BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Work problem using smart number

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 165
Joined: Wed Mar 24, 2010 8:02 am
Thanked: 2 times
Followed by:1 members

Work problem using smart number

by HPengineer » Fri Oct 15, 2010 12:56 pm
Working this problem i got stuck trying to use a smart number. Any thoughts how to complete it using a smart number for the widgets?


OG quant review #173

Running at their respective constant rates, Machine X takes 2 days longer to produce W widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take to produce 2w widgets?

Thanks in advance!!
Top
Source: — Problem Solving |
Legendary Member
Posts: 1119
Joined: Fri May 07, 2010 8:50 am
Thanked: 29 times
Followed by:3 members

by diebeatsthegmat » Fri Oct 15, 2010 7:03 pm
HPengineer wrote:Working this problem i got stuck trying to use a smart number. Any thoughts how to complete it using a smart number for the widgets?


OG quant review #173

Running at their respective constant rates, Machine X takes 2 days longer to produce W widgets than machine Y. At these rates, if the two machines together produce 5/4w widgets in 3 days, how many days would it take to produce 2w widgets?

Thanks in advance!!
https://www.beatthegmat.com/how-many-day ... 11577.html
Top
Junior | Next Rank: 30 Posts
Posts: 19
Joined: Fri Feb 19, 2010 10:35 pm

by bitsho » Sat Oct 16, 2010 2:27 am
Let total widget be 60 i.e. w= 60 . Now X & Y can produce 5/4w i.e. 75 widget in 3 days .


Now To fulfill the required condition in question stem , Y can produce 15 widget per day & X can produce 10 widget per day (i.e. 75 widget in 3 days when they work together)

So Now back to question : How long X will take to produce 2 W widget = 2*60/10 = 12 days
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 16, 2010 6:52 am
HPengineer wrote:Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce (5/4)w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A. 4
B. 6
C. 8
D. 10
E. 12
Another approach would be to plug in the answer choices, which represent the time for X to produce 2w widgets.

Answer choice E:
12 days for X to produce 2w widgets means 6 days for X to produce w widgets and 6-2 = 4 days for Y (since X take 2 days longer)
Let w = 12
Rate for X = w/t = 12/6 = 2/day
Rate for Y = w/t = 12/4 = 3/day
Combined rate for X+Y = 2+3 = 5/day
Work completed in 3 days = r*t = 5*3 = 15 widgets
Does 15 = 5/4*w? Yes, because 15 = (5/4)*12. Success!

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1