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ravitejapandiri
Machine X rate = \(\frac{1}{X}\)
Machine Y rate = \(\frac{1}{Y}\)
Combined rate = \(\frac{X+Y}{XY}\)
Combined time taken = \(\frac{XY }{ X+Y}\)
(1) Tells us that \(\frac{XY }{ X+Y} = \frac{2X}{3}\)
This tells us \(2X = Y\); INSUFFICIENT.
(2) This statement tells us that \(2X = Y\); INSUFFICIENT.
(1&2) Each statement tells us the same information; INSUFFICIENT.
Answer is E.
Similar Question: https://gmatclub.com/forum/machines-y-a ... 48321.html
Hi Bunuel,
Thank you for the detailed explanation. I got the y=2x for 1) and 2) , so I thought those both are sufficient and chose D(or may be I chose C which is definitely wrong). I should have tried to apply y=2x in xy/(x+y) = x*(2/3), then I would have known it is not sufficient and must have chosen E. But thank you for the explanations, now I know why my answer is wrong and why E is the right answer.
Thank you for the detailed explanation. I got the y=2x for 1) and 2) , so I thought those both are sufficient and chose D(or may be I chose C which is definitely wrong). I should have tried to apply y=2x in xy/(x+y) = x*(2/3), then I would have known it is not sufficient and must have chosen E. But thank you for the explanations, now I know why my answer is wrong and why E is the right answer.
avigutman
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Joined: 17 Jul 2019
Last visit: 27 Jun 2026
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Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
Video solution from Quant Reasoning starts at 23:15
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Bunuel
I know this is a silly question but I want to ask:
The general formula is,
\(\frac{1}{x} + \frac{1}{y} = \frac{1}{x+y}\)
where,
machine X takes \(x\) hours -> rate of X = \(\frac{1}{x}\)
machine Y takes \(y\) hours -> rate of Y = \(\frac{1}{y}\)
machine X and Y together take \(x+y\) hours -> rate of X and Y = \(\frac{1}{x+y}\)
(1) says that
\(x+y = \frac{2x}{3} \)
No?
I know this is a silly question but I want to ask:
The general formula is,
\(\frac{1}{x} + \frac{1}{y} = \frac{1}{x+y}\)
where,
machine X takes \(x\) hours -> rate of X = \(\frac{1}{x}\)
machine Y takes \(y\) hours -> rate of Y = \(\frac{1}{y}\)
machine X and Y together take \(x+y\) hours -> rate of X and Y = \(\frac{1}{x+y}\)
(1) says that
\(x+y = \frac{2x}{3} \)
No?
custodio
No. If machine X takes x hours to do the job, and machine Y takes y hours to do the job, then when working together they should take less time then individually to do the job, no? So, how it can be x + y hours?
The rate of machine X is 1/x and the rate of machine Y is 1/y. The combined rate of the machines is 1/x + 1/y = (x + y)/(xy). Thus, the time they need when working together to do the job is xy/(x + y) (time is the reciprocal of rate).
Hope it's clear.
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Dear experts,suggest if following approach is correct or not ?
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Posts: 137
I believe the key here is that the question is referencing HOURS and the options just mention relation to TIME. no units. This time could be seconds, minutes, hours, etc. Without any given values one can't answer number of hours..
straightaway by looking at statements we can see that both the statements are only giving information regarding x and y in relative terms. there is no new value we can find out. so clearly E is the right answer choice
Posts: 477
We got:
y = 2x
So:
y - x = x
Meaning:
the difference equals X’s time
---
To get a numerical answer, we need one actual value.
Anything giving actual time/rate/order size is enough.
Examples:
X alone takes 5 hours
Y alone takes 10 hours
Together take 10/3 hours
X rate = 20 units/hour and order size = 100
---
The statements only give a ratio:
x : y = 1 : 2
Ratios preserve structure but not size.
Examples:
x = 3, y = 6 → difference = 3
x = 10, y = 20 → difference = 10
Different answers possible, so insufficient.
y = 2x
So:
y - x = x
Meaning:
the difference equals X’s time
---
To get a numerical answer, we need one actual value.
Anything giving actual time/rate/order size is enough.
Examples:
X alone takes 5 hours
Y alone takes 10 hours
Together take 10/3 hours
X rate = 20 units/hour and order size = 100
---
The statements only give a ratio:
x : y = 1 : 2
Ratios preserve structure but not size.
Examples:
x = 3, y = 6 → difference = 3
x = 10, y = 20 → difference = 10
Different answers possible, so insufficient.
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