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In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?
Correct answer is '5'. Can you explain this answer?
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Verified Answer
In a four-digit number, the sum of the first 2 digits is equal to that...
Let the 4 digit no. be xyzw.
According to given conditions we have x+y=z+w, x+w=z,y+w=2x+2z
With help of these equations we deduce that y=2w,z=5x.
Now the minimum value x can take is 1 so z=5 and the no. is 1854, which satisfies all the conditions.
According to given conditions we have x+y=z+w, x+w=z,y+w=2x+2z
With help of these equations we deduce that y=2w,z=5x.
Now the minimum value x can take is 1 so z=5 and the no. is 1854, which satisfies all the conditions.
Most Upvoted Answer
In a four-digit number, the sum of the first 2 digits is equal to that...
Given Information:
- The sum of the first 2 digits is equal to that of the last 2 digits.
- The sum of the first and last digits is equal to the third digit.
- The sum of the second and fourth digits is twice the sum of the other 2 digits.
To find:
The third digit of the number.
Solution:
Let's assume the four-digit number as ABCD, where A, B, C, and D represent the thousands, hundreds, tens, and units digits respectively.
First Condition: The sum of the first 2 digits is equal to that of the last 2 digits.
This can be represented as A + B = C + D.
Second Condition: The sum of the first and last digits is equal to the third digit.
This can be represented as A + D = C.
Third Condition: The sum of the second and fourth digits is twice the sum of the other 2 digits.
This can be represented as B + D = 2(A + C).
Combining the Conditions:
From the second condition, we have A + D = C.
Rearranging, we get D = C - A.
Substituting this value of D in the third condition, we get B + (C - A) = 2(A + C).
Simplifying, we get B + C - A = 2A + 2C.
Rearranging further, we get B - A = A + C.
Substituting the value of A + C from the second condition, we have B - A = A + D.
Substituting the value of D from the second condition, we have B - A = A + (C - A).
Simplifying, we get B - A = C.
Conclusion:
From the above equation, we can conclude that B - A = C.
This means that the difference between the second and first digits is equal to the third digit.
Since the question asks for the third digit, we can conclude that the third digit is equal to the difference between the second and first digits.
Therefore, the correct answer is '5'.
- The sum of the first 2 digits is equal to that of the last 2 digits.
- The sum of the first and last digits is equal to the third digit.
- The sum of the second and fourth digits is twice the sum of the other 2 digits.
To find:
The third digit of the number.
Solution:
Let's assume the four-digit number as ABCD, where A, B, C, and D represent the thousands, hundreds, tens, and units digits respectively.
First Condition: The sum of the first 2 digits is equal to that of the last 2 digits.
This can be represented as A + B = C + D.
Second Condition: The sum of the first and last digits is equal to the third digit.
This can be represented as A + D = C.
Third Condition: The sum of the second and fourth digits is twice the sum of the other 2 digits.
This can be represented as B + D = 2(A + C).
Combining the Conditions:
From the second condition, we have A + D = C.
Rearranging, we get D = C - A.
Substituting this value of D in the third condition, we get B + (C - A) = 2(A + C).
Simplifying, we get B + C - A = 2A + 2C.
Rearranging further, we get B - A = A + C.
Substituting the value of A + C from the second condition, we have B - A = A + D.
Substituting the value of D from the second condition, we have B - A = A + (C - A).
Simplifying, we get B - A = C.
Conclusion:
From the above equation, we can conclude that B - A = C.
This means that the difference between the second and first digits is equal to the third digit.
Since the question asks for the third digit, we can conclude that the third digit is equal to the difference between the second and first digits.
Therefore, the correct answer is '5'.
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In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer?
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In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. 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 In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer?.
In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. 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 In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer?.
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In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer?, a detailed solution for In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer? has been provided alongside types of In a four-digit number, the sum of the first 2 digits is equal to that of the last 2 digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other 2 digits. What is the third digit of the number?Correct answer is '5'. Can you explain this answer? theory, EduRev gives you an
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