Machine A can make 200 widgets in 14 hours, Machine B can make 200 wid

Question

Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

Lampard42 · Answer

Logically C alone can make 100 widgets in 1 hour so C,B and E is eliminated.

Rate is 200/14,200/7 and 200/2 respectively. So if they work together then they can 200/14 + 200/7 + 200/2 = 2000/14 that is produce 2000 widgets in 14 hours/840 minutes. So 1000 widgets take 840*100/2000 = 42 IMO B

CareerGeek · Answer

Rate of A, B & C is 200/14, 200/7 & 200/2 hours respectively

Working together, Total rate = 200/14 + 200/7 + 200/2

—> 100 = 200(1/14 + 1/7 + 1/2)*t
—> 100 = 200(1 + 2 + 7)/14*t
—> 100 = 200*10/14*t
—> t = 14/10*1/2 = 7/10 hours
—> t = 7/10*60 = 42 minutes

IMO Option B

Pls Hit kudos if you like the solution

Posted from my mobile device

Staphyk · Answer

So we can safely forget the 0’s in the 200 and 100. since Machine A,B and C all made the same widget.

Rate of A (Ra) =2/14
Rate of B (Rb) =2/7=4/14
Rate of C (Rc)= 2/2=14/14

Total Rate (Rt) = R(a)+R(b)+R(c)
Total Rate (Rt) =2/14+4/14+14/14
 (Rt) =20/14=10/7
Total work =1
R•T=W —> (10/7)•T=1 —> T=7/10(hrs)
T=7/10•60mins = 42 mins

Answer B

Posted from my mobile device

LeoN88 · Answer

200= a14 = b7 = c2
We have to find k
(a+b+c)k = 100, replace the values of a,b and c.

TheNightKing · Answer

I liked your approach of eliminating 3 options straight up. It shows the confidence even during the exam

EgmatQuantExpert · Answer

Solution 
  Given:  
 • Machine A can make 200 widgets in 14 hours
• Machine B can make 200 widgets in 7 hours
• Machine C can make 200 widgets in 2 hours

To find:  
 • Time taken by them to complete 100 widgets when working together

Approach and Working Out:   
 • A + B + C can together make 200 widgets in  1/(\frac{1}{14} + \frac{1}{7} + \frac{1}{2}) = \frac{14}{10} = \frac{7}{5}  hours
• Therefore, they take  \frac{1}{2} * \frac{7}{5} = \frac{7}{10}  hours = 42 minutes to make 100 widgets

Hence, the correct answer is Option B.

Answer: B

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

Archit3110 · Answer

for every 200 widgets combined rate ; 1/14+1/7+1/2 = 10/14 and total time ; 14/10 ; for half widgets ie 100 ; 14/10 * 1/2 = 7/10 hrs
in mins ; 7 * 60/10 ; 42 mins
IMO b

MidhilaMohan · Answer

A-100 pins-7 hrs
B-100 pins-3.5hrs
C-100 pins- 1 hr

1/A+1/B+1/C=50/35

hence time is 35/50*60=42 mins

Shrey9 · Answer

Machine A can make 200 widgets in 14 hours, Machine B can make 200 widgets in 7 hours, and Machine C can make 200 widgets in 2 hours. How long does it take them to complete 100 widgets when working together?

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

A. 32 minutes
B. 42 minutes
C. 84 minutes
D. 90 minutes
E. 96 minutes

Solution

Work(W) = Rate(R) * Time (T)

Work ( W) is given to be 200 for A, B, and C... lets keep it the way..

Rate for A = A's work / A's Time (from the formula)
= 200/14

Similarly B's Rate = 200/7

and

C's rate = 200/2 respectively.

Their collective rate (lets say K) will be A's rate + B's rate + C's rate. (as rates can be added)

Therefore,
K = 200/14 + 200/7 + 200/2 = 2000/14

they produce 2000 widgets in 14 hours

Now we're given a new work of 100 midgets..
which we can simply put in the formula 
W = R * T
Rate we know for collective is 2000/14
and W = 100
therefore,
Time = 100/2000/14 = 100*14/2000 = 14/20

This will be in hours, now multiply it by 60 to get the value in minutes= 14*60/20 = 14*3 = 42

to get to answer option 42 mins (B)

ScottTargetTestPrep · Answer

The rate for Machine A is 200/14, for Machine B 200/7, and for Machine C 200/2. Thus, we can create the following combined rate:

200/14 + 200/7 + 200/2

200/14 + 400/14 + 1400/14 = 2000/14

So the time to completed 100 widgets is:

100/(2000/14) = 100 x 14/2000 = 14/20 = 42/60 hours = 42 minutes

Answer: B

Aboyhasnoname · Answer

Tried solving this without pen and paper. 
C alone can make 100 in 1 hour... so C,D,E are eliminated... 
Left with A and B... If C can make 100 in 1 hour that means 50 in 30 mins.. So we need A and B to make approximately 50 in those 30 mins... so can A and B make 50 in 30 mins? Let’s see... 
A 200 in 14 means.. 100 in 7 means 50 in 3.5 means 25 in 1.75.... Means 12 in somewhere around 40-50 mins ... nearly 5-6 in 30 mins
And B... will make twice of this in 30 mins.. so around 12-13... we are 10 away from our target of 50.... 
This means 30 mins not sufficient to make 100 widgets together.. need a little more time... but less than 1 hour... option B it is..

Machine A can make 200 widgets in 14 hours, Machine B can make 200 wid

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

Machine A can make 200 widgets in 14 hours, Machine B can make 200 wid

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