Xavier Aptitude Test 2023 Paper

Question : 50 of 102

Marks: +1, -0

Suppose Haruka has a special key

△

in her caculator called delta ke:
Rule 1: If the display shows a one-digit number, pressing delta key

∆

replace the displayed number with twice its value.
Rule 2: If the display shows a two-digits number, pressing delta key

∆

replace the displayed number with the number sum of two digits.
Suppose Haruka enters the valie 1 and then presses delta key

△

repeated.
After pressing the key for 68 times, what will be the displayed number?

Solution:

The first number Haruka entered is 1 .
From Rule-1, the series will be

2,4,8,16

From Rule 2, 16 will be followed by 7
Like-wise, the series will be

1,2,4,8,16,7,14,5,10,1,2,4, . . . . . .

.
The series is repeating itself for every 9 iterations.
Initially, input is 1 and after first iteration, result is 2.
This implies,

\;9 n=1

\;9 n+1=2

9 n+2=4

.
.
.
.
.

\;9 n+7=5

\;9 n+8=10

In the question, it is given that key is pressed 68 times.

68=9(7)+5

68 is in the form of

9 n+5

This implies, 7 is the output.
The answer is option A.

Go to Question:

Prev Question

Next Question