Data Sufficiency

Two sisters, Caryn and Missy, are each given an allowance by their parents in exchange for helping with household tasks. Caryn receives twice the hourly allowance that Missy receives, but Missy receives three times her hourly allowance for any hours she spends helping with laundry on Sundays. If both girls worked a whole number of hours this week and received the same dollar amount of allowance, which of the following must be true?

1 Missy made more money on Sunday than did Caryn.
11 Caryn worked fewer hours Monday through Thursday than did Missy.
111 Missy worked at least one hour on Sunday.

I only
II only
III only
I and II only
I and III only

Can plz someone help me solve it..

let m's general allowance = x. then c's = 2x and m's allowance for laundry = 3x.
m's total = ax + 3xb and c's = 2xc
ax + 3xb = 2xc or a + 3b = 2c (where a is hours spent on simple tasks by m, b is hours spent by m on laundry and c is hours spent by c)
Assuming they worked same number of hours also. then c=a+b or a + 3b = 2a + 2b or a=b and c=2a
C) true. otherwise no one worked at all.
B) monday to thursday we can't predict. we just know for the whole week.
A) suppose missy did 1 hour on sunday and 1 hour on saturday. money on sunday= 3x.
Also caryn did both hours on Sunday. money on sunday = 4x
And if caryn did only 1 hour on sunday, money on sunday=2x.
We can't say.
IMO C

The IMO is C that is only answer choice 111 is correct,that missy worked atleat one hour on sunday.. Can someone through light as to why cant it be choice E

Two sisters, Caryn and Missy, are each given an allowance by their parents in exchange for helping with household tasks. Caryn receives twice the hourly allowance that Missy receives, but Missy receives three times her hourly allowance for any hours she spends helping with laundry on Sundays. If both girls worked a whole number of hours this week and received the same dollar amount of allowance, which of the following must be true?

1 Missy made more money on Sunday than did Caryn.
11 Caryn worked fewer hours Monday through Thursday than did Missy.
111 Missy worked at least one hour on Sunday.

a I only
b II only
c III only
d I and II only
e I and III only

Hi Again... The choices A C and E are all wrong.... The IMO is either B or D , can someone help me in this...

Only 111 looks good because it is given that the dollar amount of their allowances is same, so, Missy ought to have worked at least 1 hour on Sunday

For 1 and 11, we can come up with different numbers for the hours worked to arrive at a common dollar amount. No point in actually working it out to prove the statements incorrect