Observation and matching — SSC CGL Reasoning Notes

Concepts and rules

Visual discrimination questions ask you to count shapes hidden in a line figure (triangles, squares, rectangles) or to spot the one copy of a pattern that differs from the original.

A triangle exists when 3 points are joined pairwise by drawn straight lines and the 3 points are not on one line. Lines passing through the inside do not cancel it.

A square or rectangle exists only when all 4 sides are drawn; a diagonal inside it does not matter.

Square with both diagonals: 8 triangles (4 small, 4 made of 2 small). Square with both diagonals and both midlines (lines joining midpoints of opposite sides): 16 triangles.

Triangle with k lines from the top vertex to the base (base cut into k + 1 parts): triangles = (k + 1)(k + 2)/2.

If, in addition, h lines parallel to the base cross all those lines, multiply by (h + 1), because each horizontal line acts as a new base for the same fan.

Squares in an n×n grid of small squares: 1² + 2² + … + n² = n(n + 1)(2n + 1)/6. For n = 3 this is 14 and for n = 4 it is 30.

Rectangles (squares included) in an m×n grid: choose 2 of the m + 1 horizontal lines and 2 of the n + 1 vertical lines, so the count is [m(m + 1)/2] × [n(n + 1)/2].

Fine discrimination: an original pattern and several copies differ by a swap, a reversed arrow, a missing dot or a changed shade. Compare one feature at a time, position by position.

Method and shortcuts

Step 1: name every corner and every crossing point with a letter (A, B, C …, O for the centre). Unlabelled crossings are where most counts go wrong.

Step 2: list the straight lines as point sequences, for example A–O–C for a diagonal through the centre.

Step 3: count by size: smallest regions first, then shapes made of 2 regions, then 3 or 4, then the whole figure.

Alternative for triangles: fix each point as the top vertex and count pairs of lines from it that are closed by a third line.

Use the formulas only when the figure is exactly the standard type; if one line stops short or one extra line is added, count by size instead.

For discrimination, eliminate copies with a wrong count of symbols first, then scan positions from left to right and stop at the first mismatch.

Example 1: square with diagonals

Question: Square ABCD has both diagonals AC and BD, which cross at O. How many triangles are there?

Solution: Smallest: AOB, BOC, COD, DOA = 4. Made of 2 small: ABC, BCD, CDA, DAB = 4. No triangle uses 3 small regions.

Answer: 8

Example 2: squares in a grid

Question: A big square is divided into a 4×4 grid of equal small squares. How many squares are there in all?

Solution: 1×1 squares: 16; 2×2: 9; 3×3: 4; 4×4: 1. Total 16 + 9 + 4 + 1.

Answer: 30

Example 3: exact copy

Question: Original: ▲ ● ■ ◆ ● ▲ ■ ◆ ●. Copy 1: ▲ ● ■ ◆ ● ▲ ◆ ■ ●. Copy 2: ▲ ● ■ ◆ ● ▲ ■ ◆ ●. Copy 3: ▲ ● ■ ◆ ▲ ● ■ ◆ ●. Copy 4: ▲ ● ◆ ■ ● ▲ ■ ◆ ●. Which copy is exactly the same as the original?

Solution: All copies have 9 symbols, so compare positions. Copy 1 swaps positions 7 and 8, Copy 3 swaps positions 5 and 6, Copy 4 swaps positions 3 and 4.

Answer: Copy 2

Example 4: rectangles in a grid

Question: A rectangle is divided into 2 rows and 3 columns of equal squares. How many rectangles (squares included) are there? (a) 12 (b) 18 (c) 15 (d) 20

Solution: There are 3 horizontal lines and 4 vertical lines. Any 2 horizontal and any 2 vertical lines make one rectangle: 3 × 6 = 18. Check by size: 6 single cells, 7 made of 2 cells, 2 made of 3 cells, 2 made of 4 cells (2×2 blocks), 1 made of 6 cells: 6 + 7 + 2 + 2 + 1 = 18.

