A student was asked to divide a number by 12. Instead he divided the number by 24. In doing so he got a quotient which was 16 less than the original number. Which of the following cannot be the value of that number. A) 394 B) 398 C) 396

If x is the original number,

x/24 = x-16
Comes out a fraction.

If, on the other hand, you meant to say

he got a quotient which was 16 less than the correct quotient, then we have

x/24 = x/12 - 16
x = 384

I suspect you have garbled the question.

To solve this problem, we need to find the original number that was incorrectly divided by 24, resulting in a quotient that is 16 less than the original number.

Let's represent the original number as "x".

According to the problem:
(x / 24) = (x - 16)

Now, let's solve this equation to find the value of x.

Cross-multiply:
24(x - 16) = x

Expand:
24x - 384 = x

Rearrange terms:
24x - x = 384

Combine like terms:
23x = 384

Divide both sides by 23:
x = 384 / 23

Now let's check which of the given options cannot be the value of x.

A) 394:
Substituting x = 394 into the equation:
394 / 24 = 394 - 16
16.4167 = 378 (not true)

B) 398:
Substituting x = 398 into the equation:
398 / 24 = 398 - 16
16.5833 = 382 (not true)

C) 396:
Substituting x = 396 into the equation:
396 / 24 = 396 - 16
16.5 = 380 (not true)

Therefore, none of the given options (394, 398, or 396) can be the value of the original number.