A courier company assigned each of its drivers to exactly one of three

Question

A courier company assigned each of its drivers to exactly one of three delivery zones: Harbor, Central, or Ridge. If the numbers of drivers in Harbor, Central, and Ridge were in the ratio 2:3:5, respectively, was the average number of packages delivered per driver across all three zones combined greater than 30?

(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.
(2) The total number of packages delivered by all the drivers was less than 300.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A courier company assigned each of its drivers to exactly one of three delivery zones: Harbor, Central, or Ridge. If the numbers of drivers in Harbor, Central, and Ridge were in the ratio 2:3:5, respectively, was the average number of packages delivered per driver across all three zones combined greater than 30?

(1) The average numbers of packages delivered per driver in Harbor, Central, and Ridge were 38, 27, and 25, respectively.

Let the numbers of drivers in Harbor, Central, and Ridge be 2k, 3k, and 5k. Then the overall average number of packages delivered per driver is:

(2k × 38 + 3k × 27 + 5k × 25)/(2k + 3k + 5k) =

= (76k + 81k + 125k)/(10k) =

= 28.2

Since 28.2 is not greater than 30, the answer to the question is no.

Sufficient.

(2) The total number of packages delivered by all the drivers was less than 300.

Again let the numbers of drivers be 2k, 3k, and 5k. Then the total number of drivers is 10k.

The total number of packages delivered is less than 300, so the overall average number of packages delivered per driver is less than 300/(10k).

Since k is a positive integer, 10k is at least 10. Therefore, the overall average must be less than 300/10 = 30.

So the answer to the question is definitely no.

Sufficient.

Answer: D.

Adit_ · Answer

2:3:5 ratio given.

Statement 1:
No.of packages = 38, 27 and 25.
Total packages in each area:
76x, 81x, 125x.

Avg = Total / 10x = 282x/10x = 28.2<30
Answer is NO.
SUFFICIENT.

Statement 2:
We are given total packages = 300.
300/10x is the average at critical point.
Numerator is lesser than 300 and denominator can always be more.
Even if x = 1 and numerator was 300, we get 30 only.
Not greater than 30.
Answer is NO.
SUFFICIENT.

Answer:  Option D

DropletMaverick · Answer

I think  Answer A  as the mentioned in question can we tell the average combined number of packahges is 30.
now with statment one we can definitely tell that the number is 30 exact but with statment 2 its hard to do so because the statment say the number of parcel is less than 300 and if we look at the ratio the 2:3:5 now we domt know the eaxct number of packages and that number can be anything which can qualify this ratio hence the minimum number start from 10 and it can be greater than 90 but its not the surety hence i think 
 Answer A

Adit_ · Answer

You are right about the values being anything for statement 2.
But if you notice carefully, the question stem asks if the average can be  greater  than 30.
We need not know the exact value here. We just need to prove that value is not greater than 30.
The equation is <300/10x as rightly pointed by you too. But since numerator is less than 300, 299/10 lets say is 29.9 less than 30!
Any value you thus take the average will be less than 30. Thus sufficient!

Hope it helps!

BongBideshini · Answer

Let the number of drivers in Harbor, Central, and Ridge be 2k, 3k, and 5k, respectively. Total drivers = 10k.

Overall average = Total packages / 10k

Statement (1):

Total packages = 2k(38) + 3k(27) + 5k(25)
= 76k + 81k + 125k
= 282k
Overall average = 282k / 10k =  28.2 
The answer is No
 Statement (1) is sufficient. 
 
Statement (2):

Total packages < 300
Average  <\frac{300}{10k} 
Since k>=1, a minimum of 10 drivers
The average must be  < 30 
 Sufficient.

Answer: D

A courier company assigned each of its drivers to exactly one of three

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GMAT Data Sufficiency (DS) Questions

A courier company assigned each of its drivers to exactly one of three

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