Answer: (b) 18

Example 5: square with diagonals and midlines

Question: Square ABCD (A top-left, B top-right, C bottom-right, D bottom-left) has both diagonals and both midlines EG and FH, where E, F, G, H are the midpoints of AB, BC, CD, DA; all 4 lines pass through the centre O. How many triangles are there? (a) 12 (b) 14 (c) 8 (d) 16

Solution: Smallest: the 4 quarter squares are each split by a diagonal into 2, giving 8 (AEO, EBO, BFO, FCO, CGO, GDO, DHO, HAO).

Made of 2 small: AOB, BOC, COD, DOA = 4. Made of 4 small: ABC, BCD, CDA, DAB = 4. Total 8 + 4 + 4 = 16. Triangles such as AEH do not exist because E and H are not joined.

Answer: (d) 16

Example 6: fan with parallel lines

Question: In triangle PQR, 2 lines are drawn from the top vertex P to the base QR, cutting the base into 3 parts. Then 2 lines parallel to QR are drawn across the whole triangle, cutting all 4 lines from P. How many triangles are there? (a) 18 (b) 12 (c) 15 (d) 24

Solution: Every triangle has P as its top vertex, 2 of the 4 lines from P as its sides and one horizontal line as its base. Pairs of lines from P: (k + 1)(k + 2)/2 with k = 2 gives 6. Horizontal bases: QR plus 2 parallels = 3.

Total 6 × 3 = 18. The shapes between 2 horizontal lines are trapeziums, not triangles, so nothing else is added.

Answer: (a) 18

Common mistakes

Counting only the smallest regions. Always continue to shapes made of 2, 3, 4 regions and the whole figure.

Counting a triangle whose third side is not drawn, such as AEH in a square with midlines but no inner diamond. Check that all 3 sides are drawn lines.

Counting the same triangle twice under different names (ABC and CBA). Fix one naming order, such as letters in alphabetical order.

Forgetting rectangles that are squares, or squares bigger than 1×1 in a grid.

Applying a formula to a figure that is not standard. If one line stops short, count by size.

In discrimination, judging the whole pattern at a glance. Compare position by position; a single swapped pair is the usual difference.

Practice questions

Q1. In a triangle, 3 lines are drawn from the top vertex to the base, cutting the base into 4 parts. How many triangles are there? (a) 6 (b) 8 (c) 10 (d) 12

Q2. Rectangle ABCD (AB is the top side, twice as long as BC) has both diagonals, which cross at O, and the vertical line MN joining the midpoints M of AB and N of DC, which also passes through O. How many triangles are there? (a) 10 (b) 12 (c) 8 (d) 14

Q3. Square ABCD has both diagonals, and the midpoints of its 4 sides are joined in order to form a tilted inner square. How many squares are there in the figure? (a) 6 (b) 5 (c) 4 (d) 8

Answers

Q1. (c) k = 3: (3 + 1)(3 + 2)/2 = 10. By size: 4 + 3 + 2 + 1 = 10.

Q2. (b) Smallest 6: AOD, BOC, AMO, MBO, DNO, NOC. Larger 6: AOB, DOC, ABD, ABC, ACD, BCD. Total 12.

Q3. (a) The outer square, the tilted inner square, and 4 small squares inside the inner square cut out by the 2 diagonals: 1 + 1 + 4 = 6.

Quick revision

Label every point, list lines as point sequences, count by size.

Square with diagonals: 8 triangles; add both midlines: 16.

Fan of k lines: (k + 1)(k + 2)/2, times (h + 1) for h parallel cross lines.

n×n grid: squares 1² + … + n²; m×n grid: rectangles [m(m + 1)/2] × [n(n + 1)/2].

Discrimination: same count first, then position by position.

Concepts and rules

Matching questions give an entry (a name, address, PIN code, phone number, date, file index or code) and ask which entry in another list is exactly the same, or how many pairs are identical.

Exact match means character by character: same letters, same digits in the same order, same spaces, hyphens, slashes, commas and full stops.

