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02 Jul 2025, 08:00
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C
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Difficulty:
95%
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Question Stats:
52% (02:17) correct
48%
(02:32)
wrong
based on 432
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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.
(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.
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02 Jul 2025, 08:30
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Bunuel
Experts' Global Explanation:
Let the number of songs streamed be n.
Let the number of podcasts streamed be m.
Let the average revenue from songs be s.
Let the average revenue from podcasts be p.
Since the number of songs streamed was thrice the number of podcasts streamed, n = 3m. (Equation I)
Total revenue from songs = (Number of songs streamed) x (Average revenue from songs) = ns.
Total revenue from podcasts = (Number of podcasts streamed) x (Average revenue from podcasts) = mp.
We need to find whether ns > mp.
From Equation I, this can also be expressed as: 3ms > mp.
Cancelling “m” from both sides, we get: 3s > p.
We need to find whether 3s > p.
Statement (1)
p = 12 + s (Equation II)
Possibility 1: If s = 100, then p = 112 and 3s is greater than p.
Possibility 2: If s = 1, then p = 13 and 3s is NOT greater than p.
It is NOT possible to determine with certainty whether the total revenue from songs was greater than the total revenue from podcasts. Hence, Statement (1) is insufficient.
Statement (2)
[(ns + mp)/(n + m)] > 20
(ns + mp) > 20(n + m)
From Equation I, we get: (3ms + mp) > 20(3m + m)
(3ms + mp) > 20(4m)
Cancelling “m” from both sides, we get: (3s + p) > 80 (Equation III)
Possibility 1: If s = 100 and p = 1, then 3s is greater than p.
Possibility 2: If s = 1 and p = 100, then 3s is NOT greater than p.
It is also NOT possible to determine with certainty whether the total revenue from songs was greater than the total revenue from podcasts. Hence, Statement (2) is insufficient.
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined
From Equation III; we get (3s + p) > 80
Substituting the value of “p” from Equation II in Equation III, we get;
3s + 12 + s > 80
4s > 68
s > 17
For any value of s greater than 17, the value of “3s” will always be greater than the value of “12 + s”, which also implies that 3s > p.
It is possible to determine with certainty whether the total revenue from songs was greater than the total revenue from podcasts. Hence, Statement (1) and Statement (2) combined are sufficient.
C is the correct answer choice.
General Discussion
MaxFabianKirchner
Joined: 02 Jun 2025
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Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
Posts: 65
02 Jul 2025, 08:24
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Let Ns and Np be the number of songs and podcasts, and As and Ap be their average revenues. We are given Ns = 3 * Np. The question is: Is (Ns * As) > (Np * Ap)? This simplifies to: Is 3 * As > Ap?
Statement (1) tells us Ap = As + 12. Substituting this into our question gives: Is 3 * As > As + 12? This simplifies to: Is As > 6? We don't know if As is greater than 6, so this is insufficient.
Statement (2) tells us the combined average revenue exceeded 20 cents. The formula for this is (3*As + Ap) / 4 > 20, which simplifies to 3*As + Ap > 80. This is insufficient on its own.
Combining both statements, we substitute the equation from (1) into the inequality from (2):
3*As + (As + 12) > 80
4*As + 12 > 80
4*As > 68
As > 17
Since we know for certain that As is greater than 17, we can definitively answer "Yes" to the question "Is As > 6?". The statements together are sufficient.
The correct answer is (C).
Statement (1) tells us Ap = As + 12. Substituting this into our question gives: Is 3 * As > As + 12? This simplifies to: Is As > 6? We don't know if As is greater than 6, so this is insufficient.
Statement (2) tells us the combined average revenue exceeded 20 cents. The formula for this is (3*As + Ap) / 4 > 20, which simplifies to 3*As + Ap > 80. This is insufficient on its own.
Combining both statements, we substitute the equation from (1) into the inequality from (2):
3*As + (As + 12) > 80
4*As + 12 > 80
4*As > 68
As > 17
Since we know for certain that As is greater than 17, we can definitively answer "Yes" to the question "Is As > 6?". The statements together are sufficient.
The correct answer is (C).
