Counting letters
Mother says, "Bring three bananas and two mangoes from the market." You listen carefully and bring just that. Reading the instruction in a question carefully and doing exactly that is following instructions. Here the instruction is to count letters.
Following instructions means doing step by step what the question asks. First read the instruction, then look at the letters or numbers, and finally check the answer.
Types of counting
| What is asked | How to do it |
|---|---|
| Number of one letter | Count that letter one by one |
| Letter that occurs most often | Write the count of every letter |
| Equal letters side by side | Look at neighbouring letters |
Count one letter one by one; put a tick on each letter you have counted.
- E.g. A in BANANA : B-A-N-A-N-A, A three times.
To see whether two letters occur equally often, write the count of each.
- E.g. AAKKKB : A 2, K 3, B 1.
A pair of equal letters in a row means the same letter side by side.
- E.g. In SSMMMT SS is a pair and MM, MM are two pairs.
When counting all letters do not count any letter twice.
- E.g. TOMATO has 6 letters in all; T twice.
How many times does A occur in BANANA?
- Look one by one : B-A-N-A-N-A.
- A is the first, third and sixth letter. Answer : three times.
How many times does P occur in PQRPQPRQPQ?
- P is the first, fourth, sixth and ninth letter.
- Answer : four times.
In RLLTRSLRTSLL which two letters occur equally often? (1) R, L (2) L, T (3) T, S (4) S, R
- R 3 times, L 5 times, T 2 times, S 2 times.
- T and S twice each. Answer : (3) T, S.
First read the instruction. Once you know what to count, write the count of each letter separately.
Counting the same letter twice or missing one. Tick the letters you have counted.
Memory clue : "Read the instruction, count the letter, tick it."
If there are many letters, make a list for each letter : A 3, B 2 and so on; then mistakes do not happen.
Spot the difference
| Asked | Do |
|---|---|
| How many times | Count the letter |
| Equal number of times | Write all the counts |
| Pair in a row | Look at the neighbouring letters |
Practice questions
- 1How many times does O occur in SCHOOL?
- 2How many times does A occur in ABABBABA?
- 3How many times does T occur in TOMATO?
- 4Which letter occurs most often in PQPRPQRPR?
- 5How many times does a pair of equal letters in a row occur in XYYZXYYXZ?
- 6How many times does a pair of equal letters in a row occur in MMNMMNNM?
- 7In AKBAKCAKBC which two letters occur three times each?
- 8In SSTTTUUVWW how many letters occur exactly twice?
Show answers (try them yourself first)
- 1Twice (two O).
- 2Four times (first, third, sixth, eighth).
- 3Twice (first and fifth).
- 4P (P 4, Q 2, R 3).
- 5Two (YY, YY).
- 6Three (MM, MM, NN).
- 7A and K (three each; B and C twice each).
- 8Three (S, U, W twice each).
Vowels and consonants
In the Marathi alphabet we learnt that अ, आ, इ, ई are vowels and क, ख, ग are consonants. English letters also have five vowels and the rest are consonants. We must be able to tell the vowels and consonants in a word apart.
In English there are five vowels : A, E, I, O, U. All the other letters are consonants. Y is taken as a consonant.
Vowels and consonants
| Group | Letters |
|---|---|
| Vowels | A, E, I, O, U |
| Consonants | B, C, D, F, G … (all except vowels) |
Mark each letter of the word as a vowel or a consonant.
- E.g. In EDUCATION the vowels are E, U, A, I, O, that is 5.
Consonants = total letters − vowels.
- E.g. SCHOOLBAG has 9 letters and 3 vowels, so 6 consonants.
To check "a consonant right after a vowel" look at the letter after each vowel.
- E.g. In ADMISSION after A comes D (consonant), after I comes S (consonant), after I comes O (vowel), after O comes N (consonant) : three.
If two vowels are side by side they are a pair of vowels.
- E.g. In AEROPLANE A and E are side by side; that is one pair.
How many vowels are there in EDUCATION?
- E, D, U, C, A, T, I, O, N : vowels E, U, A, I, O.
- Answer : 5.
How many consonants are there in SCHOOLBAG?
- 9 letters in all. Vowels O, O, A, that is 3.
- 9 − 3 = 6. Answer : 6.
In ADMISSION, how many vowels are immediately followed by a consonant?
- After A comes D (consonant), after I comes S (consonant), after I comes O (vowel), after O comes N (consonant).
- Three with a consonant after them. Answer : 3.
There are five vowels : A, E, I, O, U. All the rest are consonants, Y too.
Taking Y as a vowel. In the exam Y is a consonant.
Memory clue : "AEIOU five vowels; all others consonants."
First circle all the vowels; then the question becomes easy.
Spot the difference
| Asked | Do |
|---|---|
| How many vowels | Count A, E, I, O, U |
| How many consonants | Total − vowels |
| Consonant after a vowel | Look at the letter after each vowel |
Practice questions
- 1How many vowels are there in CAMEL?
- 2How many consonants are there in PENCIL?
- 3How many vowels are there in BEAUTY?
- 4How many consonants are there in COMPUTER?
