GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2019, 17:37 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Machines X and Y can work at their respective constant rates

Author Message
TAGS:

### Hide Tags

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

2
23 00:00

Difficulty:   55% (hard)

Question Stats: 64% (01:49) correct 36% (01:38) wrong based on 358 sessions

### HideShow timer Statistics

Solve Time and Work Problems Efficiently using Efficiency Method! - Exercise Question #4

Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X?

(1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.
(2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.

Option choices:
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.

To read the article: Solve Time and Work Problems Efficiently using Efficiency Method!

_________________

Originally posted by EgmatQuantExpert on 23 May 2018, 04:16.
Last edited by EgmatQuantExpert on 13 Aug 2018, 06:00, edited 1 time in total.
Director  V
Joined: 12 Feb 2015
Posts: 966
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

5
1
1
Question Stem:-
Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X?
Rephrase:-
Machines X and Y can work at their respective constant rates of 1/x and 1/y respectively (where x and y indicate time taken to complete one job).

$$\frac{y}{x}-1$$ = ? i.e can we get the value of $$\frac{y}{x}$$

Kindly note:-
When both work together means they work at a rate of $$\frac{1}{x}$$+$$\frac{1}{y}$$ = $$\frac{x+y}{xy}$$
Time taken when both machines work together = $$\frac{xy}{x+y}$$

Lets evaluate both the statements:-
Statement (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.

Therefore from (1) $$\frac{xy}{x+y}$$ = $$\frac{2y}{3}$$
which implies $$\frac{x}{x+y}$$ = $$\frac{2}{3}$$
or$$\frac{y}{x} = \frac{1}{2}$$
Since we have got the value of $$\frac{y}{x}$$ Statement 1 is sufficient; Not lets check statement 2 [Cross B,C & E] Evaluate between A & D:-

Statement (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.

There is no mention about the rate of machine X hence statement (2) is insufficient. Hence the correct answer is option A.
_________________
________________
Manish "Only I can change my life. No one can do it for me"
##### General Discussion
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

Solution

Given:
• Machine X and Y work at their respective constant rates to manufacture a certain production unit

To find:
• When both machines are working alone, the time taken by machine Y is what percentage more/less than that of machine X

Approach and Working:
If we assume the time taken by machine X and Y individually to complete the work is $$t_1$$ and $$t_2$$ respectively, then
• Time $$t_2$$ is more than time $$t_1$$ by (as a percentage) = $$\frac{(t_2 – t_1)}{t_1} * 100$$
o This can be written as = ($$\frac{t_2}{t_1}$$ – 1) * 100
[Note that if $$t_2$$ is less than $$t_1$$, then the above expression will be equal to (1 – $$\frac{t_2}{t_1}$$) * 100
• Hence, if we can find the value of the ratio $$\frac{t_2}{t_1}$$, we can find out the required percentage

Analysing Statement 1
• As per the information given in statement 1, Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.
o The time taken by both of them together to complete the job = $$\frac{t_1t_2}{(t_1 + t_2)}$$
• Given that, $$\frac{t_1t_2}{(t_1 + t_2)}$$ = $$\frac{2}{3} t_2$$
o Simplifying, we can write $$\frac{t_2}{t_1}$$ = $$\frac{2}{1}$$
Hence, statement 1 is sufficient enough to answer the question

Analysing Statement 2
• As per the information given in statement 2, Machine Y, working alone, fills a production order of twice the size in 6 hrs
o From this statement, we can say $$t_2$$ = 3 hours
o But we cannot conclude any relationship between $$t_1$$ and $$t_2$$
Hence, statement 2 is not sufficient to answer the question

Hence, the correct answer is option A.

Important Observation

• When we are calculating by what percentage one element is more/less than the other element, we only need to find out the ratio between those elements.

_________________
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

EgmatQuantExpert wrote:

Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X?

(1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.
(2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.

$$?\,\,:\,\,{T_X}\,,\,\,{T_Y}\,\,{\rm{relationship}}\,\,\,\,\,\,\left( {? = {T_X}\mathop \to \limits^{\Delta \% } {T_Y} = {{{T_Y} - {T_X}} \over {{T_X}}} = {{{T_Y}} \over {{T_X}}} - 1} \right)$$

Important: the ratio of time taken (for any given job) is the inverse of the ratio of the work done (for any given time).

$$\left( 1 \right)\,\,{{{T_{X \cup Y}}} \over {{T_Y}}} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,{{{W_{X \cup Y}}} \over {{W_Y}}} = {3 \over 2}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,{W_{X \cup Y}} = 3k \hfill \cr \,{W_Y} = 2k \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,{W_X} = k$$

$${{{W_Y}} \over {{W_X}}} = {2 \over 1}\,\,\,\,\, \Rightarrow \,\,\,\,{{{T_Y}} \over {{T_X}}} = {1 \over 2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,{T_Y} = 3{\rm{h}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{{\rm{T}}_{\rm{X}}} = 3{\rm{h}}\,\,\,\, \Rightarrow \Delta \% = 0 \hfill \cr \,{\rm{Take}}\,\,{{\rm{T}}_{\rm{X}}} = 4{\rm{h}}\,\,\,\, \Rightarrow \Delta \% \ne 0 \hfill \cr} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Intern  B
Joined: 17 Feb 2019
Posts: 2
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

