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CAT 2001 — QA Question 10

Number TheoryEasy

In a 4-digit number, the sum of the first two digits is equal to that of the last two 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 two digits. What is the third digit of the number?

Answer & solution

Correct answer: 5

  • 5

  • B

    8

  • C

    1

  • D

    4

Solution

Let the four digit number be abcd.

∴ a + b = c + d                           ...(i)

∴ a + d = c                                 ...(ii)

∴ b + d = 2 × (a + c)                  ...(iii)

Solving these equations, we get,

b = 2d

d = 4a

c = 5a

∴ c has to be a multiple of 5 and a single digit number.

The only possibility is c = 5

Hence, option (a).

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CAT 2001 QA Q10: In a 4-digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the f — Solution | TheCATExam