- 5In PRESIDENT, how many vowels are immediately followed by a consonant?
- 6In AEROPLANE, how many times do two vowels come side by side?
- 7In EDUCATIONAL, how many consonants lie between the first and the last vowel?
- 8In ELEPHANT, how many vowels are immediately preceded by a consonant?
Show answers (try them yourself first)
- 12 (A, E).
- 24 (P, N, C, L).
- 33 (E, A, U).
- 45 (C, M, P, T, R).
- 53 (S after E, D after I, N after E).
- 61 (A and E).
- 74 (D, C, T, N; the first vowel is E, the last vowel is A).
- 82 (L before E and H before A; nothing before the first E).
The position of a letter
When we stand in a queue "third from the left" and "third from the right" are different. The letters of a word are also in a row like that. When counting a position read from which end.
A word is written from left to right. Counting from the left the first letter is the one at the left; counting from the right the first letter is the last letter.
Counting positions
| What is asked | How to do it |
|---|---|
| Third from the left | 3 letters from the first |
| Third from the right | 3 letters from the end |
| Ahead of / behind a letter | Count from that letter |
To count from the left take the first letter of the word as 1.
- E.g. Third from the left in CHAMPION : C-H-A, that is A.
To count from the right take the last letter as 1.
- E.g. Third from the right in ELEPHANT : T-N-A, that is A.
Swap the first and last letters, then count.
- E.g. PLATFORM swapped : MLATFORP. Fourth from the left is T.
When counting ahead of or behind a letter take the next letter after it as 1.
- E.g. In TEACHER third to the right of A : C, H, E; that is E.
Which is the third letter from the left in CHAMPION?
- C-H-A.
- Answer : A.
Which is the third letter from the right in ELEPHANT?
- From the end T-N-A.
- Answer : A.
If the first and last letters of PLATFORM are swapped, which is the fourth letter from the left?
- After swapping it is MLATFORP.
- From the left M-L-A-T, the fourth is T. Answer : T.
First read from which end; then write 1, 2, 3 on the letters.
Mixing up left and right. "From the right" means from the end of the word.
Memory clue : "Fix the end, write the numbers."
Write the word backwards; counting from the right then works like counting from the left.
Spot the difference
| Asked | Start |
|---|---|
| From the left | First letter of the word |
| From the right | Last letter of the word |
| Ahead of a letter | The next one after that letter |
Practice questions
- 1Which is the second letter from the left in BASKET?
- 2Which is the third letter from the right in MONKEY?
- 3Which is the fifth letter from the left in COUNTRY?
- 4Which is the third letter to the right of A in TEACHER?
- 5If PLANET is written backwards, which is the second letter from the left?
- 6How many letters are there between the first L and the last L in PARALLEL?
- 7If the first and last letters of DIRECTION are swapped, which is the fifth letter from the right?
- 8If each letter of ELEVATION moves one letter ahead in the alphabet, which is the fourth letter from the left?
Show answers (try them yourself first)
- 1A (B-A).
- 2K (Y-E-K from the right).
- 3T (C-O-U-N-T).
- 4E (after A come C, H, E).
- 5E (backwards TENALP).
- 62 (the letters between are L and E).
- 7C (after swapping NIRECTIOD; from the right D, O, I, T, C).
- 8W (E L E V → F M F W).
Instructions on numbers
The teacher says, "Use the digits 3, 8, 5, 2 and write the biggest number." You arrange the digits from the biggest to the smallest and get 8532. Following instructions on digits is like that.
The digits of a number are its separate figures. The instruction may ask for the sum, counting even or odd digits, arranging digits from the biggest to the smallest, or making the biggest or smallest number.
Instructions on digits
| Instruction | How to do it |
|---|---|
| Sum of digits | Add all the digits |
| Biggest number | Arrange digits from big to small |
| Smallest number | Arrange digits from small to big |
When adding digits add each digit once.
- E.g. 5, 2, 7 : 5 + 2 + 7 = 14.
Biggest number : arrange the digits from the biggest to the smallest.
- E.g. 3, 8, 5, 2 : 8532.
Smallest number : arrange the digits from the smallest to the biggest; but 0 must not be first.
- E.g. 3, 0, 6 : the smallest three-digit number is 306.
Even digits : 0, 2, 4, 6, 8. Odd digits : 1, 3, 5, 7, 9.
- E.g. In 245386 the even digits are 2, 4, 8, 6 : four.
What is the sum of the digits 5, 2, 7?
- 5 + 2 = 7.
- 7 + 7 = 14. Answer : 14.
What is the biggest four-digit number made from the digits 3, 8, 5, 2?
- Digits from big to small : 8, 5, 3, 2.
- Answer : 8532.
What is the difference between the biggest and the smallest three-digit numbers made from the digits 5, 2, 7?
- The biggest is 752. The smallest is 257.
- 752 − 257 = 495. Answer : 495.
For a big number put the biggest digit first; for a small number put the smallest digit first (except 0).
Putting 0 first while making the smallest number. If 0 is first the number does not stay three-digit.
Memory clue : "Big = big first; small = small first, leave out zero."