The usual changes planted by examiners: 2 adjacent digits swapped (4417 and 4471), one letter dropped or doubled (Deshmukh and Desmukh), similar shapes swapped (0 and O, 1 and I, 5 and S, rn and m), and a variant spelling of a place name.

A variant spelling of a real place (Nasik for Nashik, Gauhati for Guwahati) is still a different entry in an exact-matching question.

Dates: read each date only in the format stated. In DD-MM-YYYY, 04-03-2025 is 4 March 2025; in MM-DD-YYYY the same digits mean 3 April 2025.

A date is impossible if the month is above 12 or the day exceeds the days of that month; such an entry cannot match any real date.

In a 2-list table (List I and List II), a row matches only if every field in the row matches; one wrong field makes the whole row a mismatch.

Method and shortcuts

Step 1: compare lengths first. Different numbers of characters or digit groups mean a mismatch at once.

Step 2: compare numbers in chunks of 2 or 3 digits, moving left to right, and say each chunk aloud in your head (forty-four, seventeen). Swapped digits show up as a changed chunk.

Step 3: compare words syllable by syllable, not by overall look; the eye reads Desmukh as Deshmukh unless you slow down at each syllable.

Step 4: in option questions, find the first position where the options disagree with each other; only that position needs checking against the original.

Shortcut for dates: rewrite every entry as day + month name + year before comparing; never compare raw digit strings written in different formats.

Example 1: identical pairs

Question: How many pairs are exactly identical? Pair 1: KX-4471-PB | KX-4471-PB. Pair 2: Ravi Shankar Mishra | Ravi Shanker Mishra. Pair 3: 221B, Civil Lines, Prayagraj | 221B, Civil Lines, Prayagraj. Pair 4: 0761-2457893 | 0761-2475893.

Solution: Pair 2 differs in Shankar and Shanker. In Pair 4 the chunks 457 and 475 differ. Pairs 1 and 3 match in every character.

Answer: 2

Example 2: dates in different formats

Question: How many of these entries are the date 4 March 2025, each read in the format given in brackets? Entry 1: 04-03-2025 (DD-MM-YYYY). Entry 2: 03-04-2025 (MM-DD-YYYY). Entry 3: 2025-04-03 (YYYY-MM-DD). Entry 4: 03-04-2025 (DD-MM-YYYY).

Solution: Entry 1 is day 4, month 3. Entry 2 is month 3, day 4. Entry 3 is month 4, day 3, that is 3 April. Entry 4 is day 3, month 4, also 3 April.

Answer: 2 (Entries 1 and 2)

Example 3: city and PIN table

Question: List I: Jaipur 302001, Bhopal 462001, Patna 800001, Nagpur 440001. List II: Jaipur 302001, Bhopal 462001, Patna 800001, Nagpur 440010. How many rows match exactly, and which row does not?

Solution: Compare in chunks: 302 001, 462 001 and 800 001 agree. For Nagpur, 440 001 and 440 010 differ in the last chunk.

Answer: 3 rows match; the Nagpur row does not.

Example 4: find the exact address

Question: Which entry is exactly the same as Dr. S. K. Venkataraman, 12/4, Mylapore, Chennai-600004? (a) Dr. S. K. Venkatraman, 12/4, Mylapore, Chennai-600004 (b) Dr. S. K. Venkataraman, 12/4, Mylapur, Chennai-600004 (c) Dr. S. K. Venkataraman, 12/4, Mylapore, Chennai-600004 (d) Dr. S. K. Venkataraman, 14/2, Mylapore, Chennai-600004

Solution: Option (a) drops the a in Venkataraman, option (b) spells Mylapur, option (d) has 14/2 instead of 12/4. Option (c) agrees in every character.

