A milliner bought a job lot of hats 1/4 of which were brown.

Question

A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?

(A) 1/60
(B) 2/15
(C) 3/20
(D) 3/5
(E) 3/4

MBAhereIcome · Accepted Answer

just suppose that you have a total of 60 hats.
no. of brow hats = 1/4*60 = 15 
of these hats, 4/5*15 = 12 were sold, so remaining brown hats = 3

no. of hats sold = 2/3*60 = 40
unsold hats = 20

ANS = 3/20

kevincan · Answer

Suppose he bought n hats, n/4 brown and 3n/4 not brown.

He sold 2n/3 of the hats in total ,(4/5)(n/4)=n/5 of which were brown


Remaining, then, are n/4-n/5=n/20 brown hats of a total of n/3 unsold hats.

Thus the fraction of the unsold hats that are brown is n/20 divided by n/3 =3/20

C

Alternatively, suppose there are 60 hats bought (LCM(3,4,5)). 20 were unsold, and of the 15 brown hats, 3 were unsold

pinchharmonic · Answer

i went a more difficult way to solve it,

if x = the total number of hats, then x/4 are brown hats and 3x/4 are black hats

if you sell 2/3 of the hats, and since you don't know how many of those are black or brown luckily they give you the statement that 4/5 of the brown hats were sold off in that

so 2/3x = (x/4)*(4x/5) + Y(3x/4)

I let Y be the fraction of Black hats sold, and as you can see, I included the 3x/4 which is the amount of black hats originally.

2/3*x - 1/5*x = Y(3x/4)
7x/15 = Y(3x/4)

you end up with Y = 28/60 or 14/30, or in other words, the amount of black hats sold from the original 3/4.

but earlier we also figured out that 1/5*x is the amount of brown hats sold from the original 1/4. So i guess the tricky part is realizing you need to find out what is remaining after being sold. that would equal the original amount - the sold amount.

1/4*x - 1/5*x = the remaining brown hats = 1/20*x
3/4*x - 14/30*x = the remaining black hats = 45/60*x - 28/60*x = 17/60*x

the question asks for the ratio of remaining brown to total, so divide remaining brown / total

(1/20*x) / (1/20*x + 17/60*x)
 x(3/60 + 17/60)
= 1/20*x / (x*20/60)

= 1/20 * 60/20 = 1/20 * 3 = 3/20

blink005 · Answer

We know 1/4 of the hats are brown
acc. to given conditions 4/5th of brown hats are sold
so 1/5 are unsold
i.e. 1/5*(no. of brown hats are unsold)
Let total no. of hats be H
no.of brown hats remaining=1/4*(total no. of hats)=1/4H
acc. to given conditions,
1/3 hats remain
hence no. of hats remaining=1/3H
there required fraction=(1/20*H)/(1/3*H)=3/20
3/20

Spidy001 · Answer

let T be the total and B be the brown ones.

(1/4)T = B

(2/3)T were sold, of which (4/5)T were brown. 
 left over brown hats(unsold brown hats) = (1/4)T - (4/5)T = T/20

(1/3)T were unsold.

the fraction of unsold hats that were brown = (T/20)/ ((1/3)T) = 3/20

CAMANISHPARMAR · Answer

Lets solve it by picking a smart number, say the milliner bought total 60 hats:- 2018-06-24_23-09-50.jpg Correct answer is option C

KanishkM · Answer

---------Brown---------Not Brown------
Sold-----12---------------28------------40
 Unsold---3----------------17------------20 
----------15---------------45------------60

3/20

Nikolla · Answer

I started this out by finding the LCM of the 3, 4, and 5, which is 60.

So let's say 60 total hats.

1/4 of them were brown = 15 brown hats.

He sold 2/3 of the hats, which would be 40 total, but 4/5 brown hats were sold off along with the 40, so 4/5 of 15 is 12 brown hats gone.

Left remaining are 20 hats, with 3 of them being brown.

3/20

Kinshook · Answer

Given: A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. 
Asked: What fraction of the unsold hats were brown?

Brown hats: 1/4
Other hats: 3/4
Brown hats sold: 4/5*1/4 = 1/5

Unsold hats: 1/3
Unsold brown hats :1/4 - 1/5 = 1/20

The fraction of the unsold hats were brown = (1/20)/(1/3) = 3/20

IMO C

BrentGMATPrepNow · Answer

STRATEGY CHECK: One option here is to let x = the total number of hats, and then calculate each value in terms of x. 
Another option is to assign a "nice" to the total number of hats (i.e., a number that works well with all of the fractions)  
Let's take the second approach.

The least common multiple of the three denominators (4, 3 and 5) is   60  
So, let's say there are   60   hats in the job lot.

A milliner bought a job lot of ( 60 ) hats 1/4 of which were brown.  
1/4 of   60   = 15, which means there were   15   brown hats in the job lot.

The milliner sold 2/3 of the hats including 4/5 of the brown hats.  
2/3 of   60   = 40, which means the milliner sold a total of 40 hats, and  20  hats remained unsold 
4/5 of   15   = 12, which means the milliner sold a total of 12 brown hats, and  3  brown hats remained unsold

What fraction of the unsold hats were brown?  
 3  of the  20  unsold hats were brown. 
Answer = 3/20 = C

Deepthi13 · Answer

how to chose a number according to the question ?

Bunuel · Answer

When picking numbers, we need to choose a number with which the calculations required for the question become easier. Often, it means getting an integer value for the fractions or percentages mentioned in the question. For example, for this question, choosing the least common multiple of each denominator mentioned (4, 3, and 5), which is 60, ensures that at each step of the question we get an integer value of hats, which simplifies the calculations.

Articles: 
 
  Backsolving on GMAT Math  How to Do Math on the GMAT Without Actually Doing Math  
  The Power of Estimation for GMAT Quant  
  How to Plug in Numbers on GMAT Math Questions  
  Number Sense for the GMAT  
  Can You Use a Calculator on the GMAT?  
  GMAT Math Strategies — Estimation, Rounding and other Shortcuts  
  The 4 Math Strategies Everyone Must Master, Part 1  (1. Test Cases and 2. Choose Smart Numbers.) 
  The 4 Math Strategies Everyone Must Master, part 2  (3. Work Backwards and 4. Estimate) 
  Intelligent Guessing on GMAT  
  How to Avoid Tedious Calculations on the Quantitative Section of the GMAT  
  GMAT Tip of the Week: No Calculator? No Problem.  
  The Importance of Sorting Answer Choices on the GMAT

Hope it helps.

A milliner bought a job lot of hats 1/4 of which were brown.

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

A milliner bought a job lot of hats 1/4 of which were brown.

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