Question

The number A8 is a two-digit number with a digit A and units (ones) digit 8.

Similarly, 3B is a two-digit number with tens digit 3 and units digit B.

When A8 is multiplied by 3B, the result is the four digit number 0730. That is,

A8

x 3B

C730

If A, B, and C are each different digits from 0 to 9, determine the values of A.

B. and C.

Answer 1

A = 7

B = 5

C = 2

Explanation:

We are given;

A8 × 3B = C730

Now, by inspection, in multiplication of the above, the product of 8 and B must produce a number whose unit digit is 0.

Thus,the only two single digit numbers that can fit this description for B is either 5 or 0 since if they would yield a unit digit of 0 when multiplied by8.

Now, let's test 0.

If B is 0, it means the unit digit of C730 is 0 as wanted while the remaining product of A8 and 3 should yield C73. Now product of A8 and 3 would produce a number with a last digit of 4. But our last digit there in C73 is 3. Thus, it means B cannot be 0 but is 5.

Thus, it means 3B is 35.

Now, we are told that A, B and C could be any single digit number.

from 0 - 9.

Thus, the maximum value of A is 9.

Let's try to put 9 for A and multiply by 35.

If A is 9,then 98 × 35 = 3430

It means that the maximum value of C is 3.

Thus, C can either be 3 or less than 3. So, C is either 1, 2, or 3

Now, if C = 1, it means the C730 is now 1730.

Thus,A8 will be: 1730/35 = 49.43

This is a decimal and thus, it means C ≠ 1.

Now,if C = 2, it means the C730 is now 2730.

Thus,A8 will be: 2730/35 = 78

This is a whole number and thus, it means C = 2

Now,if C = 3, it means the C730 is now 3730.

Thus,A8 will be: 3730/35 = 106.57

This is a decimal and thus, it means C ≠ 3

Thus; A8 is 78 when C = 2

So, A = 7