Answer: (c)

Example 5: look-alike characters

Question: How many pairs are exactly identical? Pair 1: QX7-8B10-LM | QX7-8B1O-LM. Pair 2: Ramnagar Colony | Rarnnagar Colony. Pair 3: 5S-2Z-I1 | 5S-2Z-I1. Pair 4: 98765-43210 | 98765-43210. Pair 5: Vasant Kunj, New Delhi | Vasant Kunj, New Dehli. Pair 6: Code 27ABCDE1234F1Z5 | Code 27ABCDE1234F1Z5. (a) 3 (b) 2 (c) 4 (d) 1

Solution: Pair 1 has digit zero on the left and letter O on the right after B1. Pair 2 has m on the left and rn on the right. Pair 5 has Delhi and Dehli. Pairs 3, 4 and 6 match character by character.

Answer: (a) 3

Example 6: all fields must match

Question: List I and List II each have 5 records (name, city, PIN). Record 1: Anil Kumar, Kanpur, 208017 | Anil Kumar, Kanpur, 208017. Record 2: Meena Iyer, Madurai, 625001 | Meena Iyer, Madurai, 625010. Record 3: Farhan Ali, Lucknow, 226001 | Farhan Ali, Lucknow, 226001. Record 4: Jaspreet Kaur, Ludhiana, 141001 | Jaspreet Kour, Ludhiana, 141001. Record 5: Sneha Patil, Nashik, 422001 | Sneha Patil, Nasik, 422001. Which records are fully identical? (a) Records 1, 3 and 5 (b) Records 1 and 3 only (c) Records 1, 2 and 3 (d) Records 3 and 4 only

Solution: Record 2 differs in the PIN (625 001 and 625 010), Record 4 in the name (Kaur and Kour), Record 5 in the city (Nashik and Nasik, a variant spelling but still a different entry). Records 1 and 3 match in all 3 fields.

Answer: (b)

Common mistakes

Reading the whole entry at a glance. The brain auto-corrects Dehli to Delhi; compare syllable by syllable.

Ignoring punctuation and spacing. 12/4 and 12-4, or 625001 and 625 001, are different entries in an exact-match question.

Comparing dates as raw digits. Convert each to day, month name and year in its own stated format first.

Accepting a record because 2 of its 3 fields match. A row matches only when every field matches.

Treating a known variant spelling as the same entry. In matching questions the spelling itself is being tested.

Practice questions

Q1. How many pairs are exactly identical? 0522-2618934 | 0522-2618934; ABJPK4417M | ABJPK4471M; Plot 9, MIDC, Pune | Plot 9, MIDC, Pune; Rohit Deshmukh | Rohit Desmukh; 11-08-2024 | 11-08-2024. (a) 2 (b) 4 (c) 3 (d) 5

Q2. A register writes dates as MM/DD/YYYY. Which entry is 9 December 2024? (a) 09/12/2024 (b) 12/09/2024 (c) 12/19/2024 (d) 09/21/2024

Q3. List I has Guwahati 781001. Which entry of List II matches it exactly? (a) Guwahati 781001 (b) Guwahati 781010 (c) Guwahatti 781001 (d) Gauhati 781001

Answers

Q1. (c) Pairs 1, 3 and 5 match. Pair 2 has 4417 and 4471; Pair 4 has Deshmukh and Desmukh.

Q2. (b) Month 12, day 09 is 9 December. Option (a) is 12 September, (c) is 19 December, (d) is 21 September.

Q3. (a) Option (b) changes the PIN, (c) doubles the t, (d) is the older spelling Gauhati.

Quick revision

Exact match = every character, digit, space and punctuation mark the same.

Check length first, then compare numbers in chunks of 2 or 3 digits.

Watch for 0/O, 1/I, 5/S, rn/m and swapped neighbouring digits.

Convert dates using the stated format before comparing.

A row matches only if all its fields match.

Concepts and rules

These questions give 2 or more entries and ask where they differ: the number of differing positions, the one entry unlike the rest, the pair that is not identical, or the entries common to 2 lists.

Position-wise difference: write the 2 strings one below the other and compare the characters in position 1, then position 2, and so on. The count of mismatched positions is the number of differences.

A swap of 2 neighbouring characters (18 becoming 81) creates 2 differing positions, not 1. A changed single character creates 1.

