For each day at sea a sailor is paid a fixed sum. For each day ahead

Question

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For each day at sea a sailor is paid a fixed sum. For each day ahead of the scheduled arrival time, he gets twice the regular daily earnings. If the total time at sea was scheduled for 20 days and a sailor earned a total of 3,850 dollars for the entire trip, how many days ahead of schedule did the ship arrive?

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

madgmat2019 · Answer

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars....I.e for that one he got 4200-3850=350 which is twice of daily earnings...
So just daily earning is 175...

So 175*20+175*x=3850
 x=1

So sufficient

(2) The sailor's regular daily earnings were $175.....Clearly sufficient as above...

So OA:D

Archit3110 · Answer

given
each day = x
scheduled days = 20
a be days before schedule
x+(20-a)*2x=3850
#1

If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

x+(20-19)*2x=4200
solve for x sufficient
#2
The sailor's regular daily earnings were $175.
x+(20-a)*2x=3850
substitue for x as 175
sufficeint
IMO D

For each day at sea a sailor is paid a fixed sum. For each day ahead of the scheduled arrival time, he gets twice the regular daily earnings. If the total time at sea was scheduled for 20 days and a sailor earned a total of 3,850 dollars for the entire trip, how many days ahead of schedule did the ship arrive?

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

exc4libur · Answer

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.   sufic.

4200-3850=350=1 day ahead of schedule=2x
(20-a)x+a2x=3850
(20-a)175+a350=3850
20*175+175a=3850
a=(3850-3500)/175=2

(2) The sailor's regular daily earnings were $175.   sufic.

(20-a)x+a2x=3850
(20-a)175+a350=3850
20*175+175a=3850
a=(3850-3500)/175=2

Answer (D)

unraveled · Answer

For each day at sea a sailor is paid a fixed sum. For each day ahead of the scheduled arrival time, he gets twice the regular daily earnings. If the total time at sea was scheduled for 20 days and a sailor earned a total of 3,850 dollars for the entire trip, how many days ahead of schedule did the ship arrive?

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

Let 'n' be the number of days by which ship arrived early and earning per day is 'e'. 
So, n*2e + (20-n)*e = 3850

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

Here 4200 - 3850 = 350 is the amount the sailor earns in a single day for arriving a day earlier i.e.
n * 2e = 350 where n = 1
e = 175

Thus, n * 2 * 175 + (20-n) * 175 = 3850. Here we can solve for 'n', n = 2

SUFFICIENT.

(2) The sailor's regular daily earnings were $175.

From statement 1 above we can see e = 175. Thus, same equation n * 2 * 175 + (20-n) * 175 = 3850 giving n = 2.

SUFFICIENT.

Answer D.

eakabuah · Answer

We know that the sailor is paid an amount of money, x, for each day. For each day ahead of scheduled arrival time, he gets 2x. Total scheduled time at sea is 20 days, and a sailor earned a total of $3,850 for the entire trip, we are to determine the number of days that the sailor arrived ahead of schedule.

Statement 1: If the ship had arrived a day ahead of schedule, the sailor would have earned $4200.
4200=19x+2x hence x=$200
but if the daily earning of the sailor is $200, then even if he arrived on schedule, meaning he used exactly 20 days, his total earnings would be equal to $4,000, which is more than the total amount of $3,850. Statement 1 suggests that the sailor is penalized for arriving late, and that is the only way his earnings could be less than $4,000.
The number of days, y, he arrived late, can be determined as follows:
3850=(20-y)*200+2*200y
3850=4000-200y+400y
150=-200y
y=-0.75, implying the sailor arrived approximately 1 day late. Statement 1 sufficient.

Statement 2: The sailor's regular daily earnings were $175.
Statement 2 is sufficient. This is because we are able to determine the number of days, y, he arrived ahead of schedule as follows:
3850=(20-y)175 + 2*175*y 
3850=3500-175y + 350y
350=175y
y=2.
Hence the sailor arrives 2 days ahead of schedule.

The answer is option D.

lacktutor · Answer

Let “x” be the regular daily earnings 
Let “a” be days ahead of schedule the ship arrived

—> (20– a)*x+ 2x*a= 3850
20x —ax + 2ax =3850
20x + ax=3850
—> a=???