Kindly note:-
When both work together means they work at a rate of 1/x+1/y = (x+y)/xy

Can somebody explain why this is?
Intern  B
Joined: 17 Feb 2019
Posts: 2
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

nsato wrote:
Kindly note:-
When both work together means they work at a rate of 1/x+1/y = (x+y)/xy

Can somebody explain why this is?
ISB School Moderator G
Joined: 08 Dec 2013
Posts: 619
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30 WE: Operations (Non-Profit and Government)
Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

nsato wrote:
nsato wrote:
Kindly note:-
When both work together means they work at a rate of 1/x+1/y = (x+y)/xy

Can somebody explain why this is?

let d1 be time taken by x and y together
d2 by x alone and
d3 by y independently.

(x+y)d1 = xd2 = yd3......................(A)

We have to find d3/d2 somehow...

Statement 2.

y*6 = 2(x+y)*d1, clearly insufficient.

Statement 1.
(x+y) (2/3) *t = y*t, solving this we get x/y as 1/2.

Putting x/y into equation (A)
we can deduce the relationship between-
1. d1 and d2
2. d1 and d3, so sufficient.

nsato if you understand equation (A) then rest of the sum will be easy for you. Check: https://gmatclub.com/forum/gmat-math-book-87417.html
Manager  B
Joined: 04 Jun 2017
Posts: 110
Location: India
Concentration: Strategy, Operations
GMAT 1: 500 Q39 V20 GPA: 3.82
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

CAMANISHPARMAR wrote:
Question Stem:-
Machines X and Y can work at their respective constant rates to manufacture a certain production unit. If both are working alone, then the time taken by machine Y is what percentage more/less than that of machine X?
Rephrase:-
Machines X and Y can work at their respective constant rates of 1/x and 1/y respectively (where x and y indicate time taken to complete one job).

$$\frac{y}{x}-1$$ = ? i.e can we get the value of $$\frac{y}{x}$$

Kindly note:-
When both work together means they work at a rate of $$\frac{1}{x}$$+$$\frac{1}{y}$$ = $$\frac{x+y}{xy}$$
Time taken when both machines work together = $$\frac{xy}{x+y}$$

Lets evaluate both the statements:-
Statement (1) Machines X and Y, working together, complete a production order of the same size in two-thirds the time that machine Y, working alone, does.

Therefore from (1) $$\frac{xy}{x+y}$$ = $$\frac{2y}{3}$$
which implies $$\frac{x}{x+y}$$ = $$\frac{2}{3}$$
or$$\frac{y}{x} = \frac{1}{2}$$
Since we have got the value of $$\frac{y}{x}$$ Statement 1 is sufficient; Not lets check statement 2 [Cross B,C & E] Evaluate between A & D:-

Statement (2) Machine Y, working alone, fills a production order of twice the size in 6 hrs.

There is no mention about the rate of machine X hence statement (2) is insufficient. Hence the correct answer is option A.

Thanks for the simplified explanation
Veritas Prep GMAT Instructor B
Joined: 01 May 2019
Posts: 50
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

nsato wrote:
nsato wrote:
Kindly note:-
When both work together means they work at a rate of 1/x+1/y = (x+y)/xy

Can somebody explain why this is?

So the rule here is that Rate of A + Rate of B = the combined Rate of A and B.

Here, if x is the time taken by Machine X to complete a job, its rate is 1/x. If y is the time taken by Machine Y to complete a job, its rate is 1/y. So the combined Rate of Machines X and Y is 1/x + 1/y.

Let's take this math step by step:

$$\frac{1}{x}+\frac{1}{y}$$

Get a common denominator by multiplying first fraction by y/y and second fraction by x/x:

$$\frac{y}{xy}+\frac{x}{xy}$$

$$\frac{y+x}{xy}$$
Manager  G
Joined: 11 Feb 2013
Posts: 230
Location: United States (TX)
GMAT 1: 490 Q44 V15 GMAT 2: 690 Q47 V38 GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Machines X and Y can work at their respective constant rates  [#permalink]

### Show Tags

Statement 1:
Let’s assume:
Total work=6 unit

Y takes 3 days to complete the work ( ie. 2 units per day)

Thus, x&y combined takes 2 days to complete the work (ie 3 units per days)

Let’s calculate UNITS PERDAY

X produces (___ )units per day
Y produces 2 units per day
========================
(X+Y) produce 3 units per day

Thus, X definitely produces 1 unit per day.
In other words, per day production capacity of X (1 unit ) is 50% of production capacity of Y (2 units).

That means, for any work x needs twice as much time as Y needs.

So, statement 1 is SUFFICIENT.

Posted from my mobile device Re: Machines X and Y can work at their respective constant rates   [#permalink] 27 Jun 2019, 08:42
Display posts from previous: Sort by

# Machines X and Y can work at their respective constant rates  