Machines \(X\) and \(Y\) produced identical bottles at different constant rates. Machine \(X,\) operating alone for \(4\) hours, filled part of a production lot; then Machine \(Y,\) operating alone for \(3\) hours, filled the rest of this lot. How many hours would it have taken Machine \(X\) operating alone to fill the entire production lot?
(1) Machine \(X\) produced \(30\) bottles per minute.
(2) Machine \(X\) produced twice as many bottles in \(4\) hours as Machine \(Y\) produced in \(3\) hours.
Answer: B
Source: GMAT Paper Tests
Machines \(X\) and \(Y\) produced identical bottles at different constant rates. Machine \(X,\) operating alone for
This topic has expert replies

 Legendary Member
 Posts: 1622
 Joined: 01 Mar 2018
 Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
 [email protected]
 GMAT Instructor
 Posts: 16140
 Joined: 08 Dec 2008
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1268 members
 GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Given: Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot.Gmat_mission wrote: ↑Sun Nov 28, 2021 6:45 amMachines \(X\) and \(Y\) produced identical bottles at different constant rates. Machine \(X,\) operating alone for \(4\) hours, filled part of a production lot; then Machine \(Y,\) operating alone for \(3\) hours, filled the rest of this lot. How many hours would it have taken Machine \(X\) operating alone to fill the entire production lot?
(1) Machine \(X\) produced \(30\) bottles per minute.
(2) Machine \(X\) produced twice as many bottles in \(4\) hours as Machine \(Y\) produced in \(3\) hours.
Answer: B
Source: GMAT Paper Tests
Let x = Machine X's RATE (in terms of the fraction of the job completed PER HOUR)
Let y = Machine Y's RATE (in terms of the fraction of the job completed PER HOUR)
So, in 4 hours, the portion of the job completed by Machine X = 4x
Likewise, in 3 hours, the portion of the job completed by Machine Y = 3y
Since the entire job is completed after both machines perform their individual tasks, we can write: 4x + 3y = 1 (1 represents the entire job completed)
Target question: How many hours would it have taken Machine X operating alone to fill the entire production lot?
Statement 1: Machine X produced 30 bottles per minute.
Since we're given no information about Machine Y, it is impossible to answer the target question with certainty
Statement 1 is NOT SUFFICIENT
Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
In 4 hours, the portion of the job completed by Machine X = 4x
In 3 hours, the portion of the job completed by Machine Y = 3y
From statement 2, we can write: 4x = (2)(3y)
Simplified to get: 4x = 6y
We now have the following system of equations:
4x + 3y = 1
4x = 6y
Since we COULD solve this system of equations for x and for y, we COULD determine Machine X's RATE, which means we COULD determine how many hours it would have taken machine X to fill the entire production lot on its own.
Of course, we would never waste valuable time on test day performing such tedious calculations. We need only determine that we COULD answer the target question.
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT
Answer: B
Cheers,
Brent