Machines X and V produced identical bottles at different GMAT data sufficiency

Question: 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?

Statement (1) Machine X produced 30 bottles per minute.
Statement (2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Answer: B

Solution and Explanation:

Approach Solution 1:
Let X flow at a rate of x bottles per hour, and Y flow at a rate of y bottles per hour.
Given: Job = 4x + 3y.
Now we have: tx = job/rate = job/x =?
(1) Machine X produced 30 bottles each minute, so 30 x 60 = 1800 bottles every hour, which is insufficient because we don't know how many bottles are in a lot (job).
(2) Machine X produced twice as many bottles in 4 hours as Machine Y did in 3 hours, therefore 4x=2*3y so, 3y=2x, which led to the following calculation:
4x+3y = 4x+2x = 6x = job.
--> tx = job/rate = job/x = 6x/x = 6 hours. Sufficient.
Correct option: B

Approach Solution 2:
Statement 1: How many bottles did machine X create in 4 hours, or 240 minutes, given that it produced 30 bottles per minute?
30* 240 = 7,200 bottles.
Although we know X's work rate, we don't know how many hours it will take X to fill the production lot because we don't know the exact dimensions of the lot.
This statement is therefore inadequate.
Let a represent the number of bottles that machine Y produces in three hours.
In comparison to Machine Y, Machine X produced twice as many bottles in 4 hours.
The number of bottles that machine X produced in 4 hours is 2a.
Thus, the total lot size is equal to a + 2a = 3a.
How long will it take X to generate 3 bottles if it produces 2 in 4 hours?
(3a * 4)/2a = 6 hours
Correct option: B

Approach Solution 3:
Prior to assessing the accuracy of each claim, I built up two simple equations for each machine using the prompt:
x∗4=n
where n is the amount of the job finished in four hours and x is the rate of Machine X.
y∗3=m
In order to maintain the fact that X and Y finish one work concurrently, n+m=1
where y is the rate of Machine Y and m is the quantity of the job accomplished in three hours (yet individually)
We won't go over this ground again because it is obvious that this is insufficient.
Here, n = 2m, or that Machine X accomplished 2/3 of the work and Machine Y completed 1/3 of the work, is evident. Since we have x * 4 = ⅔ we can calculate how long it would take Machine X to complete 1 (one complete unit) of work by substituting 2/3 for n and 1/3 for m in the equations above. Sufficient
Correct option: B

“Machines X and V produced identical bottles at different GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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