BFAR - Bureau of Fisheries and Aquatic Resources
CHED: CHED: Commission on Higher Education
CHED - Commission on Higher Education
DAR: DAR: Department of Agrarian Reform
COA - Commission on Audit
DepEd: DepEd: Department of Educations
COMELEC - Commission on Elections
DFA: DFA: Department of Foreign Affairs
DepEd - Department of Education
DND: DND: Department of National Defense
DOLE - Department of Labor and Employment
DOF: DOF: Department of Finance
DOST - Department of Science and Technology
DOH: DOH: Department of Health
NAPOCOR NAPOCOR - National Power Corporation
DO J: Department of Justice
PAGASA - Philippine Atmospheric, Geophysical and Astronomical Services Administration
DOT: DOT: Department of Tourism DTI: DTI: Department of Trade and Industry
TESDA - Technical Education and Skills Development Authority
GSIS: GSIS: Government Service Insurance system
AFP: AFP: Armed Forces of the Philippines
DPWH - Department of Public Works and Highways
BFAD: BFAD: Bureau of Food and Drugs
DSWD - Department of Social Welfare and Development
BIR: BIR: Bureau of Internal Revenue BI – Bureau of Immigration BSP: BSP: Bangko Sentral ng Pilipinas NBI – National bureau of integration CCP: CCP: Cultural Center of the Philippines WWFWWF- World wildlife fund Numerical series tests are a type of numerical aptitude test which require you to find the missing number in a sequence. This missing number may be at the beginning or middle but is usually at the end. Identify the missing number in the series.
A
B
C
D
1 4, 8, 16, 32, ?
48
64
40
46
E
A
B
C
D
E
2 4, 8, 12, 20, ?
32
34
36
38
40
A
B
C
D
E
3 54, 49, ?, 39, 34
47
44
45
46
42
A
B
C
D
E
4 ?, 19, 23, 29, 31
12
15
16
17
18
44
These number sequences can be quite simple like the examples above. However, you will often see more complex questions where it is the interval between the numbers that is the key to the sequence. Identify the missing number in the series. A B C D E 5 3, 6, 11, 18, ? 30 22 27 29 31
6 48, 46, 42, 38, ?
A 32
B 30
C 33
D 34
E 35
These numerical series test questions usually consist of four visible numbers plus one missing number. This is because the test designer needs to produce a sequence into which only one number will fit. The need to avoid any ambiguity means that if the number sequence relies on a more complex pattern then there will need to be more visible numbers. For example; Identify the missing number in the series.
7
4, 3, 5, 9, 12, 17, ?
8 5, 6, 7, 8, 10, 11, 14, ?, ?
A 32
B 30
C 24
D 26
A 19
B 17
C 15
D 16
E 22 E 21
A B C D E 9 1, ?, 4, 7, 7, 8, 10, 9, ? 6 3 11 13 12 Answers 1. B – The numbers double each time 2. A – Each number is the sum of the previous two numbers 3. B – The numbers decrease by 5 each time 4. D – The numbers are primes (divisible only by 1 and themselves) 5. C – The interval, beginning with 3, increases by 2 each time 6. B – The interval, beginning with 2, increases by 2 and is subtracted each time 7. D – Each number is the sum of the previous and the number 3 places to the left 8. C A – There are 2 simple interleaved sequences 5,7,10,14,19 and 6,8,11,15 9. A D – There are 2 simple interleaved sequences 1,4,7,10,13 and 6,7,8,9 To solve these number sequence questions efficiently, you should first check the relationship between the numbers themselves looking for some simple arithmetic relationship. Then look at the intervals between the numbers and see if there is a relationship there. If not, and particularly if there are more than 4 numbers visible, then there may be two number sequences interleaved. You will occasionally find multiplication, division, or powers used in these sequences, but test designers tend to avoid them as these operations soon lead to large numbers which are difficult to work out without a calculator. Letter of the Alphabet as Numbers Another type of number series question which appears in these tests involves the substitution of letters of the alphabet for numbers. For example A=1, B=2 etc. It may seem strange to consider these as number series questions but they do actually work in exactly the same way once you have changed them back into numbers. Identify the next letter in the series.
