Question

To floor the administrative office, a total of 3800 tiles are required. The tiles can be packed in two ways:


The number of tiles remaining outside the boxes in Case 2 will be _____

• A. 37
• B. 53
• C. 71
• D. 0 (All tiles are boxed)

Answer 1

The correct option is A 37

In both Case 1 and Case 2, we can observe:
Total number of tiles will be $Dividend$
Total number of boxes will be $Divisor$
The number of tiles in each box will be $Quotient$
And, number of tiles outside the boxes will be $Remainder$

So, for Case 1,
$Dividend=3800$
$Divisor=71$
$Quotient=53$
$Remainder=37$

Similarly, in Case 2,
$Dividend=3800$
$Divisor=53$
$Quotient=71$
$Remainder=unknown$

Now, the general form of the multiplication equation is:

$Dividend=Divisor\times Quotient+Remainder$.

So, in Case 1, the multiplication equation will be:

$3763=71\times 53+37$

Similarly, in Case 2, the multiplication statement will be:

$3763=53\times 71+UnknownRemainder$

Now, the multiplication equation can also be written as:

$Dividend=Quotient\times Divisor+Remainder$

So, for Case 1, we have:
$3763=53\times 71+37$

Comparing this to the multiplictaion equation of Case 2, we get:
$UnknownRemainder=37$

∴ The number of tiles remaining ouutside the boxes in Case 2 will be $37.$