Trends Relationships - Done on 19 Oct 2017

www.logiqids.com

Topic Note: Ability to Identify Trends/ Relationships The questions in this category can broadly be classified in t wo categories: 1) Sequencing: The questions in this category typically present a sequence and ask the child to identify either the next term or a missing term in the sequence. Some questions also ask the child to identify the wrong term in the sequence. e.g.: What would be the next term in the sequence: A, C, E, G? Fill in the missing term in the sequence: 1z, 3y, 5x, ___, 9v. Find the wrong term in the sequence: 1, 4, 7, 11, 13, 16, 19 2) Ability to Identify Relationships : The questions in this category typically present a particula r relationship between two or more words / phrases and the student has to decipher what the relationship is between the two words / phrases and apply the same to a new word. Alternately the student could also get a question where four or more words / terms are presented and the student has to find the odd one out. e.g.: If in a certain coded language BAT is written as TAB, then how will AND be written as? Please note that each topic note contains some questions which some children could find relatively difficult. However we have preferred to keep them in the topic note to give the student and parent an idea about various different type of questions. These relatively difficult questions have been highlighted in red font.

SEQUENCING These questions typically consist of a series of numbers, alphabets or symbols or a combination of either of these, which are typically connected by way of a rule or pattern. The key to solving these questions is to identify the trend or pattern and acc ordingly either find out the next term in the pattern or a missing term in the pattern or identify a wrong term in the pattern. The following explains the broad categories of patterns which one can find: IMAGE BASED PATTERNS:

These questions consist of images or symbols – two two or more which follow a particular pattern. The pattern either consists of repeating images or the images are linked by a common rule. The key here is to identify the repeating pattern or the rule which connects them. These questions could be broadly classified into three categories:  

Repeating pattern – In In this case, the images / symbols form a pattern which repeats itself Rule based pattern – In In these questions, the images are linked by way of a common rule. Some examples of such rules could be Movement of the shape or part of the shape in clockwise or anticlockwise direction o

For any queries, contact us on [email protected] or whatsapp us on +91-7045 345345

www.logiqids.com

o o

A part getting added and subtracted in the shape Abstract Pattern – these are also rule based patterns, but the patterns are not so obvious as movement in clock-wise / anti clock-wise direction or addition / subtraction in the shape, but instead follow a slightly abstract rule like increasing number of sides of the object or colours appears in the order in which they appear in t he rainbow, etc. SOLVED EXAMPLES

?

1) Identify the next term in the sequence:

Solution: Clearly as shown above the pattern

is repeating itself. Thus in the above

question, after circle, the next term would be a square again and hence the answer is The above example is a very simple form of a symbolic sequencing problem. The type of problems could vary significantly ranging from slightly longer pattern to more abstract concepts being implemented. Few of such examples are given below:

2) Identify the next term in the sequence:

Solution: The above question can be broken down to a pattern which repeats itself as follows:

A

B

Clearly as shown above the pattern

C

is repeating itself.

Block C should follow the same layout as Block A or Block B and so after the square, we should have a circle. So the next term in the sequence is A slightly more complicated question could be where the symbols are not getting repeated but following a certain pattern:


www.logiqids.com

3) Find the next term in the sequence: Solution: In this question, though no pattern is being repeated, like in the questions above, all the symbols / shapes seem to be following a certain rule: “Every shape in the sequence has one more side than the previous shape”. So the next shape in the sequence should be a

heptagon (one which has seven sides)

4) Find the next term in the sequence: Solution: In this question also, though no pattern is being repeated, all the symbols / shapes seem to be following a certain rule: “ The arrow inside the square is at 45degrees in the clockwise direction compared to the arrow in the previous square” So the next shape in the sequence should have an arrow pointing at 45 degrees clockwise from south west direction. So

the next square should have an arrow pointing in west direction 5) Which

colour

will

come

in

place

of

question

mark

in

the

last

circle?

Solution: This is a more difficult kind of abstract question. There is no set approach to solve such abstract questions. One needs to identify a way by which the shapes / symbols are related. For instance in the given question, the colour in the circles are following the sequence of rainbow colours: Violet, Indigo, Blue, Green, Yellow, Orange. So the next circle should have the Red colour to complete the sequence of rainbow colours.

