If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
If m > 0 and x is ............
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x is m percent of y => (x/y)*100 = mpzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
Therefore, (x/y) = m/100 => (y/x) = 100/m => (y/x)*100 = 10000/m
Thus y is 10000/m percent of x.
The correct answer is E.
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Can someone explain with testing values approach. Also, what does it mean when questions in terms of something ? Here we need to find out in terms of m, y is what percent of x? I could write this y = ?/100 *x but i dint get it when it says in terms of x.
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Let y=1 and m=200.pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
x is m% of y:
Thus, m = (200% of 1) = 2.
y is what percent of x?
y/x = 1/2 = 50%.
The target value is 50.
Now plug m=200 into the answer choices to see which yields the target value of 50.
Only E works:
10000/m = 10000/200 = 50.
The correct answer is E.
y is what FRACTION of x? ---> y/x.Also, what does it mean when questions in terms of something ? Here we need to find out in terms of m, y is what percent of x? I could write this y = ?/100 *x but i dint get it when it says in terms of x
To convert a fraction to a percent, we multiply by 100.
Thus:
y is what PERCENT of x? --> (y/x) * 100.
To solve the posted problem algebraically, we need to rephrase the blue expression IN TERMS OF M.
x is m percent of y:
x = (m/100) * y
x/y = m/100
y/x = 100/m.
Substituting y/x = 100/m into (y/x) * 100, we get:
(y/x) * 100 = (100/m) * 100 = 10000/m.
The correct answer is E.
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We have x is m percent of y.pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
Thus, x = m% of y
x = my/100
y = 100x/m
y = 10000x/100m
y = (10000/m)% of x
Thus, y is 10000/m percent of x.
The correct answer: E
Hope this helps!
-Jay
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Last edited by Jay@ManhattanReview on Tue Apr 03, 2018 6:31 am, edited 1 time in total.
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Jay, the correct answer to this question is E, not C.Jay@ManhattanReview wrote:We have x is m percent of y.pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
Thus, x = m% of y
x = my/100
y = 100x/m
y = (1/m)% of x
Thus, y is 1/m percent of x.
The correct answer: C
Hope this helps!
-Jay
This question is PS #194 in OG 2016, PS #181 in OG 13/2105.
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Here's a good general rule: if the question asks "what is p in terms of q?" that means that we want to ISOLATE p, and have it equal to some expression involving q:santhosh_katkurwar wrote:Can someone explain with testing values approach. Also, what does it mean when questions in terms of something ? Here we need to find out in terms of m, y is what percent of x? I could write this y = ?/100 *x but i dint get it when it says in terms of x.
p = ....q
(p equals something something q)
In this question, it's a bit more complicated, because the thing we want to isolate isn't clearly defined. Think of phrasing it this way: "what is (the percent that y is of x) in terms of m?" Let's define a new variable for (the percent that y is of x). Let's call it n. So here's what we want:
n = ...m
(n = something something m)
ALGEBRA:
If we want to do it algebraically, creating this new variable makes life a lot easier:
x is m percent of y ---> x = (m/100)y
y is what percent of x ---> y = (n/100)x
In order to get n in terms of m (but NOT in terms of x or y), we need to get rid of x and y. First, substitute what we have for x in the first equation into the 2nd:
y = (n/100)(m/100)y
y = (nm/10,000)y
Divide both sides by y:
1 = (nm/10,000)
Isolate n:
n = 10,000/m
So, we can get to answer E.
However, nearly every time I see "in terms of" in a PS question, I think about whether plugging my own numbers in might be easier. In this case - when there are 3 variables given, 1 implied - it's definitely easier! I would do things slightly differently than Mitch did (though same idea).
PLUGGING IN NUMBERS:
I'd choose an x and a y that have an easy relationship, then see what m that gives us:
x = 2
y = 10
2 is 20% of 10, so m = 20
Now what percent is 10 of 2? It's 5 times as great, so 500%. n = 500. Since n is the thing we're solving for, our target answer = 500, when we plug in 20.
A. 100m ---> 100(20) = 500? Nope.
B. 1/100m ---> 1/(100*20) = 500? Nope!
C. 1/m ---> 1/20 = 500? Nope!
D. 10/m ---> 10/20 = 500? Nope!
E. 10000/m ---> 10,000/20 = 500? YES!
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To solve, we want to first create a word translation from the information in the problem stem. We are given that x is m percent of y. We can express this as:pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?
A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m
x = (m/100)y
x = my/100
We are next asked, in terms of m, y is what percent of x? This can be expressed as:
y/x * 100 = ?
We need to manipulate our first equation until we isolate y/x.
x = my/100
Multiplying the entire equation by 100, we have:
100x = my
Then divide both sides by x:
100 = my/x
Then divide both sides by m:
100/m = y/x
The final step is to multiply both sides of the equation by 100, to convert to a percent.
100/m * 100 = y/x * 100
10,000/m = y/x * 100
Answer: E
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