Before the start of the fall service cycle, the city transit authority

Question

Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?

(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.
 (2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Before the start of the fall service cycle, the city transit authority revised Route G by increasing service frequency and adding a stop near a busy office district. Based on those changes, the authority expected the average (arithmetic mean) number of riders on Route G each weekday to increase by 20 percent. Did the average (arithmetic mean) number of riders on Route G each weekday actually increase by more than 25 percent?

Let r be the original average number of riders on Route G each weekday. Then the expected new average was 1.2r.

We need to know whether the actual new average was greater than 1.25r.

(1) The actual average (arithmetic mean) number of riders on Route G each weekday was 500 higher than expected.

So the actual average was 1.2r + 500

We need to know whether 1.2r + 500 > 1.25r:

500 > 0.05r

r < 10,000

Since r is not determined, the answer cannot be determined. Not sufficient.

(2) The actual average (arithmetic mean) number of riders on Route G each weekday was less than 12,600.

This gives only an upper bound on the actual average. By itself, it does not tell us whether the increase was more than 25 percent. Not sufficient.

(1) + (2) From statement (1), the actual average was 1.2r + 500. Using statement (2):

1.2r + 500 < 12,600

1.2r < 12,100

r < 12,100/1.2

Since 12,100/1.2 > 10,000, from r < 12,100/1.2, r may be greater than 10,000 or less than 10,000. Not sufficient.

Answer: E.

BongBideshini · Answer

Let the original average = x Expected after increase = 1.2x Did actual > 1.25x ? (1) Actual = expected + 500 = 1.2x + 500 Is 1.2x + 500 > 1.25x ? → 500 > 0.05x → x < 10000 We don’t know x , so sometimes yes, sometimes no → Not sufficient (2) Actual < 12600 We need to compare actual with 1.25x, but we don’t know x → Not sufficient (1) + (2) From (1): Actual = 1.2x + 500 Plug into (2): 1.2x + 500 < 12600 1.2x < 12100 x < 10083.33 Now check condition again: Need x < 10000 But from combined info: x < 10083.33 This still allows: x < 10000, YES 10000 ≤ x < 10083, NO Not sufficient Final Answer: E

thisisakr · Answer

Let B = average weekday riders before the fall cycle.
Expected average after changes = 1.20 × B.
The question asks: was the actual average > 1.25 × B
Let A = actual average —— A > 1.25B?

Statement 1– Actual average was 500 higher than expected
A = 1.20B + 500.
The question becomes: is 1.20B + 500 > 1.25B, which simplifies to 500 > 0.05B, meaning B < 10,000.
If B = 9,000 then A = 11,300 and 1.25B = 11,250, so A > 1.25B. Answer is YES.
If B = 11,000 then A = 13,700 and 1.25B = 13,750, so A < 1.25B. Answer is NO.
Since we do not know B, we cannot determine the answer ———- INSUFFICIENT.

Statement 2—— Actual average was less than 12,600
This gives us a ceiling on A but tells us nothing about B. Without knowing B we cannot determine whether A exceeds 1.25B.——— INSUFFICIENT.

Combining Both Statements
From Statement (1): A = 1.20B + 500.
From Statement (2): A < 12,600, so 1.20B + 500 < 12,600, giving 1.20B < 12,100, meaning B < 10,083.
The question asks if A > 1.25B, i.e., if 1.20B + 500 > 1.25B, i.e., if B < 10,000.
We know B < 10,083 but B could be, say, 10,050 (which is less than 10,083 but greater than 10,000), giving answer NO. Or B could be 9,000, giving answer YES.
We still cannot determine whether B is below or above 10,000 with certainty. ———- INSUFFICIENT.

E

Adit_ · Answer

IMO E.

Statement 1:
500 higher than expected, forming equation:
500=0.05x   
We get x=10000
We dont know the day to day actual average. INSUFFICIENT.

Statement 2:
We have less than 12600 now but we dont know anything about the percent increases.
INSUFFICIENT.

Combining the two:
If it is less than 0.05 we can have >10000 and <12600 so we dont know if it is more or less than 25%.
INSUFFICIENT.

Answer:  Option E

Before the start of the fall service cycle, the city transit authority

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