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

Redeem

tough knewton PS

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

tough knewton PS

by bblast » Thu Jun 09, 2011 5:29 am
Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

7
9
11
13
15


[spoiler]In the timed cat I tried algebraic approach which gave me an ugly quadratic mid way. Then i wasted another minute to plug choice C and D which was again difficult to solve. Try IT!!.

While reviewing later, I used a hybrid method to made a quadratic and then backsolved to E and obtained a solution.

But this aint any smart move. Even plugging involves a lot of time to solve this question.[/spoiler]

Math Gurus on this ?
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 am
Location: India
Thanked: 310 times
Followed by:123 members
GMAT Score:750

by cans » Thu Jun 09, 2011 5:39 am
bob takes t-1 hours to paint n rooms
Albert takes t hours
work=n
rate A = n/(t)
rate B = n/(t-1)
total rate = n(2t-1)/((t)*(t-1))
time to paint n rooms = (t)(t-1)/(2t-1)
to paint 3n/5 rooms = 3(t)(t-1)/5*(2t-1) = 4/3
9t^2 - 9t = 40t - 20
9t^2 -49t + 20 =0
t = (49 +-root(41)/18 = 5 hours
Thus 3n rooms means 15 hours.
IMO E
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Legendary Member
Posts: 1448
Joined: Tue May 17, 2011 9:55 am
Location: India
Thanked: 375 times
Followed by:53 members

by Frankenstein » Thu Jun 09, 2011 5:39 am
Hi,
Let the work rates of A and B be a,b resply. Work required to paint n rooms be W
So, W = a(t+1)
W = b(t)
So, a=bt/(t+1)
Also given that 3W/5 = (a+b)(4/3)
So, 3bt/5 = (bt/(t+1) + b)(4/3)
=>3t/5 = (4/3)(2t+1)/(t+1) => 9t(t+1) = 20(2t+1) => 9t^2 -31t -20 =>9t^2 -36t + 5t -20 = 0
So,(t-4)(9t+5) = 0
So, t=4
So, A takes 5 hours to finish n rooms.So, he takes 15 hours to finish 3n rooms.

Hence, E
Cheers!

Things are not what they appear to be... nor are they otherwise
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 » Thu Jun 09, 2011 6:08 am
bblast wrote:Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/5 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?

7
9
11
13
15


[spoiler]In the timed cat I tried algebraic approach which gave me an ugly quadratic mid way. Then i wasted another minute to plug choice C and D which was again difficult to solve. Try IT!!.

While reviewing later, I used a hybrid method to made a quadratic and then backsolved to E and obtained a solution.

But this aint any smart move. Even plugging involves a lot of time to solve this question.[/spoiler]

Math Gurus on this ?
We can plug in the answers, which represent the time it takes Albert to paint 3n rooms.
Given the denominators of the fractions included in the problem (3n/5 and 4/3), the correct answer is likely to be a multiple of 5 and 3.

Answer choice E: Albert takes 15 hours to paint 3n rooms.
Thus, to paint n rooms, Albert takes 15/3 = 5 hours.
Since Albert takes 1 hour longer than Bob, time for Bob = 5-1 = 4 hours.
Let n=20.
Rate for Albert = w/t = 20/5 = 4 rooms per hour.
Rate for Bob = w/t = 20/4 = 5 rooms per hour.
Combined rate for Albert and Bob = 4+5 = 9 rooms per hour.
Number of rooms to be painted = 3n/5 = (3*20)/5 = 12 rooms.
Time for Albert and Bob to paint 12 rooms = w/r = 12/9 = 4/3 hours.
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
User avatar
Legendary Member
Posts: 1077
Joined: Mon Dec 13, 2010 1:44 am
Thanked: 118 times
Followed by:33 members
GMAT Score:710

by bblast » Thu Jun 09, 2011 11:01 pm
I came across a simlar question last night in a gmat club test :

Finally I would go with such an approach in these question : I don't wana remember the quadratic formula and I wana solve this quickly.

form the combined rate equation :

1/t + 1/(t-1) = 9/20.

= 20/t + 20/(t-1) = 9

plug answer choice E. since it says 15 hours for 3n work by Albert we need to plug 5 into the equation above as the equation above is the rate equation per unit work.

20/5 + 20/4 = 9 !!

also in this method we could easily eliminate answer choices A C and D as they are not divisible by 3 . similar question from gmat club test:

It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours

E
Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

My gmat journey :
https://www.beatthegmat.com/710-bblast-s ... 90735.html
My take on the GMAT RC :
https://www.beatthegmat.com/ways-to-bbla ... 90808.html
How to prepare before your MBA:
https://www.youtube.com/watch?v=upz46D7 ... TWBZF14TKW_
Top
User avatar
Legendary Member
Posts: 516
Joined: Fri Jul 31, 2009 3:22 pm
Thanked: 112 times
Followed by:13 members

by smackmartine » Thu Jun 09, 2011 11:38 pm
IMO E
Another approach :
Applying RT=D (basic formula) , we get:
Rb(T) =n -------1 (Ra and Rb are rates of Albert and Bob,respectively)
Ra(t+1)=n -------2

Also given that (Ra+Rb)4/3 = 3n/5 -------3

As we know that we have relation between Ra and Rb from equation 1 and 2, and we can reduce equation 3 in Terms of Ra and work (3n ----> total work to be done by Albert) , we can rewrite equation 3 as :

(Ra+Ra(t+1)/t)(4/3) = 3n/5 => Ra[2+ (1/t)](20/3) = 3n

If you look at the bold part carefully, you will find that we are looking for the same in terms of Time.

A) [2+ (1/t)](20/3) = 7
1/t = (21/20)-2 (negative value) so not possible.

similarly all options will give 1/t --> negative except for option E

E) [2+ (1/t)](20/3) =15
1/t = (45/20)-2 = 5/20 = 1/4 ..Bingooo!!!
Top
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 am
Location: India
Thanked: 310 times
Followed by:123 members
GMAT Score:750

by cans » Fri Jun 10, 2011 6:16 am
It takes Jack 2 more hours than Tom to type 20 pages. Working together, Jack and Tom can type 25 pages in 3 hours. How long will it take Jack to type 40 pages?

(A) 5 hours
(B) 6 hours
(C) 8 hours
(D) 10 hours
(E) 12 hours
j=t hours; tom=t-2
total = (t)(t-2)/(2t-2)
20 pages in (t)(t-2)/(2t-2)
25 in (t)(t-2)*5/(2t-2)*4 = 3
5t^2 - 10t = 24t-24
5t^2 - 34t + 24=0
5t^2 - 30t - 4t + 24 =0
t=6
thus to write 40 pages, 12 hours
E
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Post new topic Post Reply
• Page 1 of 1