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Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A x B is maximum, find sum of digits of (A - B).
Correct answer is '56'. Can you explain this answer?
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Verified Answer
Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Fiv...
For the product to be maximum, A and B should take maximum possible values such that the difference between them is minimum.
For this, let us arrange all the pairs in descending order: 91, 87, 65, 56, 45, 43, 23, 17, 08 and 05.
As we need to have maximum possible values for A and B; first two digits of A and B must be 91 and 87.
Without loss of generality, first two digits of A are 91 and that of B are 87.
Of the remaining, the two highest numbers are 65 and 56.
There are two cases possible.
Case 1: The numbers are 9165 and 8756 Case 2: The numbers are 9156 and 8765 The difference between the numbers in case 1 and case 2 is 409 and 391 respectively. So the product will be maximum in the case 2.
Continuing the same way we form the two numbers as A = 9156431705 and B = 8765452308.
A - B = 9156431705 - 8765452308 = 390979397
Sum of the digits = 56 Answer: 56
For this, let us arrange all the pairs in descending order: 91, 87, 65, 56, 45, 43, 23, 17, 08 and 05.
As we need to have maximum possible values for A and B; first two digits of A and B must be 91 and 87.
Without loss of generality, first two digits of A are 91 and that of B are 87.
Of the remaining, the two highest numbers are 65 and 56.
There are two cases possible.
Case 1: The numbers are 9165 and 8756 Case 2: The numbers are 9156 and 8765 The difference between the numbers in case 1 and case 2 is 409 and 391 respectively. So the product will be maximum in the case 2.
Continuing the same way we form the two numbers as A = 9156431705 and B = 8765452308.
A - B = 9156431705 - 8765452308 = 390979397
Sum of the digits = 56 Answer: 56
Most Upvoted Answer
Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Fiv...
Given information:
- There are ten cards numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08.
- Five cards are chosen to form a number A with the 2-digit numbers on the cards written in some sequence.
- The remaining five cards form a number B.
- A and B are such that A x B is maximum.
To find:
The sum of the digits of (A - B).
Solution:
Step 1: Finding the maximum value of A x B:
To maximize the product A x B, we need to maximize both A and B.
Step 1.1: Finding the maximum value of A:
To maximize A, we need to arrange the 2-digit numbers on the chosen cards in descending order.
From the given cards, the five largest 2-digit numbers are 91, 87, 65, 56, and 45. Arranging them in descending order, we get A = 9187655645.
Step 1.2: Finding the maximum value of B:
To maximize B, we need to arrange the 2-digit numbers on the remaining cards in descending order.
The remaining five cards are 17, 43, 23, 05, and 08. Arranging them in descending order, we get B = 4317230805.
Step 2: Calculating (A - B):
Subtracting B from A, we get (A - B) = 9187655645 - 4317230805 = 4870424840.
Step 3: Finding the sum of digits of (A - B):
Calculating the sum of the digits of (A - B), we get:
4 + 8 + 7 + 0 + 4 + 2 + 4 + 8 + 4 + 0 = 41
Therefore, the sum of digits of (A - B) is 41.
Conclusion:
The sum of digits of (A - B) is 41, not 56. It seems there might be an error in the given correct answer.
- There are ten cards numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08.
- Five cards are chosen to form a number A with the 2-digit numbers on the cards written in some sequence.
- The remaining five cards form a number B.
- A and B are such that A x B is maximum.
To find:
The sum of the digits of (A - B).
Solution:
Step 1: Finding the maximum value of A x B:
To maximize the product A x B, we need to maximize both A and B.
Step 1.1: Finding the maximum value of A:
To maximize A, we need to arrange the 2-digit numbers on the chosen cards in descending order.
From the given cards, the five largest 2-digit numbers are 91, 87, 65, 56, and 45. Arranging them in descending order, we get A = 9187655645.
Step 1.2: Finding the maximum value of B:
To maximize B, we need to arrange the 2-digit numbers on the remaining cards in descending order.
The remaining five cards are 17, 43, 23, 05, and 08. Arranging them in descending order, we get B = 4317230805.
Step 2: Calculating (A - B):
Subtracting B from A, we get (A - B) = 9187655645 - 4317230805 = 4870424840.
Step 3: Finding the sum of digits of (A - B):
Calculating the sum of the digits of (A - B), we get:
4 + 8 + 7 + 0 + 4 + 2 + 4 + 8 + 4 + 0 = 41
Therefore, the sum of digits of (A - B) is 41.
Conclusion:
The sum of digits of (A - B) is 41, not 56. It seems there might be an error in the given correct answer.
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Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer?
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Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. 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 Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer?.
Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. 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 Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer?.
Solutions for Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer?, a detailed solution for Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? has been provided alongside types of Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Ten cards are numbered 17, 43, 56, 87, 23, 45, 91, 05, 65, and 08. Five of the ten cards are chosen and a number A is formed with the 2-digit numbers on the cards written in some sequence. B is the number formed by the numbers on remaining 5 cards. (For example: If cards numbered 17, 43, 56, 87 and 08 are chosen, A =1743568708 or 1756430887 and so on. Similarly, B is formed with the remaining cards.) If A and B are such that A xB is maximum, find sum of digits of (A - B).Correct answer is '56'. Can you explain this answer? tests, examples and also practice CAT tests.
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