Position-wise comparison works only when both strings have the same length; if a character is missing, everything after it shifts, and the question then asks only whether the entries are identical.

Odd-one-out among copies: when 3 entries are identical and 1 differs, the differing one is the answer; find it by comparing each entry with the majority, not with the first entry only.

Common entries in 2 lists: an entry is common only if it appears in exactly the same form in both lists; the same digits in a different order (3840 and 3804) are different numbers.

Method and shortcuts

Step 1: check the lengths and the separators (hyphens, spaces) first; they locate the blocks to compare.

Step 2: compare block by block; inside a mismatched block, compare character by character and mark each differing position.

Step 3 (odd one out): compare entries 1 and 2. If they agree, compare 3 and 4 with them; if they differ, entry 3 decides which of them is the odd one.

Step 4 (common entries): sort or scan the shorter list and, for each entry, look for the same leading digits in the other list before checking the rest.

Why chunking works: short-term memory holds 3 or 4 digits reliably, so comparing 3-digit chunks avoids the misreads that happen when you hold 10 digits at once.

Example 1: differing positions

Question: At how many positions do 4729183650 and 4729813650 differ?

Solution: Chunks 4729 agree. Next, 18 and 81: positions 5 and 6 differ. The rest, 3650, agrees.

Answer: 2

Example 2: odd one out

Question: Entry 1: BK-49Z-7731-QR. Entry 2: BK-49Z-7731-QR. Entry 3: BK-49Z-7371-QR. Entry 4: BK-49Z-7731-QR. Which entry is different?

Solution: Entries 1 and 2 agree, so they form the majority. Entry 3 has 7371 in place of 7731; entry 4 matches the majority.

Answer: Entry 3

Example 3: common entries

Question: List X: 3804, 3840, 4380, 8034, 3408. List Y: 3480, 8034, 4038, 3840, 8304. How many numbers appear in both lists?

Solution: 3804 is not in Y. 3840 is in Y. 4380 is not (Y has 4038). 8034 is in Y. 3408 is not (Y has 3480).

Answer: 2 (3840 and 8034)

Example 4: the non-identical pair

Question: In which pair are the 2 entries NOT identical? (a) Sri Ganganagar | Sri Ganganagar (b) 7B, Park Street, Kolkata | 7B, Park Street, Kolkata (c) 560 034 | 560 034 (d) Thiruvananthapuram | Thiruvanantapuram

Solution: Split the long word into syllables: Thi-ru-va-nan-tha-pu-ram against Thi-ru-va-nan-ta-pu-ram. The h after the second t is missing. Pairs (a), (b) and (c) agree.

Answer: (d)

Example 5: swaps and changes together

Question: At how many positions do 7KQ2-8WX5-M0N3-RT6Z and 7KQ2-8XW5-M0N3-RT9Z differ? (a) 3 (b) 2 (c) 4 (d) 1

Solution: Block 1, 7KQ2, agrees. Block 2: 8WX5 against 8XW5, the swap W/X gives 2 differing positions. Block 3, M0N3, agrees. Block 4: RT6Z against RT9Z gives 1. Total 2 + 1 = 3. Option (b) counts the swap as 1 difference.

Answer: (a) 3

Example 6: pairs differing in exactly 1 position

Question: How many of these pairs differ in exactly 1 position? PR4471 | PR4471; KL9032 | KL9023; ZX5518 | ZX5519; TN0786 | TN0786; GJ6650 | GJ6656; AP1209 | AB1209. (a) 2 (b) 4 (c) 3 (d) 5

Solution: Count differences pair by pair: PR4471 has 0; KL9032 and KL9023 have 2 (a swap); ZX5518 and ZX5519 have 1; TN0786 has 0; GJ6650 and GJ6656 have 1; AP1209 and AB1209 have 1.

Answer: (c) 3

Common mistakes

Counting a swap of 2 neighbours as 1 difference. Each of the 2 positions now holds a different character.

