A factory recently bought two machines, A and B, each operating at its

Question

A factory recently bought two machines, A and B, each operating at its own constant rate. Working alone, Machine A takes n minutes to complete a Junior order. Working alone, Machine B takes m minutes to complete a Jumbo order, which is exactly 5 times the size of a Junior order. Is n greater than m?

(1) Working alone on a Junior order, Machine B takes half as many minutes as Machine A.
(2) Machine B’s work rate is more than 3/2 times Machine A’s work rate.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A factory recently bought two machines, A and B, each operating at its own constant rate. Working alone, Machine A takes n minutes to complete a Junior order. Working alone, Machine B takes m minutes to complete a Jumbo order, which is exactly 5 times the size of a Junior order. Is n greater than m?

Treat 1 Junior order as 1 unit of work. Then 1 Jumbo order is 5 units of work.

Machine A completes 1 unit in n minutes, so its rate is 1/n units per minute.
Machine B completes 5 units in m minutes, so its rate is 5/m units per minute.

We need to determine whether n > m, or which is the same whether n/m > 1.

(1) Working alone on a Junior order, Machine B takes half as many minutes as Machine A.

If Machine B takes half as many minutes as Machine A to complete a Junior order, then Machine B completes 1 unit in n/2 minutes, so its rate is 2/n units per minute. Since Machine B’s rate is also 5/m, we have 5/m = 2/n, so n/m = 2/5, giving a No answer to the question. Sufficient.

(2) Machine B’s work rate is more than 3/2 times Machine A’s work rate.

This implies 5/m > 3/2 * 1/n, so n/m > 3/10. Thus, n/m may or may not be greater than 1. Not sufficient.

Answer: A.

Adit_ · Answer

Framing the equation first:
n =x
m =5x

Statement 1:
Machine B only takes half the time of A doing Junior order
Meaning:
To complex x B take n/2 time, so to complete 5x it will take 5n/2 time
or
m=5n/2
m=2.5n 
m>n
SUFFICIENT.

Statement 2:
To complete x items, machine A takes n mins.
To complete 5x items if will take 5n mins.

Given: Rate(b)>1.5Rate(a)
Take 1.5 as the critical point and check:
5n = 1.5m
n = 1.5/5m
Now mind you that this 1.5 is the lowest value and it will increase.
Right now n=0.xm
If you increase the numerator it could be n=1.xm
So we dont know which is greater.
INSUFFICIENT.

Answer:  Option A

HK12! · Answer

To know, whether: n>m ? Statement (1), B takes half the time of A for a Junior order. Time per Junior: B = , A = n Given: = 2m=5n m=2.5n So: m>n ⇒ n . 10n>3m This does not guarantee whether n>m or n

gmatshay · Answer

We know the rates here, they're given quite cleanly in the stem
A works at  \frac{1}{n} , B works at  \frac{5}{n}

1) says A takes half the time B does for a junior order, so  \frac{n}{2}  mins
this tells us that the rate would be  \frac{2}{n} = \frac{5}{m} 
This is a clear relationship and we can conclude which is greater
 SUFFICIENT

2) just says  \frac{5}{m} > \frac{3}{2n} 
or  \frac{n}{m} > \frac{3}{10}  (we can move things around worry free since everything here is positive)
Now,  \frac{n}{m}  could be  \frac{4}{10} , or it could be  \frac{14}{10}  (for example). Both tell a very different story
 INSUFFICIENT

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