In a four-digit number, if the sum of the first two digits is equal to that of the last two digits, the sum of the first and last is equal to the third digit and finally, the sum of the second and fourth digit is twice the sum of the other two digits, then the third digit of the number is:

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answer is A.

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Detailed Solution

Concept- To solve this question, let us assume the first, second, third and fourth digits to be “a”, “b”, “c” and “d” respectively.
Based on the conditions mentioned in theQuestion statement, we can form 3 different equations using the above assumed variables, and solving these equations will give us our desired answer as shown below.
Given, the sum of the first two digits is equal to that of the last two digits, i.e.,

And, the sum of the first and last is equal to the third digit, i.e.,

Also, the sum of the second and fourth digit is twice the sum of the other two digits, i.e.,
Question Image

Now since, a, b, c and d all are digits of a 4-digit number, “a” needs to be such a value that 8a, 5a and 4a are all single digits, and that can only be possible is either (a = 0) or (a = 1).
If (a = 0), then the number would be 0000 which is equal to 0 and not a four-digit number.
And if (a = 1), then, (b = 8), (c = 5) and (d = 4), the number is 1854 which satisfies all our question-mentioned conditions.
∴ Value of c would be 5 which is the third digit of the required number.
Hence, the correct answer is 1.

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