Problem Solving

When positive integer m is divided by positive integer n , the remainder is 12.if m/n = 24.2
,what is the value of n?
a.120
b.60
c.30
d.24
e.12

m/n = 24.2

2/10 = 12/n

n = 60

Refer this post for a detailed explanation https://www.beatthegmat.com/number-prope ... tml#415002

m/n=k+12/n where k is integer
m/n=24.2, find n?

24.2=k+12/n, k=24.2-12/n=(24.2n-12)/n
24n+n/5-12=nk, 121n/5 -nk=12
n(121/5-k)=12, n(121-5k)=60

n and k must be positive integers

>>> 5k can have either 5 or 0 at the end (short-cut for playing with numbers)
>>> n cannot be less than 1

among all answer choices A is out
possible if n=60, k=24 ans.B +
if n=30, 121-5k=2 and 119=5k, k isn't integer ans. C is out
if n=24, we get ratio ans.D is out
if n=12, 121-5k=5 and 116=5k, k isn't integer

b

ranvijay87 wrote:When positive integer m is divided by positive integer n , the remainder is 12.if m/n = 24.2
,what is the value of n?
a.120
b.60
c.30
d.24
e.12

ranvijay87 wrote:When positive integer m is divided by positive integer n , the remainder is 12.if m/n = 24.2
,what is the value of n?
a.120
b.60
c.30
d.24
e.12

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = .5.
Since the two values are equal:
Remainder/divisor = decimal.

It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = 12.
Divisor = n.
Decimal = .2 = 2/10 = 1/5.
Plugging these values into remainder/divisor = decimal, we get:
12/n = 1/5
n = 60.

The correct answer is B.

Answer is 60

In case of any remainder problem, i think this is the easiest approach

m/n=24.2

Where 24 = quotient
0.2 = remainder decimal value
12 = remainder value

So, Remainder value/divisor = remainder in decimal value....
12/n = 0.2

So, n=60

If you dont understand, see this example below:

7/2 = 3.5

and remainder of 7/2 is 1

So, 1/2 = 0.5 (remainder decimal value)

m = nx+12 -- x should be a positive integer

m/n = x + 12/n

x + 12/n = 24.2

10x + 120/n = 242

x = (242 - 120/n) /10

-- amongst the options only 60 will make x positive integer.

another method could be
24 + 0.2 = m/n
24 + 1/5 = x + 12/n

1/5 = 12/n (as these are remainders)

n = 60