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02 Jul 2025, 10:00
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From the prompt, I need to find out whether 3Px > Py, where x = rev per song and y = rev per podcast.
Using statement (1):
x = y - 12
Plugging in -> 3P(y-12) > Py. I'm only told the difference between the revenue per item, but without the actual value of the revenue per item or the quantity of items, statement (1) alone is not sufficient.
Using statement (2):
(3Px + Py) / (4P + P) > 20, P cancels out
Too many unknowns, statement (2) alone is not sufficient.
Both:
(3y + y + 12) / (4) > 20
y >17
3x > x + 12
x > 6
3P(6) > P17 -> 18P > 17P? Yes.
Both statements are sufficient
Answer: C)
Using statement (1):
x = y - 12
Plugging in -> 3P(y-12) > Py. I'm only told the difference between the revenue per item, but without the actual value of the revenue per item or the quantity of items, statement (1) alone is not sufficient.
Using statement (2):
(3Px + Py) / (4P + P) > 20, P cancels out
Too many unknowns, statement (2) alone is not sufficient.
Both:
(3y + y + 12) / (4) > 20
y >17
3x > x + 12
x > 6
3P(6) > P17 -> 18P > 17P? Yes.
Both statements are sufficient
Answer: C)
02 Jul 2025, 10:10
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Let's make some variables first to get our understanding better:
\(S\) = # of songs streamed
\(P\) = # of podcasts streamed
\(R_S\) = Total revenue from the songs streamed
\(R_P\) = Total revenue from the podcasts streamed
\(A_S\) = Avg revenue from the songs streamed
\(A_P\) = Avg revenue from the podcasts streamed
Now, it is given that, \(S = 3P\)
We are to find if \(R_S > R_P\)
Rewriting the above, we can say that, \(A_S*S > A_P*P\) (since, Avg revenue = \(\frac{Total Revenue}{# of streams}\))
Substituting \(S = 3P\) in the above equation, we get, \(3A_S > A_P\) (This is what we need to substantiate, so let' call it Equation 1)
Let's look at the statements now,
Statement 1:
The average (arithmetic mean) revenue earned per podcast stream on the platform yesterday was 12 cents more than the average revenue earned per song stream on the platform yesterday.
This means, \(A_P = A_S + 12\)
Substituting this value of \(A_P\) in equation 1, we get,
\(3A_S = A_S +12\), or \(A_S>6\)
This means, that our equation 1 is true if and only if \(A_S>6\), else not.
This statement doesn't tell us anything more, so this is insufficient.
Statement 2:
Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
This means, \(\frac{R_S + R_P}{(S+P)}\)\(>20\)
Substituting the value of \(S = 3P\), \(R_S = A_S*S\), \(R_P = A_P*P\) in the above equation, and solving we get:
\(3A_S + A_P > 80\)
This doesn't tell us anything else, so insufficient.
Statements 1 and 2 together:
We have the following:
\(3A_S + A_P > 80\) and \(A_P = A_S + 12\)
Substituting the value of \(A_P\), from the latter to the former, we get,
\(4A_S>68\) or \(A_S>17\)
Remember from our initial analysis of statement 1, we found out, that if \(A_S>6\), then our initial statement of \(R_S > R_P\) is true.
Since \(A_S>17\), we can fo sure say it is greater than 6. Hence, sufficient.
Answer is C.
\(S\) = # of songs streamed
\(P\) = # of podcasts streamed
\(R_S\) = Total revenue from the songs streamed
\(R_P\) = Total revenue from the podcasts streamed
\(A_S\) = Avg revenue from the songs streamed
\(A_P\) = Avg revenue from the podcasts streamed
Now, it is given that, \(S = 3P\)
We are to find if \(R_S > R_P\)
Rewriting the above, we can say that, \(A_S*S > A_P*P\) (since, Avg revenue = \(\frac{Total Revenue}{# of streams}\))
Substituting \(S = 3P\) in the above equation, we get, \(3A_S > A_P\) (This is what we need to substantiate, so let' call it Equation 1)
Let's look at the statements now,
Statement 1:
The average (arithmetic mean) revenue earned per podcast stream on the platform yesterday was 12 cents more than the average revenue earned per song stream on the platform yesterday.
This means, \(A_P = A_S + 12\)
Substituting this value of \(A_P\) in equation 1, we get,
\(3A_S = A_S +12\), or \(A_S>6\)
This means, that our equation 1 is true if and only if \(A_S>6\), else not.
This statement doesn't tell us anything more, so this is insufficient.
Statement 2:
Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
This means, \(\frac{R_S + R_P}{(S+P)}\)\(>20\)
Substituting the value of \(S = 3P\), \(R_S = A_S*S\), \(R_P = A_P*P\) in the above equation, and solving we get:
\(3A_S + A_P > 80\)
This doesn't tell us anything else, so insufficient.
Statements 1 and 2 together:
We have the following:
\(3A_S + A_P > 80\) and \(A_P = A_S + 12\)
Substituting the value of \(A_P\), from the latter to the former, we get,
\(4A_S>68\) or \(A_S>17\)
Remember from our initial analysis of statement 1, we found out, that if \(A_S>6\), then our initial statement of \(R_S > R_P\) is true.
Since \(A_S>17\), we can fo sure say it is greater than 6. Hence, sufficient.
Answer is C.
02 Jul 2025, 10:38
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p podcast @x
3p songs @y
3px>py?
3x>y?
1. y=x+12
3x>x+12?
x>6??...not given...NOT SUFFICIENT
2. 3x+y>80
if x=10..3x<y...No
if x=20...3x>y...Yes
NOT SUFFICIENT
together,
3x+y>80
y=x+12
x>17
YES..SUFFICIENT
Ans C
3p songs @y
3px>py?
3x>y?
1. y=x+12
3x>x+12?
x>6??...not given...NOT SUFFICIENT
2. 3x+y>80
if x=10..3x<y...No
if x=20...3x>y...Yes
NOT SUFFICIENT
together,
3x+y>80
y=x+12
x>17
YES..SUFFICIENT
Ans C
