Two machines, Y and Z, work at constant rates producing identical item

Question

Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2

A. 6
B. 9
C. 9 1/2
D. 12
E. 13 1/2

Bunuel · Accepted Answer

Machine Z is 1.5 times slower than machine Y. So, if machine Y takes 9 minutes to produce a batch of items, then it takes machine Z 9*1.5 = 13.5 minutes to produce the same number of items.

Answer: E.

saiesta · Answer

lf you assume that machine Y produces 3 items per minute then machine Z produces 2 items per minute. If machine Y takes 9 minutes to produce a batch of items, then machine Y produces 27 items in these 9 minutes. Since machine Z produces the same number of items, it should take machine Z 13.5 minutes to produce 27 items.

At times, it just helps to plug in numbers...

At times, it just helps to plug in numbers...

umg4147 · Answer

Hey awsome bunuel, i went a bit long in deducing the actual relation between the Rates.

Now atleast i know what to think when i see such question and dont need to go on the practice pad .

gracie · Answer

rate z/rate y=2/3
time z/time y=3/2
3/2*9=13 1/2 minutes

hemantbafna · Answer

Y- 3 items 
Z- 2 items 
Let the batch be of 27 items, therefore Y would take 1 min to produce 3 units and 9 mins to produce 27 items. (9 items taken is consistent with the time mentioned in the question for Y to produce the batch of items)
Time required by X to produce 27 items is 27/2 (as in 1 min X produces 2 units) = 13.5 mins or 13 1/2 mins.
 E

EgmatQuantExpert · Answer

Given

• Two machines, Y and Z, work at constant rates producing identical items.
• Machine Y produces 3 items at the same time Machine Z produces 2 items.
• Machine Y takes 9 minutes to produce a batch of items.

To Find

• Minutes it takes for machine Z to produce the same number of items.

Approach and Working Out

• Speed ratio – 
 o  \frac{Y}{Z }  =  \frac{3}{2 }

• Time ratio – 
 o  \frac{Y}{Z }  =  \frac{2}{3 }  
• Time for Y = 9 minutes.

• Time for Z =  \frac{3}{2 } × 9 minutes
 o = 13 ½ minutes

Correct Answer: Option E

Kinshook · Answer

Given: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 3 items in the same time Machine Z produces 2 items. 
Asked: If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?

Machine Y takes time to produce a batch of items = 9 mins
Machine X will take time to produce a batch of items = 9*3/2 = 27/2 = 13 1/2

IMO E

armaankumar · Answer

__ | rate | time | work |
Y)__ 1.5r___ 9____ 1
Z)___ r___ 13.5___ 1

Working behind the matrix table: 
It is given that Y produces 3 items in the same time Z produces 2
=> The rate of Y is 1.5 times faster than that of Z

I've assumed the batch size as 1 for simplicity.
In the stem, we're given:
1.5r*9=1
=> r= 1/13.5

Plugging the value of r in (Z):
1/r = 13.5

santhosh1797 · Answer

Use W= nRT formula

R1*T1 = R2*T2

3*9 = 2*T2

T2= 13.5

nimaki · Answer

|W |R |T |
Y| 27 |3 |9 |
Z| 27 |2 | X  |

T =  W /R =  27 /2
T =  13.5 Min

san10789 · Answer

Work = Rate * Time
Machine Y produces 3 items in the  same amount of time  in which machine Z produces 2 items.
Let time be  t , and Rate of Y be  y  and rate of Z be  z .
First step is to get the relation in the rates.

For Y : Work = Rate * Time
 3items = yt
For Z : Work = Rate * Time 
 2 items = zt
Using t common in above we get:
3/y = 2/z
or 
3z = 2y. We got a equations of Y and Z rates.

Now, machine Y takes 9 minutes to produce a batch of items (lets call it  B )

For Y : Work = Rate * Time
 B = y.9
minutes taken by machine Z (lets call it  T )to produce the same number  B 
For Z : Work = Rate * Time 
 B = zT
Equating above

9y = zT.
We already know 3z = 2y. Putting y = 3z/2
9*3z/2 = zT
 T = 13.5 minutes.

Maria240895chile · Answer

x=time Z and Y take
B=batch of items

\frac{1}{y}=\frac{3}{x}  and  \frac{1}{z}=\frac{2}{x}

\frac{1}{z}=\frac{2}{x} 
x=2z

\frac{1}{y}=\frac{3}{x} 
 \frac{1}{y}=\frac{3}{2z} 
 y=\frac{2z}{3}

now y takes 9 minutes in a batch

\frac{1}{y}=\frac{B}{9}  
replace the y with 2z/3

\frac{3}{2z}=\frac{B}{9}  multiply by  \frac{2}{3}  to get

\frac{1}{z}=\frac{2B}{27}

so Z takes 27 min in producing 2 Batch, so producing 1 batch takes 27/2=13,5

basanti7 · Answer

How is Z 1.5 slower than Y?

Bunuel · Answer

Since Machine Z produces 1.5 times fewer items (2 items) in the same time period as Machine Y (3 items), Machine Z is  1.5 times slower  than Machine Y.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Two machines, Y and Z, work at constant rates producing identical item

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Two machines, Y and Z, work at constant rates producing identical item

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards