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XAT 2014 — QA & DI Question 8

Simple EquationsEasy

Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi gets a number from Amitabh, he adds 50 to the number, and gives the result back to Amitabh, who doubles the number again. The first person, whose result is more than 1000, loses the game. Let ‘x’ be the smallest initial number that results in a win for Amitabh. The sum of the digits of ‘x’ is:

Answer & solution

Correct answer: 7

  • A

    3

  • B

    5

  • 7

  • D

    9

  • E

    None of these

Solution

Let the smallest number be ‘X’

​​​​​​​

Amitabh has to win and X is the least possible number in the range 1 -999 ∴ step 4 has to be the last step.
 
⇒ 16X + 750 > 1000

The least possible value of X = 16

Sum of the digit = 1 + 6 = 7

Hence, option (c).

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XAT 2014 QA & DI Q8: Amitabh picks a random integer between 1 and 999, doubles it and gives the result to Sashi. Each time Sashi ge — Solution | TheCATExam