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

 It is currently 21 Nov 2018, 00:38

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

Events & Promotions

Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

Machines X and Y can work at their respective constant rates

Author Message
TAGS:

Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2203
Machines X and Y can work at their respective constant rates  [#permalink]

Show Tags

Updated on: 13 Aug 2018, 05:00
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:20) correct 34% (01:13) wrong based on 186 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!

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Originally posted by EgmatQuantExpert on 23 May 2018, 03:16.
Last edited by EgmatQuantExpert on 13 Aug 2018, 05:00, edited 1 time in total.
Director
Joined: 11 Feb 2015
Posts: 571
Re: Machines X and Y can work at their respective constant rates  [#permalink]

Show Tags

26 May 2018, 12:57
3
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.
_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2203
Re: Machines X and Y can work at their respective constant rates  [#permalink]

Show Tags

27 May 2018, 04:32

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.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 485
Re: Machines X and Y can work at their respective constant rates  [#permalink]

Show Tags

30 Oct 2018, 02:15
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 :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Re: Machines X and Y can work at their respective constant rates &nbs [#permalink] 30 Oct 2018, 02:15
Display posts from previous: Sort by