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Minionion
Joined: 23 Jun 2025
Last visit: 05 Jan 2026
Posts: 31
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02 Jul 2025, 19:31
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Yesterday, on an audio streaming platform, the number of songs streamed was thrice the number of podcasts streamed. Yesterday, was the platform’s revenue from song streams greater than its revenue from podcast streams?
(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.
(2) Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
number of songs = s & number of podcasts = p; s = 3p -> given
Let r_s = avg revenue per song & r_p = avg revenue per podcast
Total revenue from song = R_s = s * r_s = 3p * r_s
Total revenue from podcast = R_p = p * r_p
We need to find: Rs > Rp = 3p * r_s > p * r_p = 3r_s > r_p ?
(1) r_p = r_s + 12
3r_s > r_p = 3r_s > r_s + 12
= 2r_s > 12
= r_s > 6 (assuming 6 as a minimum of r_s, 3*6 = 6+12, and for every r_s bigger than 6, 3r_s will always be greater than r_s + 12) => sufficient
(2) ( r_s*3p + r_p*p ) / 4p = (3r_s +r_p) / 4 > 20
3r_s+r_p > 80; insufficient to determine if 3r_s > r_p with this info
Answer: (1) is sufficient, (2) isn't
(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.
(2) Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
number of songs = s & number of podcasts = p; s = 3p -> given
Let r_s = avg revenue per song & r_p = avg revenue per podcast
Total revenue from song = R_s = s * r_s = 3p * r_s
Total revenue from podcast = R_p = p * r_p
We need to find: Rs > Rp = 3p * r_s > p * r_p = 3r_s > r_p ?
(1) r_p = r_s + 12
3r_s > r_p = 3r_s > r_s + 12
= 2r_s > 12
= r_s > 6 (assuming 6 as a minimum of r_s, 3*6 = 6+12, and for every r_s bigger than 6, 3r_s will always be greater than r_s + 12) => sufficient
(2) ( r_s*3p + r_p*p ) / 4p = (3r_s +r_p) / 4 > 20
3r_s+r_p > 80; insufficient to determine if 3r_s > r_p with this info
Answer: (1) is sufficient, (2) isn't
02 Jul 2025, 19:36
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Let:
S = number of songs streamed
P = number of podcasts streamed
RS = revenue from song streams
RP = revenue from podcast streams
AS = average revenue per song stream
AP = average revenue per podcast stream
We are given: S=3P.
We want to determine if RS>RP
We know that RS =S×AS and RP =P×AP.
So, we want to know if S×AS>P×AP.
Substitute S=3P:
3P×AS>P×AP
Since P must be positive (otherwise there would be no streams and no revenue), we can divide by P:
3×AS>AP
This is the inequality we need to evaluate.
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.
AP=AS+12 cents.
Now substitute this into our inequality:
We want to know if 3×AS>AS+12.
2×AS>12
AS>6 cents.
If AS>6 cents, then RS > RP
If AS≤6 cents (and AS must be positive for revenue to be generated), then RS ≤ RP
We don't know the value of AS.
Since we get different answers depending on the value of AS, Statement (1) alone is not sufficient.
Statement (2): Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
Let R total =RS + RP be the total revenue.
Let N total =S+P be the total number of streams.
The average revenue per stream is
R total / N total = {S×AS+P×AP } / (S+P)
We are given that
{S×AS+P×AP} / (S+P) >20 cents.
Substitute S=3P:
We get,
3AS+AP>80 cents.
This inequality relates AS and AP. We still need to determine if 3AS>AP.
From 3AS+AP >80:
AP>80−3AS.
Since we get different answers, Statement (2) alone is not sufficient.
Combining Statement (1) and Statement (2):
From (1): AP=AS+12.
From (2): 3AS+AP>80.
Substitute (1) into (2):
3AS+(AS+12)>80
4AS+12>80
4AS>68
AS>17 cents.
Now we can use this information to answer our target question: Is 3AS>AP?
