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Logical Reasoning • Math Puzzles, Clocks & Coding Practice Drills (60 Qs)• Official Answer Keys

CAT Math Puzzles & Clocks Practice Questions (60+ Questions)

Cryptarithmetic, Clock Angles & Coincidences, Coding Sequences, and Number Logic Puzzles

60 Total Questions
MCQ: 32 (+3 / -1)
TITA: 28 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: Math Puzzles, Clocks & Coding Practice Drills

Angle Between Clock HandsFormula #1
\theta = |30H - 5.5M|

Angle between hour hand and minute hand at H hours and M minutes.

Relative Speed of Clock HandsFormula #2
S_{rel} = 5.5∘5.5^\circ / \text{minute}

Minute hand gains 5.5 degrees on hour hand every minute.

Exam Hall Traps & Speedbreakers to Avoid
  • •Taking the reflex angle (> 180 degrees) instead of the smaller interior angle between clock hands.

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Official Exam Questions & Explanations (25 of 60)

Sorted in official convenor sequence
Question 1 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingEasy
In a certain code, 'CAT' is written as '123'. If 'MAT' is coded as '423', what is the code for 'M'?
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Official Correct Answer: A. In the code, 'M' is the only character that differs between 'CAT' and 'MAT'. Therefore, the code for 'M' is '2'.
Question 2 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingEasy
In the same code, if 'T' is coded as '3', what is the code for '123'?
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Official Correct Answer: A. Since '123' is the code for 'CAT' and '3' is the code for 'T', '123' must be 'CAT'.
Question 3 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksEasy
If the clock is 5 minutes fast, what is the actual time when the clock shows 3:20 PM?
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Official Correct Answer: A. Since the clock is 5 minutes fast, the actual time would be 5 minutes less than 3:20 PM, which is 3:15 PM.
Question 4 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingModerate
In the code, 'MAT' is written as '423'. If 'TAM' is coded as '324', what is the code for 'A'?
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Official Correct Answer: A. By comparing 'MAT' and 'TAM', it is clear that 'A' is coded as '2'.
Question 5 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingModerate
If 'CAT' is coded as '123' and 'MAT' is coded as '423', what is the code for 'C'?
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Official Correct Answer: C. By comparing 'CAT' and 'MAT', it is clear that 'C' is coded as '3'.
Question 6 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksModerate
If the clock is 5 minutes slow, what is the actual time when the clock shows 3:20 PM?
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Official Correct Answer: B. Since the clock is 5 minutes slow, the actual time would be 5 minutes more than 3:20 PM, which is 3:10 PM.
Question 7 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingHard
In the code, 'TAM' is written as '324'. If 'MAT' is coded as '423', what is the code for 'T'?
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Official Correct Answer: B. By comparing 'TAM' and 'MAT', it is clear that 'T' is coded as '2'.
Question 8 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksHard
If the clock is 10 minutes fast, what is the actual time when the clock shows 3:20 PM?
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Official Correct Answer: C. Since the clock is 10 minutes fast, the actual time would be 10 minutes less than 3:20 PM, which is 3:30 PM.
Question 9 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingEasy
In the code, 'CAT' is written as '123'. If 'TAC' is coded as '321', what is the code for 'A'?
TITA Answer:
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Official Correct Answer: 2. By comparing 'CAT' and 'TAC', it is clear that 'A' is coded as '2'.
Question 10 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksEasy
If the clock is 15 minutes slow, what is the actual time when the clock shows 3:20 PM?
TITA Answer:
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Official Correct Answer: 3:35 PM. Since the clock is 15 minutes slow, the actual time would be 15 minutes more than 3:20 PM, which is 3:35 PM.
Question 11 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingModerate
In the code, 'MAT' is written as '423'. If 'TAM' is coded as '324', what is the code for 'M'?
TITA Answer:
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Official Correct Answer: 4. By comparing 'MAT' and 'TAM', it is clear that 'M' is coded as '4'.
Question 12 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksModerate
If the clock is 20 minutes fast, what is the actual time when the clock shows 3:20 PM?
TITA Answer:
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Official Correct Answer: 3:00 PM. Since the clock is 20 minutes fast, the actual time would be 20 minutes less than 3:20 PM, which is 3:00 PM.
Question 13 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingHard
In the code, 'TAM' is written as '324'. If 'MAT' is coded as '423', what is the code for 'T'?
TITA Answer:
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Official Correct Answer: 2. By comparing 'TAM' and 'MAT', it is clear that 'T' is coded as '2'.
