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?
Thanks in advance, the explanation in the book wasn't of much help.
OG 13 PS # 95 -- Integer and remainder
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When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.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
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 = 9.
Divisor = y.
Decimal = .12 = 12/100 = 3/25.
Plugging these values into remainder/divisor = decimal, we get:
9/y = 3/25
y = 75.
The correct answer is B.
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There are a few ways to tackle this question.richewalsh 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
One way is to examine a few other fractions.
7/2 = 3 with remainder 1.
7/2 = 3 1/2 = 3.5
Notice that 0.5 = 1/2
Another example:
11/4 = 2 with remainder 3.
11/4 = 2 3/4 = 2.75
Notice that 0.75 = 3/4
Now onto the question....
So, we know that x/y = some value with remainder 9
If x/y = 96.12, we can conclude that 0.12 = 9/y
Now solve for y.
0.12 = 9/y
12/100 = 9/y [rewrite 0.12 as 12/100]
Simplify to get: 3/25 = 9/y
At this point, we might already see that y = 75. If we don't spot this, we can always cross-multiply.
We get: 3y = (25)(9)
Solve to get y = 75
Cheers,
Brent
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Hi richewalsh,
Both Mitch and Brent have provided similar algebra explanations. Here's a way to use Number Properties, the answer choices and "brute force" to find the solution.
In this prompt, we're told that X and Y are INTEGERS.
X/Y = 96.12 can be written as....
X = 96.12(Y)
The Y has to "multiply out" the .12 so that X becomes an integer. Since .12 is such a weird value, there can't be that many numbers that X and Y could be. Since none of the answers ends in 00, we need to find another way to multiply out the .12 - the only way to do it is with a multiple of 25. Eliminate A, C and E.
Between B and D, we just need to find the one that matches the rest of the info in the prompt (X/Y = 96.12 and X/Y has a remainder of 9)
Answer B: If Y = 75, then X = 7209
7209/75 gives a remainder of 9 THIS IS A MATCH
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
Both Mitch and Brent have provided similar algebra explanations. Here's a way to use Number Properties, the answer choices and "brute force" to find the solution.
In this prompt, we're told that X and Y are INTEGERS.
X/Y = 96.12 can be written as....
X = 96.12(Y)
The Y has to "multiply out" the .12 so that X becomes an integer. Since .12 is such a weird value, there can't be that many numbers that X and Y could be. Since none of the answers ends in 00, we need to find another way to multiply out the .12 - the only way to do it is with a multiple of 25. Eliminate A, C and E.
Between B and D, we just need to find the one that matches the rest of the info in the prompt (X/Y = 96.12 and X/Y has a remainder of 9)
Answer B: If Y = 75, then X = 7209
7209/75 gives a remainder of 9 THIS IS A MATCH
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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Another Problem Following the Similar Concept is as follows:
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II. 18.16
III. 17.17
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Answer: Option D
When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?
I. 15.15
II. 18.16
III. 17.17
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Answer: Option D
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And while we're at it, here's another good one that tests the same concept, but in a slightly different way:
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?
A) 2
B) 4
C) 8
D) 20
E) 45
(This is from the diagnostic test in the OG)
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t?
A) 2
B) 4
C) 8
D) 20
E) 45
(This is from the diagnostic test in the OG)
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Solution:richewalsh 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?
Thanks in advance, the explanation in the book wasn't of much help.
This problem can be solved by using the remainder formula:
When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.
In this problem we are given that when positive integer x is divided by positive integer y, the remainder is 9. Thus, we can say:
x/y = Q + 9/y
We also are given that x/y = 96.12. Using the remainder formula we see that:
x/y = 96.12
x/y = 96 + 0.12
x/y = 96 + 12/100
Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 and determine the value of y.
9/y = 12/100
12y = 9 x 100
y = 900/12 = 75
Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer, as shown here:
9/y = 3/25
3y = 9 x 25
y = 225/3 = 75
Answer: B
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I think simple way is to write it as
x/y = 96 + .12
x=96*y + .12*y
so .12y is the remainder
.12*y=9
y=9/12*100 = 75
x/y = 96 + .12
x=96*y + .12*y
so .12y is the remainder
.12*y=9
y=9/12*100 = 75