CAT Exam > CAT Questions > A number consists of 3 consecutive digits, su...
Start Learning for Free
A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.
- a)231
- b)234
- c)233
- d)232
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A number consists of 3 consecutive digits, such that the digit in the ...
Let the hundreds digit be a.
Then, the tens digit = a + 1 and the units digit = a + 2
⇒ The number = 100a + 10(a + 1) + a + 2 = 111a + 12
The number formed by reversing the digits = 100(a + 2) + 10(a + 1) + a
= 111a + 210
Since the number formed by reversing the digits exceeds the original number by 22 times, the sum of the digits
⇒ 111a + 210 - 111a - 12 = 22(a + 2 + a + 1 + a)
⇒
⇒
Hence, the required number = 111a + 12 = 111 2 + 12 = 234
Then, the tens digit = a + 1 and the units digit = a + 2
⇒ The number = 100a + 10(a + 1) + a + 2 = 111a + 12
The number formed by reversing the digits = 100(a + 2) + 10(a + 1) + a
= 111a + 210
Since the number formed by reversing the digits exceeds the original number by 22 times, the sum of the digits
⇒ 111a + 210 - 111a - 12 = 22(a + 2 + a + 1 + a)
⇒
198 = 66a + 66
⇒
a = 2
Hence, the required number = 111a + 12 = 111
×
Most Upvoted Answer
A number consists of 3 consecutive digits, such that the digit in the ...
To solve this problem, let's break it down step by step:
Step 1: Understand the problem
We are given a number consisting of 3 consecutive digits, with the greatest digit in the units place. We need to find the number, given that the number formed by reversing the digits exceeds the original number by 22 times the sum of the digits.
Step 2: Let's assume the number
Let's assume the number as ABC, where A, B, and C are consecutive digits. Since the digit in the units place is the greatest, C would be the greatest digit.
Step 3: Write the original number
The original number can be written as 100A + 10B + C.
Step 4: Write the reversed number
The reversed number can be written as 100C + 10B + A.
Step 5: Write the equation
According to the problem, the reversed number exceeds the original number by 22 times the sum of the digits. So, we can write the equation as:
100C + 10B + A = 100A + 10B + C + 22(A + B + C)
Simplifying the equation, we get:
99C = 99A + 21B
Step 6: Simplify the equation further
Dividing the equation by 33, we get:
3C = 3A + 7B
Simplifying it further, we get:
C = A + 2B
Step 7: Find the possible values of A, B, and C
Since A, B, and C are consecutive digits, they can be any of the following combinations:
A = 1, B = 2, C = 3
A = 2, B = 3, C = 4
A = 3, B = 4, C = 5
A = 4, B = 5, C = 6
A = 5, B = 6, C = 7
A = 6, B = 7, C = 8
A = 7, B = 8, C = 9
Out of these combinations, only A = 2, B = 3, C = 4 satisfies the equation C = A + 2B.
Therefore, the number is 234, which is option B.
Step 1: Understand the problem
We are given a number consisting of 3 consecutive digits, with the greatest digit in the units place. We need to find the number, given that the number formed by reversing the digits exceeds the original number by 22 times the sum of the digits.
Step 2: Let's assume the number
Let's assume the number as ABC, where A, B, and C are consecutive digits. Since the digit in the units place is the greatest, C would be the greatest digit.
Step 3: Write the original number
The original number can be written as 100A + 10B + C.
Step 4: Write the reversed number
The reversed number can be written as 100C + 10B + A.
Step 5: Write the equation
According to the problem, the reversed number exceeds the original number by 22 times the sum of the digits. So, we can write the equation as:
100C + 10B + A = 100A + 10B + C + 22(A + B + C)
Simplifying the equation, we get:
99C = 99A + 21B
Step 6: Simplify the equation further
Dividing the equation by 33, we get:
3C = 3A + 7B
Simplifying it further, we get:
C = A + 2B
Step 7: Find the possible values of A, B, and C
Since A, B, and C are consecutive digits, they can be any of the following combinations:
A = 1, B = 2, C = 3
A = 2, B = 3, C = 4
A = 3, B = 4, C = 5
A = 4, B = 5, C = 6
A = 5, B = 6, C = 7
A = 6, B = 7, C = 8
A = 7, B = 8, C = 9
Out of these combinations, only A = 2, B = 3, C = 4 satisfies the equation C = A + 2B.
Therefore, the number is 234, which is option B.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer?
Question Description
A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer?.
A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer?.
Solutions for A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A number consists of 3 consecutive digits, such that the digit in the units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digit. Find the number.a)231b)234c)233d)232Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup