Day 2 : Arithmetic and Reasoning Practice Questions

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100 Days Arithmetic & Reasoning Skills Challenge – Day 2

Place Value & Face Value | Alphabet Series

Arithmetic Topic: Place Value & Face Value
Reasoning Topic: Alphabet Series
Difficulty Level: Easy to Moderate
Recommended Time: 30–40 Minutes
Today’s Target: Understand the concepts, learn the shortcuts and solve practice questions accurately.

Part 1: Arithmetic – Place Value & Face Value

1. What is Place Value?

The place value of a digit is the value that the digit gets because of its position in a number.

For example, consider the number:

57,843

The digit 7 is in the thousands place.

Therefore:

Place value of 7 = 7 × 1,000 = 7,000

Similarly:

Digit	Position	Place Value
5	Ten Thousands	50,000
7	Thousands	7,000
8	Hundreds	800
4	Tens	40
3	Ones	3

Important Point

The place value changes when the position of a digit changes.

For example:

In 5,432, the place value of 5 is 5,000.
In 54,321, the place value of 5 is 50,000.

The digit is the same, but its position is different.

2. What is Face Value?

The face value of a digit is simply the digit itself, regardless of where it appears in the number.

For example, in:

57,843

The face value of:

5 = 5
7 = 7
8 = 8
4 = 4
3 = 3

The face value does not depend on the position of the digit.

Easy Trick to Remember

Face Value = The digit’s own value

Place Value = Digit × Position

3. Place Value vs Face Value

This is one of the most important concepts for competitive examinations.

Consider:

6,72,945

What is the place value and face value of 7?

The digit 7 is in the ten-thousands place.

Therefore:

Face value = 7

Place value = 70,000

So:

Face value tells us what the digit is.

Place value tells us what the digit is worth in that position.

4. Solved Examples – Place Value and Face Value

Example 1

Find the place value of 6 in 46,275.

The digit 6 is in the thousands place.

Therefore:

6 × 1,000 = 6,000

Answer: 6,000

Example 2

Find the face value of 6 in 46,275.

The face value is always the digit itself.

Answer: 6

Example 3

Find the difference between the place value and face value of 8 in 38,642.

Place value of 8 = 8,000

Face value of 8 = 8

Difference:

8,000 − 8 = 7,992

Answer: 7,992

Example 4

What is the sum of the place value and face value of 5 in 25,781?

Place value of 5 = 5,000

Face value of 5 = 5

Therefore:

5,000 + 5 = 5,005

Answer: 5,005

5. Indian Number System – Places to Remember

For competitive examinations, students should be comfortable with the following positions:

Position	Value
Ones	1
Tens	10
Hundreds	100
Thousands	1,000
Ten Thousands	10,000
Lakhs	1,00,000
Ten Lakhs	10,00,000
Crores	1,00,00,000

Example

In 4,56,78,321:

1 → Ones
2 → Tens
3 → Hundreds
8 → Thousands
7 → Ten Thousands
6 → Lakhs
5 → Ten Lakhs
4 → Crores

Therefore, the place value of 5 is:

5 × 10,00,000 = 50,00,000

6. Special Case: Zero

A zero can have a place value, but its place value is always 0.

Example:

50,706

The digit 0 in the hundreds place has:

Face value = 0

Place value = 0

This is an easy area for exam questions because students sometimes confuse the position of zero with its value.

7. Quick Tricks for Place Value Questions

Trick 1: Look at the position first

Don’t immediately calculate.

Example:

72,564

Question: Place value of 2?

2 is in the thousands place.

So:

2 × 1,000 = 2,000

Trick 2: Face value never changes

Whether the digit is in ones, thousands or crores:

Face value = digit itself.

Trick 3: Difference questions

If asked:

Difference between place value and face value

Use:

Place Value − Face Value

Example:

Digit = 9 in the thousands place.

9,000 − 9 = 8,991

Part 2: Reasoning – Alphabet Series

8. What is an Alphabet Series?

An alphabet series is a sequence of letters arranged according to a particular logical pattern.

