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Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4?
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Ajay attempted to add ten two-digit numbers. One of them, a, was the r...
To solve this problem, let's first analyze the given information:
1. Ajay attempted to add ten two-digit numbers.
2. One of the numbers, denoted as "a," is the reverse of another number.
3. "a" is replaced by another two-digit number, "b."
4. The reverse of "a" is replaced by the reverse of "b."
5. The average of the ten numbers after the replacement is 2.2 more than the original average.
Let's break down the steps to find the solution:
Step 1: Determine the average of the original ten numbers
- Since all the numbers are two-digit, the sum of the original ten numbers can be expressed as 10x, where x is the average.
- Let's assume that the sum of the original ten numbers is S.
Step 2: Find the sum of the ten numbers after the replacement
- After replacing "a" with "b" and the reverse of "a" with the reverse of "b," the sum of the ten numbers can be expressed as S - a + b + (reverse of a) - (reverse of b).
Step 3: Find the new average and set up the equation
- The new average is given as 2.2 more than the original average, so it can be expressed as x + 2.2.
- The sum of the ten numbers after the replacement can be expressed as 10(x + 2.2).
Step 4: Set up the equation and solve for "a" and "b"
- Equating the sum of the original ten numbers (S) with the sum of the ten numbers after the replacement (10(x + 2.2)), we get S = 10(x + 2.2).
- Simplifying the equation, we have S = 10x + 22.
- Since S is a multiple of 10 (as it represents the sum of ten two-digit numbers), it must end in a zero. Therefore, 22 must also end in a zero, which is not possible. Hence, there is no solution to this equation.
Since there is no solution, we can conclude that the given scenario is not possible.
1. Ajay attempted to add ten two-digit numbers.
2. One of the numbers, denoted as "a," is the reverse of another number.
3. "a" is replaced by another two-digit number, "b."
4. The reverse of "a" is replaced by the reverse of "b."
5. The average of the ten numbers after the replacement is 2.2 more than the original average.
Let's break down the steps to find the solution:
Step 1: Determine the average of the original ten numbers
- Since all the numbers are two-digit, the sum of the original ten numbers can be expressed as 10x, where x is the average.
- Let's assume that the sum of the original ten numbers is S.
Step 2: Find the sum of the ten numbers after the replacement
- After replacing "a" with "b" and the reverse of "a" with the reverse of "b," the sum of the ten numbers can be expressed as S - a + b + (reverse of a) - (reverse of b).
Step 3: Find the new average and set up the equation
- The new average is given as 2.2 more than the original average, so it can be expressed as x + 2.2.
- The sum of the ten numbers after the replacement can be expressed as 10(x + 2.2).
Step 4: Set up the equation and solve for "a" and "b"
- Equating the sum of the original ten numbers (S) with the sum of the ten numbers after the replacement (10(x + 2.2)), we get S = 10(x + 2.2).
- Simplifying the equation, we have S = 10x + 22.
- Since S is a multiple of 10 (as it represents the sum of ten two-digit numbers), it must end in a zero. Therefore, 22 must also end in a zero, which is not possible. Hence, there is no solution to this equation.
Since there is no solution, we can conclude that the given scenario is not possible.
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Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4?
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Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4?.
Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ajay attempted to add ten two-digit numbers. One of them, a, was the reverse of one of the others. If a was replaced by another two-digit number, b and the reverse of a was replaced by the reverse of b and the average was found, it would be 2.2 more. The sum of the digits in b exceeds the sum of the digits in a by (A) 1 (B) 2 (C) 3 (D) 4?.
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