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Difficulty:
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75% (01:46) correct
25%
(01:48)
wrong
based on 51
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If the average (arithmetic mean) energy per device needed to run 3 wall lamps and 1 floor lamp simultaneously for 30 minutes was 35 watts-hours, how much energy was consumed by the floor lamp for that time?
(1) The wall lamp that consumed the most energy consumed 20 watts-hours more than the one that consumed the least.
(2) The average energy consumption per device for the 3 wall lamps was 40 watts-hours.
(1) The wall lamp that consumed the most energy consumed 20 watts-hours more than the one that consumed the least.
(2) The average energy consumption per device for the 3 wall lamps was 40 watts-hours.
26 Feb 2026, 13:34
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Note that the energy consumption given to us in watts per hour. However, we are told that they ran for only 1/2 an hour. Keeping that in mind, let's solve it.
Let the 3 wall lamps be named as : W1, W2, W3
and, the floor lamp be named as : F
As per the prompt, (W1+W2+W3+F)/4=35
Therefore, (W1+W2+W3+F)=140
But, as stated earlier, it would have been this energy consumption if they had all ran for an hour
Since, they ran only half an hour, the result would get half :
(W1+W2+W3+F)=70
We are asked to find the value for F.
(1) The wall lamp that consumed the most energy consumed 20 watts-hours more than the one that consumed the least.
Let the consumption of energy by the wall lamps be in this order : W1<W2<W3
Therefore, as per the given : W3 = (W1 + 20)
Again, since the info given is in per hours and the wall lamp only ran half an hour, this equation would become : W3 = (W1+10)
Plugging this value in original equation we formed earlier, we would get : (2(W1)+10+W2+F)=70
From here, we can clearly see that there are 3 unknown variables, so finding a definite value of F would be impossible. Not sufficient
(2) The average energy consumption per device for the 3 wall lamps was 40 watts-hours.
As per the given: (W1+W2+W3)/3=40 OR (W1+W2+W3)=120
Again, since the info given is in per hours and the wall lamp only ran half an hour, this equation would become : (W1+W2+W3)=60
Now, we had formulated this equation earlier : (W1+W2+W3+F)=70
Plugging the latter into former would give us F=10. Sufficient
Option B
Let the 3 wall lamps be named as : W1, W2, W3
and, the floor lamp be named as : F
As per the prompt, (W1+W2+W3+F)/4=35
Therefore, (W1+W2+W3+F)=140
But, as stated earlier, it would have been this energy consumption if they had all ran for an hour
Since, they ran only half an hour, the result would get half :
(W1+W2+W3+F)=70
We are asked to find the value for F.
(1) The wall lamp that consumed the most energy consumed 20 watts-hours more than the one that consumed the least.
Let the consumption of energy by the wall lamps be in this order : W1<W2<W3
Therefore, as per the given : W3 = (W1 + 20)
Again, since the info given is in per hours and the wall lamp only ran half an hour, this equation would become : W3 = (W1+10)
Plugging this value in original equation we formed earlier, we would get : (2(W1)+10+W2+F)=70
From here, we can clearly see that there are 3 unknown variables, so finding a definite value of F would be impossible. Not sufficient
(2) The average energy consumption per device for the 3 wall lamps was 40 watts-hours.
As per the given: (W1+W2+W3)/3=40 OR (W1+W2+W3)=120
Again, since the info given is in per hours and the wall lamp only ran half an hour, this equation would become : (W1+W2+W3)=60
Now, we had formulated this equation earlier : (W1+W2+W3+F)=70
Plugging the latter into former would give us F=10. Sufficient
Option B
ExpertsGlobal5
01 Mar 2026, 09:30
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ExpertsGlobal5
Explanation:
Let W1, W2, and W3 be the energy needed to run 3 wall lamps.
Let F be the energy needed to run 1 floor lamp.
Since the average energy per device is 35 watt-hours: (W1 + W2 + W3 + F)/4 = 35 (Equation I)
We need to find whether the value of F can be determined.
Statement (1)
From Equation I:
(W1 + W2 + W3 + F) = 35 x 4
F = (35 x 4) – (W1 + W2 + W3)
Possibility 1: If W1 = 10, W2 = 20, and W3 = 30, then F = (35 x 4) – (60)
Possibility 2: If W1 = 20, W2 = 30, and W3 = 40, then F = (35 x 4) – (90)
It is NOT possible to determine the exact value of F. Hence, Statement (1) is insufficient.
Statement (2)
(W1 + W2 + W3)/3 = 40
(W1 + W2 + W3) = 120
The value of (W1 + W2 + W3) can be substituted in Equation I to determine the exact value of F. Hence, Statement (2) is sufficient.
B is the correct answer choice.
