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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?
- a)5
- b)8
- c)1
- d)4
Correct answer is option 'A'. 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. Hence option A.
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. Hence option A.
Most Upvoted Answer
In a four-digit number, the sum of the first 2 digits is equal to that...
Solution:
Let the four-digit number be represented as ABCD, where A, B, C, D are the digits in thousandth, hundredth, tenth and unit place respectively.
Given conditions are:
1. A + B = C + D
2. A + D = C
3. B + D = 2(C + A)
From equation 2, we can write A = C - D
Substituting the value of A in equation 1, we get B = 2D - C
Substituting the values of A and B in equation 3, we get D - C = 2C - 2D + 2(C - D)
Simplifying the above equation, we get 5D = 3C
Since the digits are integers, D must be a multiple of 3 and C must be a multiple of 5.
The only possible values for C are 5 and 0, but C cannot be 0 as it is the first digit of the number.
Therefore, C = 5 and D = 3.
Now, substituting the values of C and D in equations 2 and 1 respectively, we get:
A = C - D = 2
B = 2D - C = 1
Hence, the four-digit number is 2153 and the third digit is 5.
Therefore, the correct answer is option A.
Let the four-digit number be represented as ABCD, where A, B, C, D are the digits in thousandth, hundredth, tenth and unit place respectively.
Given conditions are:
1. A + B = C + D
2. A + D = C
3. B + D = 2(C + A)
From equation 2, we can write A = C - D
Substituting the value of A in equation 1, we get B = 2D - C
Substituting the values of A and B in equation 3, we get D - C = 2C - 2D + 2(C - D)
Simplifying the above equation, we get 5D = 3C
Since the digits are integers, D must be a multiple of 3 and C must be a multiple of 5.
The only possible values for C are 5 and 0, but C cannot be 0 as it is the first digit of the number.
Therefore, C = 5 and D = 3.
Now, substituting the values of C and D in equations 2 and 1 respectively, we get:
A = C - D = 2
B = 2D - C = 1
Hence, the four-digit number is 2153 and the third digit is 5.
Therefore, the correct answer is option A.
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Community Answer
In a four-digit number, the sum of the first 2 digits is equal to that...
Solution:
Let the four-digit number be ABCD where A, B, C, and D represent digits in the thousands, hundreds, tens, and ones places, respectively.
Given conditions:
1. A+B = C+D
2. A+D = C
3. B+D = 2(C+A)
Using equation 2, we can express A in terms of C and D:
A = C-D
Substituting this value of A in equation 1, we get:
C+D = C-D+B
2D = B+D
B = D
So, the number can be written as ABAB or CDCD.
Now using equation 3, we can express B in terms of C and D:
B = 2(C+A)-D
Substituting the value of B = D, we get:
D = 2(C+A)-D
2D = 2(C+A)
D = C+A
So, the number can be written as ACDA.
Now using equation 2, we get:
A+D = C
Substituting A = C-D, we get:
C-D+D = C
D = C/2
As D is a digit, C must be even and the only possible value is 4.
Therefore, the third digit of the number is 4.
Hence, the correct answer is option (d) 4.
Let the four-digit number be ABCD where A, B, C, and D represent digits in the thousands, hundreds, tens, and ones places, respectively.
Given conditions:
1. A+B = C+D
2. A+D = C
3. B+D = 2(C+A)
Using equation 2, we can express A in terms of C and D:
A = C-D
Substituting this value of A in equation 1, we get:
C+D = C-D+B
2D = B+D
B = D
So, the number can be written as ABAB or CDCD.
Now using equation 3, we can express B in terms of C and D:
B = 2(C+A)-D
Substituting the value of B = D, we get:
D = 2(C+A)-D
2D = 2(C+A)
D = C+A
So, the number can be written as ACDA.
Now using equation 2, we get:
A+D = C
Substituting A = C-D, we get:
C-D+D = C
D = C/2
As D is a digit, C must be even and the only possible value is 4.
Therefore, the third digit of the number is 4.
Hence, the correct answer is option (d) 4.
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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?a)5b)8c)1d)4Correct answer is option 'A'. Can you explain this answer?
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