NUMERICAL SERIES:

These consist of various numbers which are connected by certain rule. The numbers could be arr anged in ascending or descending order or could follow some other rule. Some examples of these patterns could be: 1) Numbers in an ascending or descending order having a constant difference between them. For example: a. 2,5,8,11,14 – first term is 2 and constant difference between two consecutive terms is 3 2) Numbers in an ascending or descending order but with the difference between them following a certain pattern. Some examples are given below:


www.logiqids.com

a. 1,3,7,13, 21 – first term is 1 and the difference between two consecutive term is itself another pattern 2,4,6 and so on i.e. numbers with a difference of 2 1 3 7 13 21 2

4 2

3)

6 2

8 2

b. 1, 2, 4, 8, 16, 32 – first term is 1 and then every subsequent term is obtained by multiplying the previous term by 2. Sequence with two numbers in each term, where one or both the numbers show an increasing or decreasing pattern. For example: a. 11/12, 15/11, 19/10, 23/9,.. – Here the top term (or the numerator) i.e. 11 keeps increasing by 4 for each term, while the bottom term i.e. 12 keeps on decreasing by 1 for each term. Thus 11 becomes 15, then 19, then 23 and so on. While 12 becomes 11, then 10, and so on.

4)

Mixed series – where the terms are from two or more series. In a case like this, the difference between two consecutive terms is UNLIKELY to follow a pattern and that’s a hint that the given series is formed by two of more series a. 11, 15, 13, 19, 15, 23, 17 – Here the difference between two consecutive terms follows the order 4, -2, 6, -4, 8, -6 and so on. Given the difference is increase and then decreasing and then increasing again, one must examine if this sequence has two or more series. Lets first look for two series. Taking alternate numbers in the sequence, we get two series as 11, 13, 15, 17 and 15, 19, 23. Clearly the sequence consists of two series – the first one having a difference of 2 between two consecutive terms and the second one having a difference of 4 between two consecutive terms.

5)

Pyramid series – In this series the difference between two consecutive terms follows an increasing or decreasing trend, but does not really follow any other particular pattern. In this case the student should first find the difference between two consecutive terms, then the difference between the “numbers obtained for difference between two consecutive terms” and continue till u get the same difference. a. Find the next term in the series: 1,6,14, 27, 47, 76,? As shown below, this is a type of pyramid series i.e. the difference between the numbers representing the “difference between two consecutive terms” will become constant at some point. In order to calculate the last term, the student will need to back calculate each term as shown below:


www.logiqids.com 1

6

5

14

8

3

27

13

5

2

47

20

7

2

29

9

2

116

76

40

11

2

6) Numbers following an abstract pattern. Some examples are given below: a. 1, 4, 9, 16, 25 – Every term in the series follows the pattern : 1 2, 22, 32, 42, 52 b. 1,1,2,3,5,8,13,21 – Starting from the third term, every term in the series is a sum of the two terms preceding it. Thus 3rd term 2 is the sum of 1 + 1; Fourth term 3 is a sum of 2+1; fifth term 5 is a sum of 3 + 2 and so on c. 1, 4, 9, 61, 52, 63, 94 – one of the more difficult questions – here every term is a square of a natural number, but each term is put down in reverse. So 1 2 stays as 1, so does 22 and 32, as all of these are single digits. 42 is 16 which is shown as 61; Similarly 25, 36 and 49 are shown as 52, 63 and 94 respectively.

The best way to solve a numerical sequence problem is to follow the following steps:  





 

F ind the difference between two consecutive terms for the full sequence I f the difference is constant, the question is solved and you can find the next term by adding the difference to the last term I f the difference is not constant identify if the difference follows a particular pattern, e.g 2, 4, 6, 8. I f it does, identify what the next term should be in the sequence of differences (eg in 2,4,6,8, the next term will be 10). A dd this difference to the last term and find out the next term I f the difference is not constant there could be wo possible cases – either a pyramid series or mixed series F or pyramid series keep checking the difference as explained above – go to 3 or max 4 layers. F or a mixed series, the student should check if the given sequence comprises two or three series. To check if it’s a combination of two series, the student should take alternate terms together and see if they comprise a series. To check if it’s a c ombination of three series, the student should



take terms which are separated by two terms between them and see if they comprise a series. I f none of the above thing works, it is very likely that the question comprises an abstract series. F or which student can check for things like: I f the term is the sum of terms before o o o

