Problem Solving

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%


Thanks

is the answer B?

i get that answer this way: given the "simple" fractions as found in question, let's assume the factory produces 100 switches. of the 100 switches, 1/5 (or 20) are defective while 4/5 (80) are not defective. of the 1/5 (or 20) defective switches, 4/5 (or 16) are rejected while 1/5 (or 4) are not (and subsequently sold). of 80 switches that are not defective, 1/20 (or 4) are mistakenly rejected and not sold, leaving 76 switches to be sold. combined, there are 80 switches out of 100 produced that are sold.

the question asks for what fraction of sold switches that are defective. thus, 4 (defective sold switches) out of 80 (total of sold switches) is 1/20, or 5%.

SEE ATTACHMENT FOR PROPER GIRD


in these type of questions, always use a grid


that is:



D= defective
R=Rejected



D Not D Total


R

Not R


Total




D= defective
R=Rejected


Say out of 100 total

Out of 100 1/5 are defective= 20
4/5 of those are rejected= 16

We also know 4/5 are not defective=80

1/20 of Not D= 4

Plug into grid

D Not D Total

R 16 4


Not R


Total 20 80 100



Now by simply adding and subtracting from the subtotal, you get all the other numbers



D Not D Total


R 16 4 20


Not R 4 76 80


Total 20 80 100



4/80= 5%

Ans B

One-fifth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the nondefective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?

(A) 4%
(B) 5%
(C) 6.25%
(D) 11%
(E) 16%

Total produced = 100
1/5 or 20 defective
4/5 of defective switches = 16
Total Non-defective switches = 100 - 20 = 80
1/20 of total non-defective switches are rejected = 80/20 = 4
So total rejected = 4 + 16 = 20
Total sold = 100 - (4 + 16) = 80
Total sold but defective = 20 - 16 = 4
Hence % = 4/80 * 100 = 5%

Hello!
This seems like such an easy problem, but somehow, I am completely missing the caveat!

I am getting an answer of 25% which is clearly wrong!
What am I doing wrong? I have attached the chart I am working off of attached here.
Is it something to do with the 'mistakenly labeled rejected' bit? Or a calculation error that I am overlooking?

So confused!

nk18967 wrote:Hello!
This seems like such an easy problem, but somehow, I am completely missing the caveat!

I am getting an answer of 25% which is clearly wrong!
What am I doing wrong? I have attached the chart I am working off of attached here.
Is it something to do with the 'mistakenly labeled rejected' bit? Or a calculation error that I am overlooking?

So confused!

Your matrix is perfect, but you're answering the wrong question.
Question: If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
The middle row of your matrix indicates that 80 switches are not rejected and thus are sold.
Of these 80 switches, 4 are defective:
4/80 * 100 = 5%.

OMG! THANK YOU! Haha!
You are right, I was answering the ratio of total defective to total sold!
I spent 20 minutes trying to understand what I was doing wrong before posting!

GMATGuruNY wrote:

nk18967 wrote:Hello!
This seems like such an easy problem, but somehow, I am completely missing the caveat!

I am getting an answer of 25% which is clearly wrong!
What am I doing wrong? I have attached the chart I am working off of attached here.
Is it something to do with the 'mistakenly labeled rejected' bit? Or a calculation error that I am overlooking?

So confused!

Your matrix is perfect, but you're answering the wrong question.
Question: If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
The middle row of your matrix indicates that 80 switches are not rejected and thus are sold.
Of these 80 switches, 4 are defective:
4/80 * 100 = 5%.

nk18967 wrote:OMG! THANK YOU! Haha!
You are right, I was answering the ratio of total defective to total sold!
I spent 20 minutes trying to understand what I was doing wrong before posting!

This happens to me more or less daily! I've learned over time that if I'm really confident in my approach but I'm not getting the wrong answer:

i) I made an arithmetic mistake somewhere;
ii) I answered the wrong question;
iii) I wrote something down wrong
iv) I'm really wrong, and I'm about to learn something important

To avoid (i), try not to compute and think/solve at the same time. To avoid (ii), write down what you're asked for before starting to solve (e.g. "John's salary in October", "the number of alpacas at the petting zoo on Tuesday"). To avoid (iii) write BIG, CLEAR, and NEAT: no scribbling!