CAT Exam > CAT Questions > The ratio of the sum to product of two digits...
Start Learning for Free
The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.
- a)84
- b)62
- c)51
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The ratio of the sum to product of two digits of a two-digit number is...
Let one of the digits be x.
∴ The other digit will be x + 4
Now,
6x + 12 = 2x2 + 8x
x2 + x - 6 = 0
x = 2, -3
Since, -3 cannot be one of the digits the digits are 2 and 6.
Thus, 62 is the number with highest value which can be formed using the two digits.
Hence, option 2.
∴ The other digit will be x + 4
Now,
6x + 12 = 2x2 + 8x
x2 + x - 6 = 0
x = 2, -3
Since, -3 cannot be one of the digits the digits are 2 and 6.
Thus, 62 is the number with highest value which can be formed using the two digits.
Hence, option 2.
Most Upvoted Answer
The ratio of the sum to product of two digits of a two-digit number is...
Given:
- The ratio of the sum to product of two digits of a two-digit number is 2:3.
- One digit exceeds the other by 4.
To find:
- The highest value that can be formed using the two digits.
Solution:
Let the two digits of the number be x and x+4, where x+4 is the larger digit.
Step 1: Formulate the equation:
According to the given conditions:
- The ratio of the sum to product of the two digits is 2:3.
- The sum of the two digits is x + (x+4) = 2x + 4.
- The product of the two digits is x(x+4) = x^2 + 4x.
Therefore, the equation becomes:
(2x + 4) / (x^2 + 4x) = 2/3.
Step 2: Solve the equation:
Cross-multiplying the equation, we get:
3(2x + 4) = 2(x^2 + 4x).
Simplifying further:
6x + 12 = 2x^2 + 8x.
Rearranging the equation:
2x^2 + 8x - 6x - 12 = 0,
2x^2 + 2x - 12 = 0.
Factoring the quadratic equation, we get:
2(x^2 + x - 6) = 0.
(x^2 + x - 6) = 0.
(x + 3)(x - 2) = 0.
So, we get two possible values for x: -3 and 2.
Step 3: Find the highest value:
Since the number is a two-digit number, the digit cannot be negative. Therefore, x = 2.
The two digits of the number are 2 and 6 (2+4).
To find the highest value, we need to place the larger digit in the tens place and the smaller digit in the units place. Hence, the highest value that can be formed using the two digits is 62.
Therefore, the correct answer is option B) 62.
- The ratio of the sum to product of two digits of a two-digit number is 2:3.
- One digit exceeds the other by 4.
To find:
- The highest value that can be formed using the two digits.
Solution:
Let the two digits of the number be x and x+4, where x+4 is the larger digit.
Step 1: Formulate the equation:
According to the given conditions:
- The ratio of the sum to product of the two digits is 2:3.
- The sum of the two digits is x + (x+4) = 2x + 4.
- The product of the two digits is x(x+4) = x^2 + 4x.
Therefore, the equation becomes:
(2x + 4) / (x^2 + 4x) = 2/3.
Step 2: Solve the equation:
Cross-multiplying the equation, we get:
3(2x + 4) = 2(x^2 + 4x).
Simplifying further:
6x + 12 = 2x^2 + 8x.
Rearranging the equation:
2x^2 + 8x - 6x - 12 = 0,
2x^2 + 2x - 12 = 0.
Factoring the quadratic equation, we get:
2(x^2 + x - 6) = 0.
(x^2 + x - 6) = 0.
(x + 3)(x - 2) = 0.
So, we get two possible values for x: -3 and 2.
Step 3: Find the highest value:
Since the number is a two-digit number, the digit cannot be negative. Therefore, x = 2.
The two digits of the number are 2 and 6 (2+4).
To find the highest value, we need to place the larger digit in the tens place and the smaller digit in the units place. Hence, the highest value that can be formed using the two digits is 62.
Therefore, the correct answer is option B) 62.
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
The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
Question Description
The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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 The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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 The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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 The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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 The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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 The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The ratio of the sum to product of two digits of a two-digit number is 2 : 3. If one of the digits exceeds the other by 4, then find the number of highest value which can be formed using the two digits.a)84b)62c)51d)Cannot be determinedCorrect 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