Working in a South Side studio at a constant rate, Kanye can drop a fu

Question

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Kudos for a correct solution.

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Kudos for a correct  solution .

Harley1980 · Answer

Rate of Kanye =  \frac{1}{5}

Rate of Common =  \frac{1}{x}

Total rate  \frac{1}{5}+\frac{1}{x}=\frac{1}{2}

\frac{1}{x}=\frac{1}{2}-\frac{1}{5}=\frac{3}{10}

x = \frac{10}{3} = 3 \frac{1}{3}

Answer is A

GMATinsight · Answer

Let's say

Total Work = 10 Units

Since, Kanye can drop a full-length platinum LP in 5 weeks
therefore, Kanye's work per week = 10/5 = 2 units

Since, Kanye and common together can drop a full-length platinum LP in 2 weeks
therefore, Kanye's work per week = 10/2 = 5 units

i.e. Common's 1 week work = 5 units - 2 units = 3 units
therefore Common will drop a full-length platinum LP in = 10/3 = 3 1/3 days

Answer: Option  A

Zhenek · Answer

Damn, my method seems quite lengthy, I'd love to see more compact ones.
 S  - work,  V_k  - Kanye's productivity,  V_c  - Common's.
We got 3 equations in a system:
 1)\frac{S}{V_k} = 5  
 2)\frac{S}{V_c} = x 
 3)\frac{S}{(V_k + V_c)} = 2 
Divide 1) by 2) (can do that coz no null variables)
 V_c = \frac{5}{x}*V_k 
Insert  V_c  into 3) and divide 1) by 3) 
 (V_k + \frac{5}{x}*V_k)/V_k = \frac{5}{2} 
 2 + \frac{10}{x} = 5 
 \frac{10}{x} = 3 
 x = \frac{10}{3}  which matches option A

SavageBrother · Answer

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Kudos for a correct solution.

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 week

Kanye: 1/5 lp per week
Common: 1/x lp per week (C)

K + C = 1/2 lp per week
1/5 + C = 1/2 
2/10 + C = 5/10
C = 3/10

Common can make 3/10 lp in a week, so it will take him 3 1/3 weeks to make an LP.

A.

EMPOWERgmatRichC · Answer

Hi All,

This question is a wordy variation on a standard "Work Formula" question. When you have 2 entities sharing a task, you can use the following formula to figure out how long it takes for the 2 entities to complete the task together.

Work = (A)(B)/(A+B) where A and B are the individual times required to complete the task

Here, we're given the rates as 5 weeks and X weeks AND we're given the end result as 2 weeks. Using the Work Formula, we have...

(5)(X)/(5+X) = 2

Now we just have to do a little algebra:

5X = 10 + 2X
3X = 10
X = 10/3 weeks

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks. Working at his own constant rate, Common can drop a full-length platinum LP in x weeks. If the two emcees work together at their independent rates, they can drop a full-length platinum compilation LP in 2 weeks. Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Kudos for a correct solution.

(A) 3 and 1/3 weeks
(B) 3 weeks
(C) 2 and 1/2 weeks
(D) 2 and 1/3 weeks
(E) 2 weeks

Kudos for a correct  solution .

Harley1980 · Answer

Rate of Kanye = \frac{1}{5}

Rate of Common =  \frac{1}{x}

Combined rate =  \frac{1}{5}+\frac{1}{x}=\frac{1}{2}

\frac{1}{x}= \frac{1}{2}-\frac{1}{5}=\frac{3}{10}

x = \frac{10}{3} = 3 \frac{1}{3}  weeks

Answer is A

EMPOWERgmatRichC · Answer

Hi All,

This question is a wordy variation on a standard "Work Formula" question. When you have 2 entities sharing a task, you can use the following formula to figure out how long it takes for the 2 entities to complete the task together.

Work = (A)(B)/(A+B) where A and B are the individual times required to complete the task

Here, we're given the rates as 5 weeks and X weeks AND we're given the end result as 2 weeks. Using the Work Formula, we have...

(5)(X)/(5+X) = 2

Now we just have to do a little algebra:

5X = 10 + 2X
3X = 10
X = 10/3 weeks

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

SherLocked2018 · Answer

A for me too. 
2 individual rates and the combined rate is given. So we have to solve for x : 
1/5 + 1/x = 1/2 
=> x=10/3 Thus A.

ManviSharma · Answer

Hi,

Kanye 1 week work = 1/5
Common's 1 week work = 1/x
Both ( K+C) 1 week work = 1/5 + 1/x = 1/2

Therefore, 1/x = 1/2- 1/5 = 3/10
 = 3 1/3 Weeks = Ans A

Bunuel  - Please share the OA?

EMPOWERgmatRichC · Answer

Hi ManviSharma,

The Official Answer will be revealed on Sunday, but I think that you can tell from your own post (and everyone else's posts) that you have the correct answer.

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Now, while your instinct may be to Go! and speed through your initial read of this rate problem, remember: slow motion (is) better than no motion. As you read each sentence, you should start jotting down variables and relationships so that by the time you get to the question mark you have actionable math on your noteboard and you don’t have to read the question all over again to get started. You should be thinking:

Working in a South Side studio at a constant rate, Kanye can drop a full-length platinum LP in 5 weeks.

Rate (K) = 1 album / 5 weeks

Working at his own constant rate, Common can drop a full-length platinum LP in x weeks.

Rate (C) = 1 album / x weeks

If the two emcees work together…

I’m adding these rates, so their combined rate is 1/5 + 1/x

…they can drop a full-length platinum compilation LP in 2 weeks.

And they’re giving me the combined rate of 1 album / 2 weeks, so 1/5 + 1/x = 1/2

Assuming no efficiency is lost or gained from working together, how many weeks would it take Common, working alone, to drop a full-length platinum LP?

I’m using that equation to solve for Common’s time, so I’m solving for x.

Now by this point, that slow motion has paid off – your equation is set, your variable is assigned, and you know what you’ve solving for. Your job is to solve for x, so:

1/5 + 1/x = 1/2, so let’s get the x term on its own:

1/x = 1/2 – 1/5. and we can combine the two numeric terms by finding a common denominator of 10:

1/x = 5/10 – 2/10

1/x = 3/10, and from here you have options but let’s cross multiply:

10 = 3x, so divide both sides by 3 to get x alone:

10/3 = x, and that doesn’t look like the answer choices so let’s convert to a mixed number: 3 and 1/3 (there’s that number again), for answer choice A.

What’s the real lesson? It’s like Common says: slow motion (is) better than no motion, so you should read just a little slower but have some scratchwork to show for your initial read of the prompt. If you can:

-assign variables
-jot down relationships or equations
-write down which variable the answer wants

You’ll have a lot more to show for your initial 30 seconds with each problem, and you’ll find that you solve problems much more quickly this way because you have less wasted time. So heed Common’s uncommon wisdom (which is really just common sense): the best way to Go is to remember that slow motion > no motion.

ScottTargetTestPrep · Answer

1/5 + 1/X = 1/2

2X + 10 = 5X

10 = 3X

X = 10/3 = 3 ⅓ weeks

Answer: A

Working in a South Side studio at a constant rate, Kanye can drop a fu

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

Working in a South Side studio at a constant rate, Kanye can drop a fu

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