If it’s obtained as multiplication of terms before

I f it involves squares or cubes (not relevant for students below grade 4)


www.logiqids.com

ALPHABETICAL SERIES:

These questions comprise of various letters which are arranged in alphabetical or non-alphabetical letter and follow a certain rule. Some examples are given below: 1) Alphabets in an alphabetical or reverse alphabetical order where the difference between every two consecutive terms follows a pattern. Some examples are given below: a. A, C, E, G, I – first term is A and then the alphabets appear in an alphabetical order but skip each alternate alphabet b. S, R, Q, P – first term is S and alphabets are following reverse alphabetical order. The next term will be O. c. A, B, D, G, K – first term is A and the difference follows the following pattern: No alphabet skipped between A and B  

One alphabet skipped between B and D



Two alphabets skipped between D and G

Thus if we take the number of alphabets which are skipped between two consecutive terms, they follows the pattern 0,1,2,3, etc. Thus the alphabetical pattern derives itself from a numerical pattern for difference between two consecutive terms. d. BDF, CFI, DHL, EJO – first, second and third letters of each term are moved forward by one, two and three places respectively to obtain the first, second and third letter of the next term. B moved forward by one becomes C D moved forward by two becomes F F moved forward by three becomes I 

  

So BDF becomes CFI and similarly CFI would become DHL and so on. e. QPO, NML, KJI, ___, EDC - Each term of the series consists of letters in a reverse alphabetical order. Thus the missing term is HGF f. Word appearing in alphabetical / order – e.g. ABACK, ACID, ADDITION, AEON.. Here the second letter in the word follows the alphabetical order starting from B. In such a question there can be multiple possible answers for the next term, but out of the four options only one will fit. So the student should select the one which is the correct answer from the options. 2)

Alphabets arranged in a particular pattern with some letters missing in the pattern: a. a b c a b c a b c _ b _: Alphabets are following the pattern a b c which is getting repeated and hence the missing alphabets are a and c b. a a b b a a b b _ a b _ : Here a a b b is getting repeated. Hence the missing letters are a and b so that they complete the sequence a a b b

3)

Alphabets related by some abstract rule. Some examples are given below: a. Find the missing term in A, E, I, _ , U – the alphabets given here are vowels arranged in alphabetical order. So the missing alphabet is O


www.logiqids.com

b. Find the missing term in U, O, I, _ , A – the alphabets given here are vowels arranged in reverse alphabetical order. So the missing alphabet is E c. Find the missing term in V, I, R, A, T, K, O, _, L, I – the alphabets given here seem to represent the name of a famous cricketer VIRAT KOHLI, So the missing term is H d. ELFA, GLHA, ILJA, ______, MLNA - The second and fourth letters in the series, L and A , are static. The first and third letters consist of an alphabetical order beginning with the letter E. So the missing word will have L and A at the second and fourth place respectively. And the remaining letters will be such that they continue the alphabetical order series which started with the first term. E and F in the first term, G and H in the second term, I and J in the third term and so K and L in the fourth term. So t he missing term is KLLA

WRONG TERM SERIES:

Sometimes, a question is asked to find out the wrong number in a series. This is a bit more difficult. This is because from the point where you get a wrong number, all other succeeding numbers would : also look wrong. See the following example Example No. 1: Find the wrong number in the following series.

2 4 8 17 32 64 Solution: In this question, if you start from the beginning, the difference between first two terms is 2, then its 4, then the difference is 9, then 15 and then 32. If you observe the trend in the dif ference, you will realise that the difference should have followed the pattern 2, 4, 8, 16, 32. Thus the fourth term should be 16 and not 17. Example No. 2: Find the wrong number in the following series.

15 46 63 71 75 77 78 Solution: In this question, if you start from the beginning, the difference between first two terms is 31, then the difference between second and third term is 17, the difference between third and fourth term is 8. So it is difficult to find a correlation between terms. Instead if one start s backwards, one can see that difference between last two terms is 1, and that between second last and third last is 2 and then 4 and so on 8,16 and 32 should have been the difference. Thus the second term should have been 15 + 32 = 47 and not 46. On replacing 46 with 47, one can see that the difference between every two consecutive terms follows the pattern + 32, + 16, + 8, + 4 and so on. Example No. 3: Find the wrong number in the following series.

