.45 > 82.31

3.) Reverse the answer. Since 82.45 > 82.31, – 82.31 > – 82.45.

7 Tips in Answering Reading Comprehension Questions

Reading comprehension questions is one of the types of test in the Civil Service Examination and is usually included in many Standard English tests. Reading comprehension questions are not very difficult, but they take a lot of time. However, with practice and correct strategy, you might be able to reduce the time you spend on the questions, increase your chance of passing the examination, and even get a high score. Below are some of the tips that you can use in answering reading comprehension questions.

7 Tips in Answering Reading Comprehension Questions

1.) Before reading the passage, read the questions first (not the choices). If you know the questions, then you can choose what to take note while reading.

2.) Pay attention to the first and last sentences in the each paragraph. Usually, those sentences state the main idea of the passage.

3.) Most passages have clues about the important ideas. Phrases like “note that,” “clearly,” and “do not overlook” give you hints on which ideas to focus on.

4.) Read ALL the choices. Do not rush answering if you think you found the correct answer. The next answer might be a better answer.

5.) Take note of the difference between the true answer and correct answer. Carefully read the passage and understand the ideas it communicates. Be sure that your answer is based on the passage and not your own opinion.

6.) Do not spend a lot of time in one question. If you cannot find the answer even if you refer to the passage, eliminate the obviously wrong choices, and choose your answer from the remaining choices.

7.) Review your answers. If you finished the exam early, go back to the questions where you have doubts. Reread the passage and answer the question.

I hope these tips can help you in your endeavor to pass the Civil Service Exam or any other exam for that matter. Good luck and share these tips to your friends.

Solving Quadratic Word Problems in Algebra

Quadratic Equations are equations of the form ax^2 + bx + c = 0 where a, b and c are real numbers and a \neq 0. Depending on the form of the equation, you can solve for x by extracting the quare root, factoring, or using the quadratic formula.This type of equation appears in various problems that involves multiplication and usually appears in the Civil Service Exams.

The following series details the method and strategies in solving problems involving quadratic equations.

How to Solve Quadratic Word Problems Part 1 is about solving problems involving consecutive integers. In this problem, the product of consecutive numbers is given and factoring was used to solve the problem.  » Read more

How to Solve Quadratic Word Problems Part 3

In the previous two posts (Part 1 and Part 2), we have discussed two problems involving quadratic equations. The first one is

A rectangular flower garden with dimensions 3m by 7m is surrounded by a walk of uniform width. If the area of the walk is 11 square meters, what is the width of the walk in meters?


If we let x be the width of the walk, then the length of the walk becomes x + 7 + x = 7 + 2x and the width becomes x + 3 + x = 3 + 2x as shown in the figure below.


We know that the area of the garden (the inner rectangle) is equal 7 \times 3 = 21 square meters. The area of the larger rectangle is equal to

(3 + 2x)(7 + 2x) = 21 + 14x + 6x + 4x^2 = 21 + 20x + 4x^2.

Now, to get the area of the walk, we have to subtract the area of the garden from the area of the large rectangle. That is,

area of the larger rectangle – area of the smaller rectangle = 11

4x^2 + 20x + 21 - 21 = 11

4x^2 + 20x = 11

Subtracting 11 from both sides, we have

4x^2 + 20x -11 = 0.

Now, the quadratic equation is not factorable, so we use the quadratic formula in order to find the value of x. In using the quadratic formula, we want to identify the values of a, b, and c in the equation ax^2 + bx + c = 0 and substitute in the quadratic formula

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

From the equation above, a = 4, b = 20 and c = -11. Substituting these values in the quadratic formula, we have

x = \dfrac{-20 \pm \sqrt{(-20)^2 - 4(4)(-11)}}{2(4)}

= \dfrac{-20 \pm \sqrt{400 + 176}}{8}

= \dfrac{20 \pm 24}{8}

That means that we have two roots

x_1 = \dfrac{-20 + 24}{8} = \dfrac{1}{2}

x_2 = \dfrac{-20 - 24}{8} = \dfrac{-44}{8} = \dfrac{-11}{2}.

As we can see, we x_2 is not a possible root because it is negative. Therefore, the acceptable answer to the problem is

x_1 = \dfrac{1}{2}.

This means that the width of the walk is ½ meters.

Check: If the width of the walk is ½ meters, then the length of the larger rectangle is 1/2 + 7 + 1/2 = 8 and the width is 1/2 + 3 + 1/2 = 4. The area is (8)(4) = 32 sq. m.

Now the area of the walk is 21 meters and 32 - 21 = 11 sq. m. which is the area of the walk indicated in the problem. Therefore, we are correct.

You can also watch the Youtube video below regarding the discussion above.


December 2015 Region 5 Civil Service Subprof Exam Result – List of Passers

Below is the list of passers from Region 5 of the Civil Service Exam Subprofessional Examination conducted on December 6, 2015.

Seq No Region Exam No Name
1 05 713558 BARRIOS, CELSO JR E
4 05 713561 ZUNIEGA, LIEZL S
*** Nothing Follows ***


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