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
Answer: B
Source: Official Guide
When positive integer \(x\) is divided by positive integer \(y,\) the remainder is 9. If \(x/y = 96.12,\) what is...
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There are a few ways to tackle this question.Gmat_mission wrote: ↑Sun Sep 12, 2021 9:27 amWhen 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
Answer: B
Source: Official Guide
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 crossmultiply to get: 3y = (25)(9)
Solve to get y = 75
Cheers,
Brent