10 21 43 85 175 Solution: In this question, every subsequent term is obtained by multiplying the previous term by 2 and adding 1 to the total. But the error lies where instead of 43x2 + 1 = 87, 85 has been given. So 85 is the wrong number. For any queries, contact us on [email protected] or whatsapp us on +91-7045 345345

www.logiqids.com

LINKED SERIES:

In this type of questions, two or more series are linked and they follow a similar pattern. The student has to analyse the logic from the first series and apply the same logic to form the second series, and answer the given questions. See the following example. Example No. 1: In the following question a series is given and it is followed by the starting point of another series. After this, a question is given, you have to complete the second series by applying the same logic as in the first given series, and then you have to answer the question.

5 8 12 17 23 30 9 a b c d e Which number should come in place of c? Solution: In this question, it can be analyzed that the difference between the numbers is 3, 4, 5, 6 and 7. So you have to apply the same logic and start the series with 9. The firs t number after 9 would be 9 + 3 = 12 (this would replace letter a), the second number would be 12 + 4 = 16 (this would replace letter b) and the third number would be 16 + 5 = 21 (this would replace the letter c). You need not to go further because the question is related to c only. Another variant of linked series could be questions consisting of three sequences with three different elements (usually capital letters, digits and small letters). Each capital letter is found to correspond to one unique number and a unique small letter. The student has to decipher this linkage and accordingly fill the right term in the question. An example is given below. Example No. 2: In the following question, choose the numbers in the order which will be filled in the spaces marked with a question mark:

B ___ a

___ ___ ___

___ 4 a

D 1 ___

___ 2 c

A ___ c

B ___ ___

D ? ___

A ? ___

B ? ___

Solution: Clearly in the second series, as shown in column number 4, 1 occurs in the position of “D” and so the first question mark under “D” should have the number 1. Similarly “c” corresponds to “2” and to “A”. So the second question mark under “A” should have t he number 2. Also as shown in first column “B” corresponds to “a” and as shown in the third column “a” corresponds to “4”. Thus the question mark under B will be replaced by “4”. ALPHABETICAL + NUMERICAL SERIES

Sometimes the question involves both numerical and alphabetical te rm. Such questions can broadly be of two types: 

Given sequence comprises two series, where one series involves alphabets and second series involves numbers For any queries, contact us on [email protected] or whatsapp us on +91-7045 345345

www.logiqids.com

Eg: 1A, 3B, 5C, 7D, .. – this involves two series 1,3,5,7 and A, B, C, D… 

The numbers are related to the alphabets. Some examples of such relationship could be: o Number represents the position of the alphabet in the English alphabet e.g. A is 1, B is 2 and so on e.g.: A1, E5, I9, and so on – here the series moves as the vowel and the number represents the position of the letter in the English alphabet. o Number represents reverse position of the alphabet / position considering Z as 1 e.g. A is 26, B is 25. In case of a word, the number could represent 1) the number of letters in the word e.g.: o WORD4, 2) the number of vowels in the word egWORD1 3) the number of consonants in the word egWORD3 4) the number of repeating letters in the word e.g. WORD0, WOOD2 5) the sum or product of the positions of each letter in the word number obtained eg: BAD7 or BAD8 – here B is 2, A is 1 and D is 4 – their positions in the English alphabet. So in BAD7, 7 represents the sum of 1+2+4 and in BAD8, 8 represents the product of 1x2x4.

ABILITY TO IDENTIFY RELATIONSHIPS In these cases, you are typically given two words which are related by some rule and one needs to decipher that rule and apply it on the other word given in the question. Some examples are given below: 1) Deciphering the code Question: If in a certain code language, 15789 is written as EGKPT and 23461 is written as ALURE, how will 23549 be written be written as Solution: In this case, the student needs to study which number relates to which alphabet and just apply those codes to the given questions. Thus for 23549, one can see that 2 corresponds to A, 3 to L, 5 to G, 4 to U and 9 to T. So the answer is ALGUT. 2) Decoding Sentences Question: If in a certain code language, “tee see pee” means “drink fruit juice” and “see kee lee” means “Juice is sweet” and “lee ree mee” means “He is intelligent” how will sweet be written as in this language? Solution: In this case, the words common b etween “drink fruit juice” and “Juice is sweet” is “Juice” and similarly in the coded language for these two phrases, “see” is common. So see means juice. Similarly between the second and the third statement, “is” is common and in the coded language “lee” is common. So in the phrase “see kee lee”, see represents Juice, lee represents “is” and so sweet is being represented by “ kee”. 3) Coding by reversing the order of the alphabets Question: If in a certain code language, BAT is written as TAB, how will AND be written as Solution: In this case, the alphabets in the words BAT are reversed to arrive at the coded word TAB. So AND when coded will become DNA. For any queries, contact us on [email protected] or whatsapp us on +91-7045 345345

