I struggle with this sort of problem and the explanation from the OG was less than helpful. What's the best way to approach this?
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
Thanks,
Jeremy
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Dealing with Remainders
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GMATGuruNY
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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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ceilidh.erickson
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I like Mitch's explanation a lot, but the other way you could solve this is as a system of equations.
If, when we divide x by y, we get a remainder of 9, we could say that y times something plus 9 equals x:
ny + 9 = x
Then we're told that x/y = 96.12, which means that n must equal 96:
96y + 9 = x
We can also rearrange our given equation to say 96.12y = x.
Since both equations are equal to x, we can say:
96y + 9 = 96.12y
9 = 0.12y
y = 75
If, when we divide x by y, we get a remainder of 9, we could say that y times something plus 9 equals x:
ny + 9 = x
Then we're told that x/y = 96.12, which means that n must equal 96:
96y + 9 = x
We can also rearrange our given equation to say 96.12y = x.
Since both equations are equal to x, we can say:
96y + 9 = 96.12y
9 = 0.12y
y = 75
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Hi jjayhart,
Both Mitch and Ceilidh 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.
Since X/Y = 96.12, 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 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 Ceilidh 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.
Since X/Y = 96.12, 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 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
