Q7 REPRESENTATIONS

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

Write Here