www.logiqids.com

4) Coding by following a certain rule for movement of alphabets in a word Question: If in a certain code language, GIFT is written as TGFI, how will BEST be written as Solution: In this case, the alphabets in the words GIFT are rearranged in a particular order, which needs to be applied to BEST too. In GIFT the first and fourth letters are interchanged and placed in first and second positions (TG) and second and third l etters are interchanged and placed in third and fourth positions (FI). Applying the same rule BEST will be coded as TBSE. 5) Coding based on number of alphabets appearing in a given word Question: If in a certain code language, BAD is coded as 3, GIFT is coded a 4, FLIGHT is coded as 6, how will CHILDREN be coded as Solution: In this case, the code represents the number of alphabets in a given word. Since BAD has three alphabets, the code is 3; similarly for GIFT, the code is 4 and for FLIGHT the code is 6. So for CHILDREN the code should be 8, as CHILDREN has 8 alphabets. 6) Coding by replacing alphabets by numbers where numbers represent their position in the English alphabet; i.e. A is replaced by 1, B by 2, C by 3 and so on Question: If in a certain code language, BAD is coded as 214, how will CAP be coded as Solution: In this case, the alphabets are replaced by numbers which represent their position in the English alphabets. Since B is the second letter in English Alphabet, it is replaced by 2. Similarly since D is the 4 th letter, it is replaced by 4. Thus CAP would be coded as 3116. 7) Coding by replacing alphabets by the next alphabet which occurs in the English language; i.e. A is replaced by B, B by C, C by D and so on Question: If in a certain code language, BAT is coded as CBU, how will CAP be coded as Solution: In this case, the alphabets are replaced by another alphabet, which occurs next in the English language. So in BAT, B is replaced by C, A is replaced by B and T is replaced by U. Following the same rule for CAP, C should be replaced by D, A b y B and P by Q. So the answer is DBQ. 8) Coding by replacing alphabets with the corresponding alphabet in the reverse alphabetical order i.e. replace A by Z, B by Y, C by X and so on. Question: If in a certain code language, BAT is coded as Y ZG, how will CAP be coded as? Solution: In this case, the alphabets are replaced by corresponding alphabet in revere alphabetical order; i.e. Replace A by Z, B by Y, C by X and so on. In BAT, B is replaced by Y, A by Z and T by G (T is the 20 th alphabet from the beginning; G is the 20 th alphabet from the end). Following the same rule for CAP, C should be replaced by X, A by Z and P by K. So the answer i s XZK . There could be some abstract questions also for relationship type questions. Few such examples are given below:


www.logiqids.com

9) If in a certain code language, SYSTEM is coded as ESYSTM and CLIMATE is coded as IAECLMT, how will COMPUTER be coded as? Solution: In this case, the coding rule being followed is that all the vowels in a word are being moved at the beginning of the word and then they are followed by the consonants in the word. Thus in SYSTEM, there is only one vowel i.e. E which is moved to the beginning of the word and the remaining letters come as is. So SYSTEM is coded as ESYSTM. Similarly, for CLIMATE, the vowels are I, A and E. Putting all the vowels upfront (in the same order in which they occur in the word), we get IAECLMT. So COMPUTER should be coded as OUECMPTR. ODD ONE OUT Similar to above questions, the student could also be asked to find the odd one out from a group of things given to them. Most of the time, the student would need to think on the same concepts as that of sequencing or coding (as explained above) and figure out a relationship connecting the various things. An example is given below  

Find the odd one out from: 2, 6, 9, 12, 18 – Answer is 9 as it is the only odd number Find the odd one out from: BD, IK, NP, XY, AC – The odd one out here is XY as all the other terms have letters which are separated by one alphabet in English language. i.e. B and D are separated by C; I and K are separated by J, and so on