Comparing every entry with entry 1 only. If entry 1 is the odd one, all others will look wrong; compare with the majority.

Treating numbers with the same digits as equal (3840 and 3804). Order matters.

Reading long words whole. Split them into syllables so a missing letter cannot hide.

Losing your place in long strings. Use the hyphens as anchors and compare block by block.

Practice questions

Q1. At how many positions do 58203716 and 58230761 differ? (a) 3 (b) 4 (c) 2 (d) 5

Q2. Which entry is different from the other 3? (a) HR-26-DQ-5521 (b) HR-26-DQ-5521 (c) HR-26-QD-5521 (d) HR-26-DQ-5521

Q3. List X: 6175, 6517, 7165, 5716, 1657. List Y: 6157, 7165, 5761, 1657, 6715. How many numbers appear in both lists? (a) 1 (b) 3 (c) 4 (d) 2

Answers

Q1. (b) 582 agrees; then 03 against 30 (2 positions), 7 agrees, 16 against 61 (2 positions). Total 4.

Q2. (c) It has QD where the other 3 have DQ.

Q3. (d) Only 7165 and 1657 appear in both; 6175, 6517 and 5716 have look-alikes in Y but not exact copies.

Quick revision

Same length? Then compare position by position, block by block.

A neighbour swap = 2 differing positions; a changed character = 1.

Odd one out: compare with the majority, not with entry 1.

Common entries must be exact; same digits in a new order do not count.

Concepts and rules

Code-classification questions give a structure for roll numbers, admit-card codes or centre codes and a set of rules, and ask which code belongs to which group, hall or centre, how many codes fall in a group, or which code is invalid.

Structure used here: roll number = 2-digit year + 2-letter state + 3-digit centre code + 4-digit serial. In 25UP1040217 the year is 25, the state UP, the centre 104 and the serial 0217.

Fields have fixed positions, so a field is read by its place, not by its look: the 3 digits after the state letters are always the centre code, even if they look like part of the serial.

Leading zeros are part of the field: serial 0048 is the number 48 for parity and divisibility, but it occupies 4 positions.

Ordered rules: when rules are numbered and applied in order, a code goes to the first rule it satisfies and is not checked against later rules. A later rule can never override an earlier one.

Combined conditions: a rule with and needs every part true; a rule with or needs at least 1 part true.

Check digit: some codes end in a digit computed from the others, for example the units digit of the sum of the first 6 digits; a code whose last digit disagrees is invalid.

Method and shortcuts

Step 1: draw vertical bars between the fields of each code, for example 25 | UP | 104 | 0217, before applying any rule.

Step 2: make a small table with one row per code and one column per field that the rules use (state, centre, serial parity and so on).

Step 3: apply the rules in order to each row and write the group in the last column; cross out a row as soon as a rule catches it.

Shortcut: for a count question, apply the rule that matters to the asked group last, after removing every code caught by earlier rules.

Parity and divisibility depend only on the last digits: a serial is even if its last digit is even, and divisible by 5 if it ends in 0 or 5.

Example 1: reading the fields

Question: Using the structure above, what are the state, centre code and serial of 25MP2160048?

Solution: Split as 25 | MP | 216 | 0048.

Answer: State MP, centre 216, serial 0048.

Example 2: grouping by centre code

Question: Centre codes starting with 1 are Group A, with 2 are Group B and with 3 are Group C. Classify 25UP1040217, 25MP2160048, 25RJ3010562, 25UP1180009, 25BR2050711 and 25DL1990130.

Solution: Centre codes are 104, 216, 301, 118, 205 and 199. Starting with 1: 104, 118, 199. Starting with 2: 216, 205. Starting with 3: 301.

Answer: Group A 3, Group B 2, Group C 1.

Example 3: halls by serial parity

Question: For the same 6 roll numbers, an even serial goes to Hall 1 and an odd serial to Hall 2. Which roll numbers go to Hall 2?

Solution: Serials are 0217, 0048, 0562, 0009, 0711 and 0130. The odd ones end in 7, 9 and 1.

