govind_raj_76 wrote:Chris joined IBC consulting. The password given to Chris to access the computer lab is a 4 digit number. The 'n' th digit of the password is the remainder when expression n^2 + 24n + 61 is divided by the expression n+3 after substituting the value of n.
What is the password that Chris got fot the computer lab ?
A. 4567
B. 3456
c. 2311
d. 2341
e. 2345
Please assist.
Definitely want to use the answer choices to cut down the math.
Before we dive in to calculations, let's look at the 4 digits.
First digit: choices are 4, 3, 2, 2, 2
Second digit: choices are 5, 4, 3, 3, 3
Third digit: choices are 6, 5, 1, 4, 4
Fourth digit: choices are 7, 6, 1, 1, 5
Since the third and fourth digits have more options, we should calculate those first - we'll be able to eliminate more choices.
Let's use the 4th digit.
If n=4, then:
n^2 + 24n + 61 = 16 + 96 + 61 = 173
n+3 = 7
173/7 = 24rem5
Only (E) ends in 5... choose (E)!
If we had gotten a remainder of 1, both (C) and (D) would still be in the running and we'd have calculated the 3rd digit as well (since that's the only difference between the two numbers).