Given above are just a few examples of questions to get st udents started in thinking about solving such questions. There could be several other ways of arriving at such relationships, which the students will need to work out themselves looking at the question.


www.logiqids.com

PRACTICE QUESTIONS:

Directions for Questions 1 to 8: There is a problem figure on the left hand side, which represents a series, while there are a few options on the right hand side, one of which is the answer. Find the image from the answer figures which will form the next term or the missing term of the series:

1)

2)

3)

4)

5)

6)


www.logiqids.com

7)

8) 9) Find the next term in the series: 36, 30, 24, 18,… A. 7 B. 10 C. 12 D. 13 10) Find the next term in the series: 1, 2, 3, 5, 8, A. 7 C. 12

B. 10 D. 13

11) Find the next term in the series: 7, 10, 8, 11, 9, 12,? A. 7 B. 10 C. 12 D. 13 12) Find the next term in the series: P, O, N, M, L,? A. K B. Q C. R D. J 13) Find the next term in the series: A, D, G, J, ? A. K C. M

B. L D. J

14) Find the next term in the series: 36, 34, 30, 28, 24, ? A. 22 C. 23

B. 20 D. 26

15) Find the next term in the series: 22, 21, 23, 22, 24, 23, ? A. 22 B. 25 C. 24 D. 27 16) Find the next term in the series: 2A, 4D, 6G, 8J, ? A. 12M B. 12L C. 10M D. 10J


www.logiqids.com

17) Find the next term in the series: 53, 53, 40, 40, 27, 27, ? A. 53 B. 14 C. 24 D. 27 18) Find the next term in the series: 21, 9, 21, 11, 21, 13, 21, A. 16 B. 21 C. 24 D. 15 19) Find the next term in the series: 3, 4, 7, 8, 11, 12, ? A. 22 C. 14

B. 15 D. 17

20) Find the next term in the series: 8, 22, 8, 28, 8, 34, 8? A. 28 C. 40

B. 24 D. 27

21) Find the next term in the series: 1Z, 2X, 3V, ___ A. 4W C. 4Y

B. 5W D. 4T

22) Find the missing term in the series: SCD, TEF, UGH, ____,WKL A. VIJ B. VKL C. WIJ D. TKL

23) Find the missing term in the series: CMM, EOO, GQQ, _____, KUU A. ISS B. JKK C. MSS D. JMM 24) Find the missing term in the series: A1B2C3D4E5__G7H8 A. F6 B. F9 C. 6F D. E6 25) Find the next term in the series: 3, 6, 12, 21, 33, 48, ? A. 56 C. 76

B. 66 D. 68

26) Identify the odd one out: A. FOREST0 C. NATION2

B. TREE2 D. FOLLOW2


www.logiqids.com

27) Identify the odd one out: A. FOREST6 C. NATION5

B. TREE4 D. FOLLOW6

28) If BOWLED is coded as LEDWOB, how will SINGLE be coded as? A. ELGSIN B. GLESIN C. GLENIS D. ELGNIS 29) If NISHIT is coded as IINSHT, how will DEEPTI be coded as? A. EEPTID B. EEIDPT C. EEITPD D. EEIDTP 30) If BAD is coded as 214 and GET as 7520, how will DEEP be coded as? A. 45516 B. 4556 C. 4456 D. 45515 31) Find the next 5 terms in the series : 122333444455555666? A. 66677 B. 77777 C. 67777 D. 66777 32) Find the next term in the series : 1234543211232? A. 5 C. 3

B. 4 D. 1

33) Find the next term in the series :11,24,39,416,525,636,? A. 747 B. 749 C. 832 D. 943 34) Find the next term in the series : 4/6, 8/5, 12/4, 16/3 ? A. 17/3 C. 20/2

B. 20/3 D. 20/1

35) Find the next term in the series: EARN, EBB, ECHO, EDWARD? A. EEL B. EYE C. EAR D. EFA


www.logiqids.com

ANSWERS 1) 2 2) 3 3) 5 4) 5 5) 4 6) 4 7) 4 8) 3 9) C 10) D 11) B 12) A 13) C 14) A 15) B 16) C 17) B 18) D 19) B 20) C 21) D 22) A 23) A 24) A 25) B 26) D 27) C 28) C 29) B 30) A 31) A 32) D 33) B 34) C 35) A


Trends Relationships - Done on 19 Oct 2017

Recommend Documents