To find a difference make the biggest and the smallest numbers and subtract.
Spot the difference
| Asked | Do |
|---|---|
| Big number | Digits in descending order |
| Small number | Digits in ascending order, 0 not first |
| Even digits | 0, 2, 4, 6, 8 |
Practice questions
- 1What is the sum of the digits 6, 3, 9?
- 2How many digits in 245386 are even?
- 3What is the smallest four-digit number made from the digits 7, 2, 9, 4?
- 4What is the biggest three-digit number made from the digits 4, 0, 8?
- 5What is the smallest three-digit number made from the digits 3, 0, 6?
- 6What is the sum of the odd digits in 7351246?
- 7What is the difference between the biggest and the smallest three-digit numbers made from the digits 9, 4, 1?
- 8What is the sum of the first, third and fifth digits of 43917?
Show answers (try them yourself first)
- 118 (6 + 3 + 9).
- 24 (2, 4, 8, 6).
- 32479 (digits in ascending order).
- 4840 (digits in descending order).
- 5306 (0 is not first).
- 616 (7 + 3 + 5 + 1).
- 7792 (941 − 149).
- 820 (4 + 9 + 7).
Words and mixed instructions
In school the names in a class are arranged alphabetically, that is in the order they come in a dictionary. Sometimes a teacher gives two instructions together : "Read the digits and add 2 to the even ones." Both instructions have to be followed one by one.
Instructions on words include alphabetical order, counting letters and replacing vowels. Mixed instructions have two or three instructions one after another.
Words and mixed instructions
| Instruction | How to do it |
|---|---|
| Alphabetical order | By the first letter; if the first letters are equal, by the second |
| Counting letters | Count the letters one by one |
| Two instructions | Do the first, then the second on its answer |
Alphabetical order : in the order A, B, C …; if the first letters are equal look at the second.
- E.g. APPLE, MANGO, BANANA, CHERRY : APPLE, BANANA, CHERRY, MANGO.
To count the letters of a word count them one by one.
- E.g. ELEPHANT : 8 letters.
If there are two instructions, do the first and then the second on its answer.
- E.g. 4, 7, 2, 9 : add 2 to the even numbers, then the sum : 6, 7, 4, 9 = 26.
If told to change letters, make the same change on every letter.
- E.g. In MARKET put * in place of every vowel : M*RK*T.
APPLE, MANGO, BANANA, CHERRY are arranged in dictionary order. Which is third?
- APPLE, BANANA, CHERRY, MANGO.
- The third is CHERRY. Answer : CHERRY.
Which of MANGO, ORANGE, PEAR, FIG has the most letters?
- Letters : MANGO 5, ORANGE 6, PEAR 4, FIG 3.
- Answer : ORANGE.
Add 2 to every even number among 4, 7, 2, 9 and then add all the numbers.
- 4 → 6, 7 stays, 2 → 4, 9 stays.
- 6 + 7 + 4 + 9 = 26. Answer : 26.
Follow the instructions one by one; write the answer of the first instruction before doing the second.
Trying to do both instructions at once. First the first, then the second.
Memory clue : "One instruction, one step; write and move on."
For alphabetical order circle the first letters of all the words; the smallest comes first.
Spot the difference
| Instruction | Do |
|---|---|
| Alphabetical order | From A towards Z |
| Count letters | Count one by one |
| Two instructions | First, then second |
Practice questions
- 1Which of CAT, BAT, RAT, MAT comes first in the dictionary?
- 2How many letters are there in ELEPHANT?
- 3Which of ROSE, LOTUS, JASMINE, TULIP comes last in the dictionary?
- 4Subtract 1 from every odd digit in 2, 5, 8 and then add all three digits.
- 5Write * in place of every vowel in MARKET.
- 6How many of 3, 8, 5, 10, 7 are even and greater than 6?
- 7If the vowels in ABCDEFGH are removed, how many letters are left?
- 8Which of RAIN, SUN, STORM, FOG has the most vowels?
Show answers (try them yourself first)
- 1BAT.
- 28.
- 3TULIP.
- 414 (2 + 4 + 8).
- 5M*RK*T.
- 62 (8 and 10).
- 76 (after removing A and E).
- 8RAIN (A and I; the others have only one).
Quick revision of the whole lesson
| Topic | Memory clue |
|---|---|
| Counting letters | Read the instruction, count the letter, tick it |
| Vowels and consonants | AEIOU five vowels; all others consonants |
| Position of a letter | Fix the end, write the numbers |
| Instructions on numbers | Big = big first; small = small first, leave out zero |
| Words and mixed instructions | One instruction, one step |
| Checking | Does the answer match the instruction? |
🎯 Most important points for the exam
- First read the instruction carefully; then follow it step by step.
- While counting letters tick each letter.
- There are five vowels : A, E, I, O, U; all the rest are consonants.
- When counting a position first fix from which end.
- Biggest number : digits in descending order; smallest : ascending order, 0 not first.
- If there are two instructions do the first and only then the second.
- After getting the answer check that it matches the instruction.
"Read the instruction, follow each step, check at the end."