Answer: 25UP1040217, 25UP1180009 and 25BR2050711.

Example 4: a combined condition

Question: A candidate sits in Room S if the centre code is from 200 to 299 and the serial is divisible by 5. Who sits in Room S? (a) 25MP2160048 (b) 25UP1040215 (c) 25BR2050710 (d) 25RJ3010565

Solution: (a) centre 216 is in range but 0048 ends in 8. (b) 0215 ends in 5 but centre 104 is out of range. (d) 0565 ends in 5 but centre 301 is out of range. (c) centre 205 is in range and 0710 ends in 0.

Answer: (c)

Example 5: rules in order

Question: Rule 1: state DL goes to Lab 1. Rule 2: otherwise, a centre code starting with 3 and a serial above 0500 goes to Lab 2. Rule 3: otherwise, an even serial goes to Lab 3. Rule 4: all others go to Lab 4. How many of 25DL3010600, 25UP3020750, 25RJ3010412, 25MP1040217, 25BR2050710, 25DL1180009, 25HR3990501 and 25UP2160048 go to Lab 3? (a) 2 (b) 4 (c) 5 (d) 3

Solution: Rule 1 takes 25DL3010600 and 25DL1180009. Rule 2 takes 25UP3020750 (302, 0750) and 25HR3990501 (399, 0501). 25RJ3010412 fails Rule 2 because 0412 is not above 0500.

Rule 3 on the remaining 4: 0412, 0710 and 0048 are even, 0217 is odd. Lab 3 gets 3. Counting every even serial from the start would wrongly give 5 (adding 0600 and 0750), option (c).

Answer: (d) 3

Example 6: check digit

Question: An admit-card code has 7 digits; the 7th digit must equal the units digit of the sum of the first 6 digits. Which code is invalid? (a) 4031277 (b) 5520318 (c) 9100448 (d) 2671006

Solution: (a) 4 + 0 + 3 + 1 + 2 + 7 = 17, ends in 7, valid. (b) 5 + 5 + 2 + 0 + 3 + 1 = 16, needs 6 but has 8. (c) 9 + 1 + 0 + 0 + 4 + 4 = 18, ends in 8, valid. (d) 2 + 6 + 7 + 1 + 0 + 0 = 16, ends in 6, valid.

Answer: (b)

Common mistakes

Reading fields by look instead of position. Mark the bars first; the centre code is always the 3 digits after the state letters.

Applying a later rule to a code already caught by an earlier rule. Once a code is placed, stop checking it.

Treating and as or. In Example 4, a serial ending in 5 is not enough when the centre code is out of range.

Misreading above 0500 as 0500 or more. A serial of exactly 0500 is not above 0500.

Including the check digit itself in the sum. Add only the digits the rule names.

Practice questions

Q1. With Group C meaning a centre code starting with 3, how many of 25UP3020750, 25RJ2010412, 25MP3990217, 25BR1050710 and 25HR3000501 are in Group C? (a) 2 (b) 3 (c) 4 (d) 1

Q2. Using the 4 ordered rules of Example 5, which lab does 25DL3990800 go to? (a) Lab 2 (b) Lab 3 (c) Lab 1 (d) Lab 4

Q3. Using the check-digit rule of Example 6, which code is valid? (a) 3141593 (b) 2718283 (c) 1602187 (d) 1123585

Answers

Q1. (b) Centre codes 302, 201, 399, 105, 300; those starting with 3 are 302, 399 and 300.

Q2. (c) Rule 1 applies first because the state is DL, even though Rule 2 would also fit (399, 0800).

Q3. (a) 3 + 1 + 4 + 1 + 5 + 9 = 23, ends in 3. The others: sum 28 needs 8, sum 18 needs 8, sum 20 needs 0.

Quick revision

Split every code into fields by position before reading any rule.

Ordered rules: the first rule that fits decides; stop there.

And needs all parts; or needs at least 1.

Even or divisible by 5: look only at the last digit.

Check digit: add only the named digits and compare the units digit.