( Statement1): 
19x + 2x = 4200
21x = 4200
x= 200
—> 20x + ax= 3850
20*200+ 200*a= 3850
200a=— 150
a= —3/4= —0.75
Looks like the ship arrived 0.75 days later than expected. 
(Anyway, “a” can be found.)
—> sufficient

(Statement2): x= $175
20x + ax= 3850
x( 20+a)= 3850
20+a= 3850:175= 22
a= 2 days ahead of schedule

Sufficient

The answer is D.

Posted from my mobile device

minustark · Answer

For each day at sea a sailor is paid a fixed sum. For each day ahead of the scheduled arrival time, he gets twice the regular daily earnings. If the total time at sea was scheduled for 20 days and a sailor earned a total of 3,850 dollars for the entire trip, how many days ahead of schedule did the ship arrive?

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175
Lets say, each day's earnings is x. Earnings for each day ahead of the scheduled arrival time is 2x. The ship arrives y days ahead.

From Statement 1, we get, 2x = 4,200 - 3,850 = 350. So, x = 175.  SUFFICIENT  to find out the days ahead of schedule the ship arrive

From statement 2, we can get x = 175. So, 20 days earnings = 3500. It is also  SUFFICIENT  to answer the question.

D is the correct answer.

joohwangie · Answer

For each day at sea a sailor is paid a fixed sum. For each day ahead of the scheduled arrival time, he gets twice the regular daily earnings. If the total time at sea was scheduled for 20 days and a sailor earned a total of 3,850 dollars for the entire trip, how many days ahead of schedule did the ship arrive?

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

(2) The sailor's regular daily earnings were $175.

let's x be the fixed amount a sailor earn per day.
let's y be the actual day the sailors spend.

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.
4200=19x+2x(20-19)
21x=4200
x=200
3850=y(200)+400(20-y)
y=20.75

sufficient

(2) The sailor's regular daily earnings were $175.
x=175
3850=y(175)+350(20-y)
y=18

sufficient

therefore, D

stne · Answer

(1) If the ship had arrived one day ahead of the schedule, the sailor would have earned 4,200 dollars.

If the sailor arrived one day ahead of schedule that means he was at sea for 19 days , for those 19 days he earned a fixed sum and for the single day that he arrived early he earned double the fixed sum
So let fixed sum be x then:
19x + 2x=4200
21x=4200
x=200, why is this not coming to 175 ? Maybe I am missing something, can somebody please clarify ? 
 madgmat2019   exc4libur   lnm87   lacktutor   joohwangie 
Or are the statements not consistent?

lacktutor · Answer

I think, you’re right. Not both statements give the same value all the time. Especially, both of them are sufficient. 
—> once I saw this kind of question in overlapping data sufficiency question.

Posted from my mobile device

stne · Answer

Hi  lacktutor ,

Thanks for responding.
Actually both the statements have to always be consistent, the ones you saw couldn't possibly be official questions, could they? Let me know, till now all of us are of the opinion that both the statements have to always be consistent. Please share link if possible. Thank you.

unraveled · Answer

stne  You have taken a reference of 20 days that's why you are getting different values.

Instead, from question we can't say anything about either 3850 or 4200 being earnings of 20 days +/- days of arrival/delay.
All we can infer from statement 1 is that for one day arriving early the sailor gets 4200-3850 = 350 more which means that 
2 * earnings per day = 350
i.e. earnings per day = 175

Hope this makes sense.

Funny, how we can still arrive at answer D even if we take 20 days reference point only to get amused with different 'earning per day' values for each statement.

stne · Answer

I think you may have a point, the word " Schedule " in the main stem and " schedule" in statement 1 may be causing the confusion.
Statement (1) says one day ahead of schedule and the main stem says 20 days is the schedule no naturally one can assume he arrived in 19 days.  lnm87  let me know what you think. Thanks.

unraveled · Answer

The thing is 3850 is actually earned by sailor, but in how many days - we don't know. In statement 1, 4200 is the hypothetical earning for arriving a day earlier compared to 3850. Also, on the hindsight, if questions asks to find the number of days sailor arrived early, it can't be possible to that the statements leads to find out delays instead. Still, if it troubles, try approaching the question with statement 2 first(suggesting only for this question though at times you can do that with questions). You will surely sail

across question trouble-free.

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For each day at sea a sailor is paid a fixed sum. For each day ahead

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For each day at sea a sailor is paid a fixed sum. For each day ahead

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