3 employers rake the beach each day. working together,

Question

3 employers rake the beach each day. working together, employees A and B can rake the beach in 3 hours, whereas A and C can rake the beach in 2.5 h. working together, can A,B, and C rake the beach in less than 2 h?

1. B rakes faster than A
2. working alone, C can rake the beach in less than 5 h

walker · Answer

D

Let a,b,c - rates of A,B, and C.

3*a+3*b=1 ==> a+b=1/3
2.5*a+2.5*c=1 ==> a+c=2/5

t(a+b+c)=1 ==> a+b+c=1/t and t should be less then 2 ==> a+b+c>1/2

1. a+b=1/3 and b>a mean that a<1/6
a+b+c = a+b+a+c-a = 1/3+2/5-a > 1/3+2/5-1/6 = (10+12-5)/30 = 17/30 > 1/2. suff.

2. c>1/5.
a+b+c = 1/3+c > 1/3+1/5 = (3+5)/15 = 8/15 > 1/2. suff.

marcodonzelli · Answer

walker...can the formula ABC/AB+AC+BC be applied in this case?

walker · Answer

Sorry, I cannot understand logic of the formula...

marcodonzelli · Answer

this is the formula to calculate the total time spent by 3 people. i.e. if A spends 3 hours, B 1 hour, C 2 hours we have

(AB)/A+B=(3*1)/4....TOTAL TIME A AND B TOGETHER
(BC)/B+C=(1*2)/3...TOTAL BC
 and so.....

walker · Answer

I see. 

a=1/A, b=1/B, c=1/C

t=1/(a+b+c)=1/(1/A+1/B+1/C)=ABC/(BC+AC+AB)

marcodonzelli · Answer

exactly, you're great at math! although I applied this formula in this case I wasn't able to solve the problem...

walker · Answer

1/(1/A+1/B+1/C) is more appropriate rather then ABC/(BC+AC+AB)

the problem says something about C, A, B but does not about BC, AC etc.

vscid · Answer

that was a good one marc.

ashkrs · Answer

I am getting C . I know I am wrong . But please correct me.

A B C are hours which they can do raking alone.

1/A + 1/B = 1/3
1/A + 1/C = 1/2.5 = 2/5

Stmnt 1. B is faster means 1/A < 1/6 
Adding both the questions we have
1/A + 1/A + 1/B + 1/C = 1/3 + 2/5
 1/A + 1/B + 1/C = 1/3 + 2/5 - 1/6 = ( 10 + 12 - 5 ) / 30 = 17/30
Work which can be done by all three 30/17 < 2 hours . So not suff .

Stmnt 2 - suff.

walker · Answer

you are right. "(10+12-5)/30 = 17/30" instead of "(15+6-5)/30 = 16/30" 1/t=1/A + 1/B + 1/C > 1/3 + 2/5 - 1/6 = ( 10 + 12 - 5 ) / 30 = 17/30 1/t>17/30 ==> t<30/17<2 working together, can A,B, and C rake the beach in less than 2 h? Yes. t<30/17

marcodonzelli · Answer

let's also reason this way:

A and B together is 3
A and C together is 2.5

1. B rakes faster than A. if A and B were equal, then they would be 6 and 6. thus, B<6 and A >6. at the same time if A and C were equal they would be 5 (theri sum is 10). if A<6, C<4. let's say A and B together x. we know that XC/X+C is the total amount of time needed by the three. substitute any value <4 for C and 3 for x. we obtain only values <2. suff

2. C<5. it means A>5 and B<7. let's say A and C together y: yB/y+B is the formula for the three. substitute . we obtain only values <2. suff.

neeraj.kaushal · Answer

Answer D 
I would do it this way
 
1/3 = 1/ta + 1/tb ( ta and tb are times of A and B)
1/2.5 = 1/ta + 1/tc

we need to get if tabc < 2hr

statement 1 : tb<ta assume any value for tb and find ta from above equation , putting that value in second equation we get tc .we can find tabc from
 1/tabc = 1/ta + 1/tb +1/tc 
sufficient

similarly second is sufficient

GMATBLACKBELT · Answer

1/A+1/B=1/3

1/A+1/C=2/3

The best way to work these problems is to take the "worst scenario or most extreme scenario" case.
 
1: B is faster than A. This means that B dsnt equal A. Lets make B equal to A just to get a bearing. (Wel make them equal b/c we can say B is just slightly bigger than A, but the difference is so small its negligable, hence our extreme scenario).

So 1/6+1/6=1/3 --->

Lets find C:
Lets say A is 1/6 ---> 2/3 - 1/6: So C is 1/2. This is our worst case scenario: we can see that C will be around 1/2 or larger. Thus we can definitively say that the job will be done in less than 2 hours.

2: Lets say that C is 1/5.

thus A is 7/15. Again we can say that the job will be done in less than 2 hours.

D

3 employers rake the beach each day. working together,

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