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

Let
the 1st,
2nd,
3rd and
4th digits
be a, b, c and d respectively.

Then, a + b = c + d ----------(i) a + d = c ----------(ii ) b + d = 2(a + c)
----------(iii)

from eqn. (i) and (ii),

a + b = a + 2d →b = 2d

and eqn
(iii);

2d + d = 2(a + a + d) → 3d = 2(2a + d)
→ d = 4a or, a = d/4

Now, from eqn. (ii),

a + d = (d/4) + d = 5d/4

Or, c = 5d/4

If d = 4, then c = 5 If d = 8, then c = 10

But the value of c should be less than 10

Hence, value of c would be 5

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