Machines J, K, and L each operate at a constant rate. J and K, working

Question

Machines  J ,  K , and  L  each operate at a constant rate.  J  and  K , working together, can complete a given order in 6 hours. How long will it take  J ,  K , and  L , working together, to complete the order?

(1) Machine  K  operating alone takes 15 hours to complete the order.
(2) Machines  J  and  L , working together, take half as long as  J  and  K  do.

Bunuel · Accepted Answer

GMATNinja Video Solution:

https://www.youtube.com/watch?v=erk_2Wng0fE

GMATcracker101 · Answer

So we have -

Machine J - a work per hour 
Machine K - b work per hour 
Machine L - c work per hour

As per the Q - Total work = 6a + 6b

S1 - 15b = 6a + 6b --> 2a = 3b

S2 - 3a + 3b = 6a + 6b --> using the info in S1 we get - 3c = 7a

take a = 3k

we get b = 2k and c = 7k

So, since T.W = 6a + 6b = 5k * 6

Time taken by Machine J, K, L all working together = 5k * 6/12K = 2.5 h

Usernamevisible · Answer

Given:

J + K = 1/6

Need: J + K + L

---

(1)

K = 1/15

J = 1/6 − 1/15 = 1/10

L unknown.

Not sufficient.

---

(2)

J + L take half as long as J + K.

J + K = 6 hours ⇒ J + L = 3 hours

So:

J + L = 1/3

Knowing J + K = 1/6 and J + L = 1/3 does not determine L.

Not sufficient.

---

(1) + (2)

J = 1/10

L = 1/3 − 1/10 = 7/30

J + K + L
= 1/10 + 1/15 + 7/30
= 2/5

Time = 1 ÷ (2/5) = 5/2 = 2.5 hours

Sufficient.

Answer: C.

rockstar09rulez · Answer

Let j, k, l take j, k, and h hours respectively. Work = w

Working together: W = R * T
w = (w/6 + 2/l) * time
So, to get time we need the value of l

Stmt 1: k takes 15 hours, but this tells us nothing about l. This statement can help us get to j, but we won't be able to find l. INSUFF
Stmt 2: will give us an equation in j and l. Again insuff, since we don't have the value of j to find l. We only have combined rate of j and k available.

1 and 2 together - From statement 1, we get j and put in the result of Stmt 2 to get l. SUFF. Hence (C) is the answer

nammolestias · Answer

pre thinking =j+k=1/6

statement 1)k=1/15
solving j+(1/15)=1/6
j=1/10
we also want to find time taken by l to find time taken by j+k+l
therefore insufficient

statement 2)from here we get to know j+l=(j+k)/2 which is insufficient

combining both statement we get the ans hence sufficient

vasu1104 · Answer

rate for j = x
rate for k = y
rate for l = p

when j and k work together, time taken is 6 hr.
so a = (x+y)6

find = time taken when all three work together.
say work = a

time for all three= work/ rate = a / x+y+p
we can put value of a in here.

6(x+y) / x+y+p. basically we need to find this equation.

S-1
K takes 15 hrs.
a = 15y
but we cant use this into eqn.
not sufficient.

S-2
time for J and L together = a/ x+p
time for j and K together = a/x+y

a/x+p = (1/2) (a/x+y)

but not enough to get us to ans.
not sufficient.

S-1&2

we know a= 15y.
and we also know time taken when j and k work together.
its a = 6(x+y)
use a value in here and find one variable in terms of other.

15y = 6x+6y
6x= 9y
x= 3y/2

now from S-2 we can find value of p.

a/x+p = (1/2) (a/x+y)

x+p = 2(x+y)
p= x +2y

now in our actual eqn, we can put value of p and also value of x in terms of y.

upon doing it, we can easily find the ans.

Choice C

Machines J, K, and L each operate at a constant rate. J and K, working

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GMAT Data Sufficiency (DS) Questions

Machines J, K, and L each operate at a constant rate. J and K, working

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