Substitute AP=AS+12:
Is 3AS>AS+12?
Is 2AS>12?
Is AS>6?
We found from combining both statements that AS>17 cents.
If AS>17 cents, then it is definitely true that AS>6 cents.
Since AS>6 cents, the inequality 3AS>AP is true.
Therefore, RS > RP
Both statements together are sufficient.
Final answer: C
S = number of songs streamed
P = number of podcasts streamed
RS = revenue from song streams
RP = revenue from podcast streams
AS = average revenue per song stream
AP = average revenue per podcast stream
We are given: S=3P.
We want to determine if RS>RP
We know that RS =S×AS and RP =P×AP.
So, we want to know if S×AS>P×AP.
Substitute S=3P:
3P×AS>P×AP
Since P must be positive (otherwise there would be no streams and no revenue), we can divide by P:
3×AS>AP
This is the inequality we need to evaluate.
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.
AP=AS+12 cents.
Now substitute this into our inequality:
We want to know if 3×AS>AS+12.
2×AS>12
AS>6 cents.
If AS>6 cents, then RS > RP
If AS≤6 cents (and AS must be positive for revenue to be generated), then RS ≤ RP
We don't know the value of AS.
Since we get different answers depending on the value of AS, Statement (1) alone is not sufficient.
Statement (2): Yesterday, the average revenue per stream, calculated across both songs and podcasts, exceeded 20 cents.
Let R total =RS + RP be the total revenue.
Let N total =S+P be the total number of streams.
The average revenue per stream is
R total / N total = {S×AS+P×AP } / (S+P)
We are given that
{S×AS+P×AP} / (S+P) >20 cents.
Substitute S=3P:
We get,
3AS+AP>80 cents.
This inequality relates AS and AP. We still need to determine if 3AS>AP.
From 3AS+AP >80:
AP>80−3AS.
Since we get different answers, Statement (2) alone is not sufficient.
Combining Statement (1) and Statement (2):
From (1): AP=AS+12.
From (2): 3AS+AP>80.
Substitute (1) into (2):
3AS+(AS+12)>80
4AS+12>80
4AS>68
AS>17 cents.
Now we can use this information to answer our target question: Is 3AS>AP?
Substitute AP=AS+12:
Is 3AS>AS+12?
Is 2AS>12?
Is AS>6?
We found from combining both statements that AS>17 cents.
If AS>17 cents, then it is definitely true that AS>6 cents.
Since AS>6 cents, the inequality 3AS>AP is true.
Therefore, RS > RP
Both statements together are sufficient.
Final answer: C
02 Jul 2025, 20:56
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Let the values be the following:
Number of Songs: 3x
Number of Podcasts: x
STATEMENT 1
Revenue per Song: y
Revenue per Podcast: y+0.12
To Prove:
Total Revenue from Songs > Total Revenue from Podcasts
3xy > x(y+0.12)
3y>y+0.12
2y>0.12
y>0.06
Insufficient
STATEMENT 2
Average Revenue per stream > 0.2
Insufficient
S1 and S2 Together
(3xy+x(y+0.12))/4x>0.2
(4y+0.12)/4>0.2
y+0.03>0.2
y>0.17
Hence y>0.06 as required for Revenue of Song to be greater than Revenue for Podcast
Hence C is the answer
Number of Songs: 3x
Number of Podcasts: x
STATEMENT 1
Revenue per Song: y
Revenue per Podcast: y+0.12
To Prove:
Total Revenue from Songs > Total Revenue from Podcasts
3xy > x(y+0.12)
3y>y+0.12
2y>0.12
y>0.06
Insufficient
STATEMENT 2
Average Revenue per stream > 0.2
Insufficient
S1 and S2 Together
(3xy+x(y+0.12))/4x>0.2
(4y+0.12)/4>0.2
y+0.03>0.2
y>0.17
Hence y>0.06 as required for Revenue of Song to be greater than Revenue for Podcast
Hence C is the answer