The task is usually to find:

the next letter
the missing letter
the wrong letter
the position of a letter
the letter at a particular position
the pattern followed by the letters

Alphabet series questions are common in reasoning and aptitude preparation, and converting letters into numerical positions is one of the easiest ways to solve them.

9. Alphabet Position – Must Remember

There are 26 letters in the English alphabet.

Letter	Position	Letter	Position
A	1	N	14
B	2	O	15
C	3	P	16
D	4	Q	17
E	5	R	18
F	6	S	19
G	7	T	20
H	8	U	21
I	9	V	22
J	10	W	23
K	11	X	24
L	12	Y	25
M	13	Z	26

Important Memory Points

Try to remember:

A = 1

E = 5

J = 10

O = 15

T = 20

Y = 25

These landmark letters can make position questions much faster.

10. Type 1 – Simple Forward Alphabet Series

Example:

A, B, C, D, ?

The letters are moving forward one position.

Therefore:

Answer = E

Example

C, D, E, F, ?

Answer:

11. Type 2 – Reverse Alphabet Series

Example:

Z, Y, X, W, ?

The letters are moving backward one position.

Therefore:

Answer = V

Example

T, S, R, Q, ?

Answer:

12. Type 3 – Alphabet Series with Skips

Sometimes letters are skipped according to a fixed pattern.

Example:

A, C, E, G, ?

Convert to positions:

A = 1
C = 3
E = 5
G = 7

The pattern is:

+2, +2, +2

Therefore:

7 + 2 = 9

9th letter = I

Answer: I

Example

B, E, H, K, ?

Positions:

2, 5, 8, 11, ?

The pattern is:

Therefore:

11 + 3 = 14

14th letter = N

Answer: N

13. Type 4 – Increasing Gaps

Sometimes the gap between letters increases.

Example:

A, B, D, G, K, ?

Positions:

A = 1
B = 2
D = 4
G = 7
K = 11

Differences:

+1, +2, +3, +4

Next difference = +5

11 + 5 = 16

16th letter = P

Answer: P

14. Type 5 – Alternating Pattern

Some series use two patterns alternately.

Example:

A, C, B, D, C, E, ?

Observe:

A → B → C → ?

C → D → E

The two sequences are interlinked.

Therefore, the next letter is:

Students should separate odd-position and even-position terms when a simple pattern is not immediately visible.

15. Type 6 – Position-Based Alphabet Questions

These questions ask you to find a letter based on its position.

Example

Which letter is 5th to the right of C?

C = 3

Move five places:

D → 1
E → 2
F → 3
G → 4
H → 5

Therefore:

Answer = H

Example

Which letter is 4th to the left of M?

M = 13

Move four places backward:

L → 1
K → 2
J → 3
I → 4

Answer = I

16. Reverse Position Shortcut

A useful shortcut for alphabet position questions is:

Reverse position = 27 − Forward position

For example:

A is 1st from the left.

From the right:

27 − 1 = 26

So A is 26th from the right.

Similarly:

M = 13th from the left

27 − 13 = 14

Therefore M is 14th from the right.

This relationship is widely used in alphabet-position reasoning questions.

17. Solved Alphabet Series Examples

Example 1

Find the next letter:

D, F, H, J, ?

Positions:

4, 6, 8, 10

Pattern = +2

Next = 12

12th letter = L

Answer: L

Example 2

Find the missing letter:

Z, W, T, Q, ?

Positions:

26, 23, 20, 17

Pattern = −3

Next = 14

14th letter = N

Answer: N

Example 3

Find the next letter:

B, D, G, K, ?

Positions:

2, 4, 7, 11

Differences:

+2, +3, +4

Next difference = +5

11 + 5 = 16

16th letter = P

Answer: P

Example 4

Which letter is 7th to the right of H?

H = 8

8 + 7 = 15

15th letter = O

Answer: O

18. How to Solve Alphabet Series Quickly

Use this order:

Step 1

Write the alphabet positions mentally.