Question 14 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingEasy
A code '743' represents 'window'. '392' represents 'mirror'. Which number represents 'mirt' in the code system?
TITA Answer:
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Official Correct Answer: 92. In the given code, '3' represents 'wi', '9' represents 'm', '2' represents 'r', and '4' represents 'n'. Therefore, 'mirt' is coded as '92'.
Question 15 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingModerate
If '521' represents 'cat', '213' represents 'bat', and '137' represents 'rat', what does '521' + '213' + '137' represent?
TITA Answer:
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Official Correct Answer: catbatrat. The number '521' is common in all three codes, representing 'cat'. The remaining numbers represent 'bat' and 'rat'. Therefore, the combined code represents 'catbatrat'.
Question 16 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingHard
In a code system, '932' represents 'clock', '275' represents 'lock', and '753' represents 'clo'. Which of the following represents 'clo'?
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Official Correct Answer: C. 'clo' is a part of both 'clock' and 'lock'. The code '753' matches the part 'clo'.
Question 17 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksEasy
If the minute hand of a clock moves 120 degrees, how many minutes have passed?
TITA Answer:
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Official Correct Answer: 20. Since the minute hand moves 360 degrees in 60 minutes, it moves 120 degrees in 20 minutes.
Question 18 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksModerate
A clock shows the time as 3:15 PM. How many degrees does the hour hand move from 3:00 PM to 3:15 PM?
TITA Answer:
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Official Correct Answer: 7.5. The hour hand moves 30 degrees per hour and 0.5 degrees per minute. From 3:00 PM to 3:15 PM, it moves 7.5 degrees.
Question 19 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksHard
At what time between 4 and 5 o'clock will the hands of a clock form an angle of 90 degrees?
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Official Correct Answer: B. The formula for the angle between the hour and minute hands is |30H - 5.5M|. Setting this to 90 degrees and solving for M when H is 4, we get M = 16.2 minutes.
Question 20 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingEasy
If '456' represents 'sun', '567' represents 'moon', and '678' represents 'star', what number represents 'moon'?
TITA Answer:
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Official Correct Answer: 567. The number '567' directly represents 'moon' in the given code system.
Question 21 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingModerate
In a code system, '123' represents 'cat', '345' represents 'bat', and '567' represents 'rat'. Which number represents 'bat'?
TITA Answer:
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Official Correct Answer: 345. '345' is the code for 'bat' in the given system.
Question 22 of 60
ThinkCAT Practice SetDILRLogical Reasoning • Coding/DecodingHard
If '789' represents 'dog', '890' represents 'cat', and '901' represents 'rat', which number represents 'cat'?
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Official Correct Answer: B. The code '890' directly represents 'cat' in the given code system.
Question 23 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksEasy
At 6 o'clock, what is the angle between the hour and minute hands of a clock?
TITA Answer:
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Official Correct Answer: 180. At 6 o'clock, the hour hand and minute hand are exactly opposite each other, forming a 180-degree angle.
Question 24 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksModerate
At what time between 3 and 4 o'clock will the hands of a clock be in the same straight line but not together?
TITA Answer:
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Official Correct Answer: 3:40.5. The formula for the angle between the hour and minute hands is |30H - 5.5M|. Setting this to 180 degrees and solving for M when H is 3, we get M = 40.5 minutes.
Question 25 of 60
ThinkCAT Practice SetDILRLogical Reasoning • ClocksHard
At what time between 2 and 3 o'clock will the hands of a clock form a right angle?
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Official Correct Answer: B. The formula for the angle between the hour and minute hands is |30H - 5.5M|. Setting this to 90 degrees and solving for M when H is 2, we get M = 32.7 minutes.

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Frequently Asked Questions about CAT Math Puzzles & Clocks Practice Questions (60+ Questions)

What concepts are covered in the Math Puzzles, Clocks & Coding Practice Drills practice module?

This module covers Math Puzzles, Coding/Decoding, Clocks with 60 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for Math Puzzles, Clocks & Coding Practice Drills questions?

The ideal target pace is 10 to 12 mins / caselet. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for Math Puzzles, Clocks & Coding Practice Drills?

Official past year exam questions are available in our CAT Logical Reasoning PYQ Hub module.

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