How many positive two-digit numbers, ab, are possible such that ab is

Hi All,

From the answer choices, we know that there cannot be that many 2-digit numbers that fit the given 'restrictions' in the prompt, so we really just have to go about finding them with a bit of brute-force. The answers are 'close together' though, so you should insist on writing everything on the pad so that you don't accidentally miss one of the numbers (and choose one of the wrong answers).

We're asked to find the number of positive two-digit numbers that are divisible by 8 AND the sum of the two digits is divisible by 8.

We can list the numbers one at a time, then note whether the sum of the digits is divisible by 8 or not:

16 no
24 no
32 no
40 no
48 no
56 no
64 no
72 no
80 YES
88 YES
96 no

Final Answer:

GMAT assassins aren't born, they're made,
Rich

a b digit_sum divisible by 8
2 6 8 NO
4 4 8 NO
6 2 8 NO
8 0 8 YES
8 8 16 YES

{80,88} => (C)

How many positive two-digit numbers, ab, are possible such that ab is divisible by 8 and the sum of a and b is divisible by 8?

A. 0
B. 1
C. 2
D. 3
E. 4

Let the number N be of the form ab, written as

N = 10*a + b (Note : a is not equal to 0..since N is 2-digit number)
= 9*a + (a + b)

Given, N mod 8 = 0
ie, 9*a + (a + b) mod 8 = 0......(1)

Also, Given, (a+b) mod 8 = 0..........(2)

Using (1) and (2) ,
9*a mod 8 also needs to be = 0

Possible only for a = 8
simultaneously, (a+b) mod 8 = 0................(3)

Since, b can only be a single digit number, so b = 0 or 8..........(4)

From (3) and (4), we get ab = 80 and 88
(Only TWO such positive 2-digit numbers possible)

(C) is the correct answer