Step 2

Check whether the letters are moving:

+1
−1
+2
−2
+3
−3

Step 3

If there is no simple pattern, check whether the gaps are increasing or decreasing.

Step 4

If still unclear, separate odd and even positions.

Step 5

For position questions, convert the letter to its numerical position.

This approach helps avoid guessing and improves speed. Letter-series questions commonly use forward/backward order, fixed skips, position arithmetic, reverse patterns and alternation.

19. Common Mistakes to Avoid

Mistake 1: Confusing face value with place value

Remember:

Face value = digit

Place value = digit × position

Mistake 2: Counting alphabet positions incorrectly

Don’t count from A every time.

Memorise the landmark positions:

A=1, E=5, J=10, O=15, T=20, Y=25

Mistake 3: Ignoring reverse direction

If the question says:

“to the left”

move backward.

If it says:

“to the right”

move forward.

Mistake 4: Missing the skip pattern

For:

A, D, G, J, ?

Don’t simply look at the letters visually.

Positions:

1, 4, 7, 10

Pattern:

Therefore:

13 = M

20. Day 2 Quick Revision Sheet

Arithmetic

Face Value

= The digit itself.

Place Value

= Digit × value of its position.

Example:

In 7,245:

Face value of 2 = 2

Place value of 2 = 200

Reasoning

Alphabet positions:

A = 1
B = 2
C = 3
…
M = 13
…
Z = 26

Reverse position:

27 − Forward Position

Example:

R = 18

Reverse position:

27 − 18 = 9

So R is 9th from the right.

21. Day 2 Practice Questions

Arithmetic – Place Value & Face Value

1. What is the place value of 6 in 46,321?

2. What is the face value of 8 in 78,456?

3. Find the difference between the place value and face value of 5 in 35,724.

4. What is the place value of 7 in 7,54,321?

5. What is the sum of the place value and face value of 4 in 24,681?

6. In 9,08,765, what is the place value of 8?

7. What is the face value of 3 in 63,219?

8. Find the difference between the place value and face value of 9 in 19,543.

9. What is the place value of 2 in 2,45,678?

10. In 8,76,543, which digit has a place value of 70,000?

Reasoning – Alphabet Series

11. Find the next letter:

A, C, E, G, ?

12. Find the next letter:

B, E, H, K, ?

13. Find the next letter:

Z, X, V, T, ?

14. Find the missing letter:

D, G, J, M, ?

15. Find the next letter:

A, B, D, G, K, ?

16. Which letter is 5th to the right of F?

17. Which letter is 4th to the left of P?

18. Which letter is 10th from the left?

19. Which letter is 8th from the right?

20. Find the next letter:

C, F, I, L, ?

22. Answers

Arithmetic

6,000
8
4,995
7,00,000
4,004
8,000
3
8,991
2,00,000
7

Reasoning

23. Day 2 Challenge

Arithmetic Challenge

Topic: Place Value & Face Value

Target: 10 Questions

Time: 10 Minutes

Goal: 90% Accuracy

Reasoning Challenge

Topic: Alphabet Series

Target: 10 Questions

Time: 10 Minutes

Goal: 90% Accuracy

Total Challenge

20 Questions | 20 Minutes

Try to solve the questions without looking at the explanations. After completing the test, check your answers and identify the questions where you made mistakes.

24. Today’s Learning Goal

By the end of Day 2, you should be able to:

✓ Identify the place value of any digit
✓ Identify the face value of any digit
✓ Calculate the difference between place value and face value
✓ Understand the Indian number system
✓ Remember important alphabet positions
✓ Solve forward and reverse alphabet series
✓ Identify skipped-letter patterns
✓ Solve position-based alphabet questions
✓ Recognise increasing-gap and alternating patterns
✓ Improve both speed and accuracy

Remember

Arithmetic:
Face Value = Digit
Place Value = Digit × Position

Reasoning:
A=1, B=2, C=3 … Z=26

Reverse Position:
27 − Forward Position

Practice these concepts regularly, and many basic aptitude and reasoning questions can become quick-scoring questions.

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