XAT 2023 — QA & DI Question 6
Suppose Haruka has a special key â in her calculator called delta key:
Rule 1: If the display shows a one-digit number, pressing delta key â replaces the displayed number with twice its value.
Rule 2: If the display shows a two-digit number, pressing delta key â replaces the displayed number with the sum of the two digits.
Suppose Haruka enters the value 1 and then presses delta key â repeatedly.
After pressing the â key for 68 times, what will be the displayed number?
Answer & solution
7
- B
4
- C
10
- D
2
- E
8
Initially the number = 1
Output when â is pressed 1 time = 2 [Single digit number 1 is doubled]
Output when â is pressed 2 times = 4 [Single digit number 2 is doubled]
Output when â is pressed 3 times = 8 [Single digit number 4 is doubled]
Output when â is pressed 4 times = 16 [Single digit number 8 is doubled]
Output when â is pressed 5 times = 7 [Digits of 2-digit number 16 are added]
Output when â is pressed 6 times = 14 [Single digit number 7 is doubled]
Output when â is pressed 7 times = 5 [Digits of 2-digit number 14 are added]
Output when â is pressed 8 times = 10 [Single digit number 5 is doubled]
Output when â is pressed 9 times = 1 [Digits of 2-digit number 10 are added]
After 9 steps we get back the same input 1.
Hence, when the input is 1, we will get the same output at the end of 9 or 18 or ... or 63 steps.
∴ Output at the end of 68 steps will be same as the output at the end of 5 steps i.e., 7.
Hence, option (a).