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In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be?
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In a four digit number the sum of the digits in the units and the tens...
**Introduction:**
Let's assume the four-digit number as ABCD, where A represents the thousands place, B represents the hundreds place, C represents the tens place, and D represents the units place.
**Given Conditions:**
1. The sum of the digits in the units and tens places is equal to the sum of the other two digits.
2. The sum of the digits in the tens and hundreds places is twice the sum of the other two digits.
3. The sum of the digits of the number is more than 20.
**Analysis:**
Let's consider the sums of the digits:
1. Sum of units and tens = C + D
2. Sum of other two digits = A + B
3. Sum of tens and hundreds = B + C
4. Sum of other two digits = A + D
5. Sum of all digits = A + B + C + D
From condition 1, we can write:
C + D = A + B
From condition 2, we can write:
B + C = 2(A + D)
From condition 3, we know that the sum of the digits is more than 20:
A + B + C + D > 20
**Solving the Equations:**
Let's solve the equations using the given conditions:
From equation 1, we have:
C = A + B - D
Substituting this value in equation 2, we get:
B + A + B - D = 2(A + D)
2B + A - D = 2A + 2D
B - A - D = D
Now, substituting this value in equation 1, we get:
A + B - D + D = A + B
A = A
This implies that the value of A can be any digit from 0 to 9.
**Finding the Digit in the Units Place:**
Since A can be any digit from 0 to 9, and the sum of the digits is more than 20, the digit in the units place can be any digit from 1 to 9.
Let's assume the four-digit number as ABCD, where A represents the thousands place, B represents the hundreds place, C represents the tens place, and D represents the units place.
**Given Conditions:**
1. The sum of the digits in the units and tens places is equal to the sum of the other two digits.
2. The sum of the digits in the tens and hundreds places is twice the sum of the other two digits.
3. The sum of the digits of the number is more than 20.
**Analysis:**
Let's consider the sums of the digits:
1. Sum of units and tens = C + D
2. Sum of other two digits = A + B
3. Sum of tens and hundreds = B + C
4. Sum of other two digits = A + D
5. Sum of all digits = A + B + C + D
From condition 1, we can write:
C + D = A + B
From condition 2, we can write:
B + C = 2(A + D)
From condition 3, we know that the sum of the digits is more than 20:
A + B + C + D > 20
**Solving the Equations:**
Let's solve the equations using the given conditions:
From equation 1, we have:
C = A + B - D
Substituting this value in equation 2, we get:
B + A + B - D = 2(A + D)
2B + A - D = 2A + 2D
B - A - D = D
Now, substituting this value in equation 1, we get:
A + B - D + D = A + B
A = A
This implies that the value of A can be any digit from 0 to 9.
**Finding the Digit in the Units Place:**
Since A can be any digit from 0 to 9, and the sum of the digits is more than 20, the digit in the units place can be any digit from 1 to 9.
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In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be?
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In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? 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 digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? 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 digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be?.
In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? 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 digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? 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 digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be?.
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In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be?, a detailed solution for In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? has been provided alongside types of In a four digit number the sum of the digits in the units and the tens places is equal to the sum of the other two digits. The sum of the digits in the tens and the hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digit in the units place can be? theory, EduRev gives you an
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