At a distribution center, stations A and B scan packages at their

Question

At a distribution center, stations A and B scan packages at their respective constant rates. How many more hours does it take station B, working alone, to scan a new shipment of packages than it takes station A, working alone?

(1) The ratio of the time it takes station B, working alone, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 1.

(2) The ratio of the time it takes stations A and B, working together, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 5.

M47-212

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a distribution center, stations A and B scan packages at their respective constant rates. How many more hours does it take station B, working alone, to scan a new shipment of packages than it takes station A, working alone?

Let a be the number of hours station A takes to scan the shipment alone, and let b be the number of hours station B takes to scan the shipment alone. The question asks for b - a.

(1) The ratio of the time it takes station B, working alone, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 1.

So b = 4a. This gives only the relationship between the two times, not the actual number of hours. Insufficient.

(2) The ratio of the time it takes stations A and B, working together, to scan the shipment to the time it takes station A, working alone, to scan the shipment is 4 to 5.

Station A’s rate is 1/a, and station B’s rate is 1/b. Thus, their combined rate is:

1/a + 1/b = (a + b)/(ab)

So the time they take together is:

ab/(a + b)

Statement (2) tells us that the ratio of the together time to station A’s alone time is 4 to 5:

/a = 4/5

b/(a + b) = 4/5

5b = 4a + 4b

b = 4a

This gives the same relationship as statement (1), but not the actual value of a or b. Insufficient.

(1)+(2) Each statement gives the same relationship: b = 4a. Thus, even after combining the statements, we still know only the relationship between the two times, not the actual value of either time. Therefore, b - a cannot be determined. Not sufficient.

Answer: E.

vasu1104 · Answer

work = p
rate of A = x
time for A = p/x
rate of B = y
time for B = p/y

p/y = t + p/x
t = p/y - p/x
t = p(1/y - 1/x)

need p, x, y to find t.

S-1
Tb / Ta = 4/1
(p/y) / ((p/x) = 4/1

we get, x/y = 4/1
or x= 4y.

upon using this into our original eqn, we get,
p (4y - y/ 4y^2) = t
p(3y/4y^2 ) =t

still 2 unknowns. not sufficient.

S-2
Ta + Tb / Ta = 4/5
(p/x+y) / (p/x) = 4/5
 
x/x+y = 4/5

we get, x= 4y

this is same as first statement.
not sufficient.

S- 1&2.
in both statement we get x= 4y.
no value of p and y. 
not sufficient.

choice E

SS990 · Answer

Given: A and B are working alone

to find : Tb-Ta

(1) T  b:Ta=4:1 This is not sufficient to get the absolute time difference between B and A 
 
(2) T(a&b): Ta = 4:5 i.e R (a&b): Ra=5:4 i.e Rb: Ra=1:4 ..which is same as above statement and hence not sufficient.

So the answer is E

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