If m is an integer such that m/8

Question

If m is an integer such that m/8 = 5,477.875, what is the remainder when integer m is divided by 16?

A. 1
B. 7
C. 9
D. 11
E. 15

kevincan · Accepted Answer

I know how it discouraging it is not to have an explanation waiting for you when you’ve tried a question, so I’m going to post one ! I’m looking forward to alternatives .
 
We can write m/8 as 5477 +7/8.

If we divide both sides by two, we get m/16 =5477/2 + 7/16

Because 5477 is an odd number, 5477/2 is equal to K +1/2, where k is an integer

Thus m/16 = k + 1/2 + 7/16

And so m/16 = k + 15/16

We can conclude that when k is divided by 16 the remainder is 15

poojaarora1818 · Answer

Solution:

I try to solve it by applying the formula  Dividend = Quotient * Divisor + Remainder .

As we know m is some integer that  \frac{m}{8}  = 5477.875

Let's deal with the decimals first and convert it into fraction.

\frac{m}{8 } = 0.875 =>  \frac{7}{8}

Now, put it into the formula Dividend = Quotient * Divisor + Remainder.

m = 5477 * 8 + 7 => 5477 can be wrtten as 2 * 2738 + 1.

Let's put it into the equation m = Q8 + R => 8 * 2 * 2738 +1 + 7 => 16 * 2788 + 8 +7=> 16 * 2788 + 15.

Hence, Option E

Adit_ · Answer

remainder leads to giving .875.
875/1000 = 7/8

Hence m = 8*5477+7

8*5477+7 mod 16 = 8*5+7 mod 16 = 47 mod 16 = -1 = 15.
Answer:  Option E

egmat · Answer

Let's break this into two clean steps.

Step 1: Find m.

We're told m/ 8  =  5477.875 . The decimal  0.875  tells us the remainder when m is divided by  8 .

Remainder =  0.875  ×  8  =  7

So m =  8  ×  5477  +  7  =  43816  +  7  =  43823 .

Step 2: Find the remainder when m is divided by 16.

Note that   16  =  8  ×  2 . So let's rewrite m in a way that makes dividing by  16  easy.

m =  8  ×  5477  +  7

Is  5477  divisible by  2 ? No —  5477  =  2  ×  2738  +  1 .

So:  8  ×  5477  =  8  × ( 2  ×  2738  +  1 ) =  16  ×  2738  +  8 .

Now plug back in:

m =  16  ×  2738  +  8  +  7  =  16  ×  2738  +  15

The  16  ×  2738  part is perfectly divisible by  16 , so the remainder is  15 .

Answer: E

Key principle:  When a problem gives you a decimal result of division (like  5477.875 ), the decimal part directly gives you the remainder — just multiply it back by the divisor ( 0.875  ×  8  =  7 ). Then to find the remainder with a new divisor ( 16 ), rewrite the expression and simplify.

If m is an integer such that m/8

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If m is an integer such that m/8

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