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In a 4-digit number, the sum of the first two digits is equal to that of last two digits. The sum of the first and last digits is equal to third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?

In a 4-digit number, the sum of the first two digits is equal to that of last two digits. The sum of the first and last digits is equal to third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number? Correct Answer 5

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 = 2dand eqn (iii);2d + d = 2(a + a + d)
→3d = 2(2a + d) → d = 4a or, a = $$\frac{{\text{d}}}{4};$$
→Now, from eqn. (ii),
a + d = $$\frac{{\text{d}}}{4}$$ + d = $$\frac{{{\text{5d}}}}{4}$$ = cOr, c = $$\frac{5}{{4{\text{d}}}}$$The value of d can be either 4 or 8.If d = 4, then c = 5If d = 8, then c = 10But the value of c should be less than 10Hence, value of c would be 5

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