In a factory that produces computer circuit boards, 4.5

Just for the sake of some intuition one should consider this:

That actual 4.5 percent figure that got fixed from the entire amount is equal to 90 percent that got fixed. The 4.5 percent here is adjusted to the 10 percent that gets escaped. So the 4.5 percent of all boards that are found to be defective already includes the adjustment that 10 percent escaped. So in other words after 10 percent escapes that figure is 4.5 percent of total boards. So we need to figure out what the original defective boards in percentage were.

As we know 10% escaped and wasn't caught,
We also know that when we originally found 4.5% of boards and fixed them before selling them
So that 4.5% was in reality only 90% of all defective board since we missed 10%
So, 90% of all defective boards = 4.5% of all boards

So, (10% of y + 4.5% of x) = total number of defective boards = y

Key word here "found"

i think total cb and defective cb are not required because (X/Y)*(Y/total) is the answer where x is defective and not repaired and y is defective and total is total no of bulbs.

Answer: B

X = all boards
4.5% * X = all boards that are DEFECTIVE and repaired before being sold

Y = all DEFECTIVE boards
100% all boards - 10% all DEFECTIVE boards that are NOT being repaired before being sold = 90%

90% * Y = all DEFECTIVE boards that are repaired before being sold

.9*Y = .045*X
Y = (.045/.9) * X
Y = .05
Y = 5%

As 10% of all defective boards are sold without being repaired, (100 - 10)% = 90% of all defective boards are sold after being repaired

So, 90% of all defective boards = 4.5% of all boards
--> 100% of all defective boards = (4.5/90)*100% = 5% of all boards

T - total boards
D - ALL defective boards.

\(\frac{90}{100}*D=\frac{4.5}{100}* T\)

D = 5% of Total.

B is answer.

Or similarly one can use smart numbers:

Let's say total produced were 1000

So we have that 45 were defective and repaired
Since 10% were not repaired, 90% of boards were defective and repaired
The 9/10x = 45, where 'x' is the total number of defective boards.

x = 50

Therefore percentage defective 50/1000 = 5%

Hope this clarifies
Cheers
J

Total production = 1000
Defective goods sold without repairing = 100
Non defective ( Ready for sale ) = 900
Defective and repaired before sold = 45

Thus out of 900 Good items produced in the factory 45 are found defective

Percentage of defective goods = 45/900 * 100 =>5%

Alternatively, this question can be viewed as an overlapping set with 2 variables.

Defective Not defective
Repaired 4.5
Not repaired 0.1x
Total x

Thus, 4.5 + 0.1x = x
Solve for x:
x=5

defective=100
defective & sold=10% 0f defective
defective & not sold=90%
90%=4.5
100%=5
ans: B

Here's what I did. Say, Total produced= 100 and Total defective=x. Repaired and sold 4.5% of 100=4.5, sold without repair=.10x, then .10x+4.5=x. We can solve for X=5, that is (5/100)%= 5%. Answer choice B.

Since 10 percent of all defective boards are sold without being repaired, 90 percent of all defective boards are sold after being repaired, and this number is also the 4.5 percent of all boards produced. Thus if we let d = the number of defective boards and n = the total number of boards, we have:

0.9d = 0.045n

d/n = 0.045/0.9 = 45/900 = 5/100 = 5%

Answer: B

Hi All,

While this question is older - and the concept (subgroups within subgroups) is relatively rare - you can solve this problem in a couple of different ways. Here's how you can use a mix of TESTing VALUES and TESTing THE ANSWERS to get the answer:

We're told that a factory produces circuit boards and 4.5% of all boards produced are found to be defective AND then repaired before being sold. However, 10% of all defective boards are sold WITHOUT being repaired. We're asked for the percentage of boards produced in the factory are defective.

From the prompt, it's clear that not all of the defective boards are repaired, so the percentage of defective boards MUST be greater than 4.5%. Let's TEST Answer B...

Answer B: 5%

IF....
there are 1,000 total boards,
5% would be (.05)(1,000) = 50 total defective boards
4.5% would be (.045)(1,000) = 45 defective boards REPAIRED, which leaves 5 defective boards (out of 50 defective boards) NOT REPAIRED... 5/50 = 10%. This matches what we were told, so this MUST be the answer.

Final Answer:

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

One way to find the percentage of defective boards would be to find the total number produced and the total number defective (including those repaired and those not repaired). But in this problem, we don't have enough information to solve it this way. We have 2 unknowns (total boards, total defective) but no way to write 2 distinct equations.

But notice that we don't actually need to solve for either of the unknowns – we only need to find the percentage that are defective, which is really just the ratio of the defective boards to the total boards. So, if we could find just one linear equation relating the 2 unknowns, we could solve it for the ratio of the 2 unknowns.

Let t = the total number of boards produced and let d = the number that are defective (including those repaired and those not repaired). We are told that 10% of all defective boards are not repaired, which implies that 90% of all defective boards are repaired.

Therefore, 90% of d = (0.90)(d) = the number of defective boards that are repaired. But we also know something else about the number of defective boards that are repaired: it is equal to 4.5% of all boards produced, or t. So we also have (0.045)(t) = the number of defective boards that are repaired. Since they both represent the same thing, we can set these two expressions equal to each other: (0.90)(d) = (0.045)(t). We can't solve for t or d but we can solve for their ratio, or d/t , which will represent the percentage of all boards that are defective. First, divide both sides by 0.90 to get d = 0.045(t)/0.90, or d = 0.05 t. Then divide both sides by t to get d/t = 0.05, or 5%. So the answer is Choice (B).

Another approach is to use the Double Matrix Method.
This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of circuit boards, and the two characteristics are:
- defective or not defective
- repaired or not repaired

Since we're looking for a certain percentage, let's make things easy on ourselves and examine a population of 100 circuit boards.
We're told that 4.5 percent of all boards produced are found to be defective AND are repaired
4.5% of 100 = 4.5
So, we'll place 4.5 in the top-left box, since it represents circuit boards that are defective and have been repaired.



Next, we're told that 10 percent of all defective boards are sold without being repaired
Since we aren't told how many defective boards there are, let's let x = the total number of defective boards among the 100 boards
If there are x defective boards, then 0.1x represents the number of defective boards that are NOT repaired.
We get the following:


At this point, recognize that the two boxes in the top row must add to x
So, we can write: 4.5 + 0.1x = x
Subtract 0.1x from both sides to get: 4.5 = 0.9x
Divide both sides by 0.9 to get: 5 = x

If x = 5, then we know that there are 5 defective circuit boards out of a population of 100 circuit boards.

5/100 = 5%, so 5% of the circuit boards are defective.

Answer: B

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:



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