Problem Solving

When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Ok - I don't remember the secret my princeton review teacher, Brian taught us on how to do these. I do remember a little nugget of esoterica taught by Becky from the Hard Math course, that "the largest remainder is always one less than the divisor". I feel like that info is useful here, just don't know how.

Just looking @ it, I recognize that this is @ least a medium difficulty question, so right off the bat I eliminated (A) and (E) because those answers are also in the problem itself, and then I got rid of (C) because 48 is 1/2 of 96. Then I looked at (B) and (D) and decided that for some reason 75 seemed like a scarier number than 25 so I picked (B) and got it right without doing it or having any clue as to how to put it together. I got lucky.

I looked at the OG explanation and know that there's no way on test day I'll be able to put their explanation (the long way) to good use. What little esoterica am I supposed to see from the "remainder" details of the question stem in order to explain what I'm looking for? I feel like "the remainder is 9" explains something that to one who understands it is able to put that info to good use.

Thanks in advance.

Please keep in mind that X & Y both are integers.
So, X/Y=96.12
=> X-96Y=0.12Y

So 0.12Y is the reminder and this is equal to 9.
so Y=9/0.12 or Y=75.
OA is B

Lets say, 10 is divided by 7

10/8 or 1.25 --> This can be represented as an improper fraction 1(2/8)
Here 1 is the quotient, and 2 is the remainder
2/8 = 0.25


Similarly, for X/Y = 96.12
96 is the quotient
0.12 = Remainder/Y
12/100 = 9/Y
Y = 9*(100/12) = 75

Option B

jzw wrote:When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Ok - I don't remember the secret my princeton review teacher, Brian taught us on how to do these. I do remember a little nugget of esoterica taught by Becky from the Hard Math course, that "the largest remainder is always one less than the divisor". I feel like that info is useful here, just don't know how.

Just looking @ it, I recognize that this is @ least a medium difficulty question, so right off the bat I eliminated (A) and (E) because those answers are also in the problem itself, and then I got rid of (C) because 48 is 1/2 of 96. Then I looked at (B) and (D) and decided that for some reason 75 seemed like a scarier number than 25 so I picked (B) and got it right without doing it or having any clue as to how to put it together. I got lucky.

I looked at the OG explanation and know that there's no way on test day I'll be able to put their explanation (the long way) to good use. What little esoterica am I supposed to see from the "remainder" details of the question stem in order to explain what I'm looking for? I feel like "the remainder is 9" explains something that to one who understands it is able to put that info to good use.

Thanks in advance.

When given a quotient (in this case x/y), the remainder of x/y can ALWAYS be found by multiplying the decimal portion of x/y by y. Since all remainders are integers by nature, let's first eliminate any choice that doesn't end in a 0 when multiplied by 2 (from the last digit of .12):

This leaves B and D: 25 and 75.

Now let's do the math for each and see which gives us 9 as the remainder...

12/100 * 25 = 12/4 = 3 NOPE
12/100 * 75 = 36/4 = 9 YUP

D it is.

Simple and easy way is,
Since X & Y are integers, REMAINDER = VALUE AFTER DECIMAL PLACE * Y

So, 9 = 0.12 * Y
Therefore, Y = 9 / 0.12

= 9/ (12/100)
= 9*100 / 12
= 3/4 *100
= 75

jzw wrote:When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Ok - I don't remember the secret my princeton review teacher, Brian taught us on how to do these. I do remember a little nugget of esoterica taught by Becky from the Hard Math course, that "the largest remainder is always one less than the divisor". I feel like that info is useful here, just don't know how.

Just looking @ it, I recognize that this is @ least a medium difficulty question, so right off the bat I eliminated (A) and (E) because those answers are also in the problem itself, and then I got rid of (C) because 48 is 1/2 of 96. Then I looked at (B) and (D) and decided that for some reason 75 seemed like a scarier number than 25 so I picked (B) and got it right without doing it or having any clue as to how to put it together. I got lucky.

I looked at the OG explanation and know that there's no way on test day I'll be able to put their explanation (the long way) to good use. What little esoterica am I supposed to see from the "remainder" details of the question stem in order to explain what I'm looking for? I feel like "the remainder is 9" explains something that to one who understands it is able to put that info to good use.

Thanks in advance.

jzw wrote:When positive integer X is divided by positive integer Y, the remainder is 9. If X/Y = 96.12, what is the value of Y?

(A) 96
(B) 75
(C) 48
(D) 25
(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.
Notice that 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, the decimal = .12 = 12/100 = 3/25.
Since remainder/divisor = 3/25, the divisor y must be a multiple of 25.

ALWAYS LOOK AT THE ANSWER CHOICES.
Only B is a multiple of 25.

The correct answer is B.

Here is the complete calculation if we plug into the formula remainder/divisor = decimal:
Remainder = 9.
Divisor = y.
Decimal = .12 = 12/100 = 3/25.
9/y = 3/25
y = 75.