10 B, E, H, K, ?
A, Z, 11B, Y, ?
12 T, V, X, Z, ?
i
ii
iii
iv
L
M
N
O
i
ii
iii
iv
C
X
D
V
V P
V H
i
ii
iii
iv
V
Y
B
A
W
Q
Answers 16. iii – There are two letters missing between each one, so N is next. 17. i – There are 2 interleaved sequences A,B,C and Z,Y, so C is next. 18. ii – Miss a letter each time and ‘loop’ back, so B is next. Because arithmetic operations cannot be performed on letters there is less room for ambiguity in these questions. This means that interleaved sequences can be used with fewer visible letters than in questions that use numbers. Question 17 for example can use 2 interleaved sequences even though only four letters are visible. This would be very difficult to achieve with numbers. It is implicit in these ‘alphabetic sequence’ questions that the sequence ‘loops’ back around and starts again. See question 18. It is important to recognize this as it is not usually stated explicitly – you are just expected to know it. If you see more than one of these questions in a test then it is almost certainly worth taking the time to write out the letters of the alphabet with their ordinal numbers underneath. You can then treat these questions in a similar way to number series questions. This can save a lot of time overall and avoid simple mistakes.
If you are told that you need to sit a numerical reasoning test as part of the job selection process and you want to prepare for it properly, then you should ask which type of questions it contains. Specifically, is it just numerical series or does it also contain data interpretation, computation or estimation questions. These sample question papers each contain 22 questions and have a suggested time limit of 20 minutes. The questions are presented in Letter/A4 format for easy printing and self-marking
Number series tests present numerical sequences that follow a logical rule which is based on elementary arithmetic. An initial sequence is given from which the rule is to be deduced. You are then asked to predict the next number that obeys the rule. The difficulty level of these questions can increase in two ways; first, the logic behind the sequence becomes less trivial and demands attention and creativity; second, the missing number can be positioned at an early stage, thus preventing you from deciphering the hidden rule by looking only at the previous numbers in the sequence.
Number Series - examples and general tips See some general solving tips for number series test. In JobTestPrep's preparation package you will find all tips for solving number series tests. 1. Examine the difference between adjacent numbers.
a. In a simple series, the difference between two consecutive numbers is constant. Example: 27, 24, 21, 18, __ Rule: There is a difference of (-3) between each item. The missing number in this case is 15. b. In a more complex series the differences between numbers may be dynamic rather than fixed, but there still is a clear logical rule. Example: 3, 4, 6, 9, 13, 18, __ Rule: Add 1 to t he difference between two adjacent items. After the f irst number add 1, after the second number add 2 and after the third number add 3, etc. In this case, the missing number is 24. 2. See whether there is a multiplication or division pattern between two adjacent numbers. Example: 64, 32, 16, 8, __ Rule: Divide each number by 2 to get the next number in the series. The missing number is 4. 3. Check whether adjacent numbers in the series change based on a logical pattern. Example: 2, 4, 12, 48, __ Rule: Multiply the first number by 2, the second number by 3 and the third number by 4, etc. The missing item is 240. 4. See if you can find a rule that involves using two or more basic arithmetic functions (+, -, ÷, x). In the below series, the functions alternate in an orderly fashion. Example: 5, 7, 14, 16, 32, 34, __ Rule: Add 2, multiply by 2, add 2, multiply by 2, etc. The missing item is 68. Tip: Series’ in this category are easy to identify. Just look at the numbers that do not appear to have a set pattern. Important: In a series that involves two or more basic arithmetic functions, the differences between adjacent items effectively create their own series. We recommend that you try to identify each pattern separately. Example: 4, 6, 2, 8, 3, ___ Rule: In this series, the differences themselves create a series: +2, ÷3, x4, -5 The numbers advance by intervals of 1 and the arithmetic functions change in an orderly sequence. The next arithmetic function in the series should be +6, and so the next item in the series is 9 (3+6 = 9).
