There are exactly three stepsSteps 1, 2, and 3, in that orderused to

Question

There are exactly three steps—Steps 1, 2, and 3, in that order—used to assemble light bulbs at a particular factory. Some of the bulbs fail to make it through every step in the assembly process; if a bulb fails a given step, it will not proceed to the next step. For the most recent month, the factory manager knows the number of bulbs that were started as well as each of the following:

A = the number of bulbs making it through Step 1 only;

B = the number of bulbs making it through at least Step 2;

C = the number of bulbs making it through all three steps.

The manager wishes to know the fraction of the bulbs that made it through Step 1 that also made it through all three steps. In the table, choose for Numerator and Denominator the expressions that will give the factory owner the fraction desired. Make only two selections, one in each column.

ID: 700176

Bismuth83 · Accepted Answer

1. Draw out the process described in the problem.

2. Mark on the diagram what the manager wants us to find. D and N are the denominator and numerator, respectively.

3. Note the known number of bulbs for the most recent month (A,B,C).

4. Looking at the previous 2 diagrams, notice that N = C and D = A + B. So, the answer is \(\frac{C}{A+B}\).

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KarishmaB · Answer

A - the number of bulbs that made it through Step 1 ONLY. So they made it through Step 1 but not through Step 2. So they failed at step 2 so were discarded. Say there were 100 of these. 
B - The number of bulbs that made it through at least Step 2. So they are the ones that succeeded at steps 1 and 2 both. What happened at step 3, we don't know. Say there were 500 of these.

This means that  100 + 500 = 600 bulbs came out of Step 1 but 100 were discarded at Step 2 while 500 succeeded at Step 2.  This is the most important point in this question.

C - The ones that made it through all 3 steps. Some part of the 500 that succeeded at step 3 too. Say 450.

The fraction of the bulbs that made it through Step 1 that also made it through all three steps = 450/600
Hence, ANSWER will be  \frac{C}{(A+B)}

chetan2u · Answer

A = the number of bulbs making it through Step 1 only;  A gives ONLY Step 1

B = the number of bulbs making it through at least Step 2;  B gives AT LEAST Step 2, so this will include all those who went through Step 2 ( would include those clearing all three too)

C = the number of bulbs making it through all three steps.  C gives those pass all three

The manager wishes to know the fraction of the bulbs that made it through Step 1 that also made it through all three steps.

So, Denominator: bulbs that made it through Step 1. This would be equal to Only Step 1 (but not beyond) + At least Step 2 ( would include all clearing step 1 and then Step 2) = A + B
Numerator: All three steps is given by C.

Answer =  \frac{C}{A+B}

Elite097 · Answer

KarishmaB  if we use A+B as denominator won't there be an overlap of bulbs in A and B also?

Elite097 · Answer

KarishmaB  makes sense now, so basically are we saying each of these 600 bulbs are unique and not being double or triple counted?

Anonymous · Answer

I built correctly the fraction but I don't get it why in the denominator isn't it the sum of all 3 since if they passed every step or at least the first 2, they must have passed step 1. Could you please help me clear this out?

chetan2u · Answer

A is only step 1. 
B is at least step 2, so step 2 + step 3
C is step 3.

Total is 1+2*3 = 1+(2+3) = A+B

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Anonymous · Answer

Yeah but since B passed at least step 2, it means that it has gone through step 1 and made it till step 3 (since it says  at least step 2 ).

s1   yes   / yes/     yes
 s2   no    yes      yes
 s3   no    yes      yes
      A        B           C

So, B and C are essentially the same and therefore in the denominator we want those who passed only step 1 (A) and those who passed beyond step 1 (B,C which is at it's shown above 2C or 2B).

The fraction finally becomes C/(A + 2B).

chetan2u · Answer

B contains C, so why should you add C again. 
B is not equal to C, it is B=C+those who did not move ahead of step 2 but crossed 1

Anonymous · Answer

Partially I agree,  chetan2u  that there is no need to add another time C. But I've stuck in the other part, since we know from the stem that in order to move on to the next step the bulb has to make it through the current one.

So, if it has make it through at least the second (as it is mentioned for B), this means that it has passed the first one (to reach the 2nd) and managed to complete the second so as to move on to the final stage and complete it. That's exactly what happened with C as it mentions that C is the bulbs that made it through all 3 steps.

For this reason, I cannot understand why C is subset of B and they are not equal?

Can anyone give another perspective in the explanation - reasoning ?  manasp35   GMATCoachBen   KarishmaB   avigutman   chetan2u

manasp35 · Answer

but has it passed the third step ? C includes bulbs that have passed all 3 stages. B includes bulbs that passed all three stages + bulbs that passed only 2 stages but failed at 3rd stage.

Anonymous · Answer

so it's possible that some of the B bulbs moved on to the final stage (so as to satisfy the "at least two") but they failed to complete it... now I got it, thanks a lot !!

KarishmaB · Answer

I have provided my perspective in the comment above.

cookiemonsterpsy · Answer

took 9 mins to solve this got it right but my brain hurts lol

Gemmie · Answer

Total number of bulbs making through Step 1 
= Number of bulbs making through Step 1 only + Number of bulbs making through more than Step 1 (i.e at least Step 2)
= A + B

Fraction =  \frac{C}{A + B}

PB005 · Answer

Attaching a solution (image):

ChiranjeevSingh · Answer

Passage Analysis

There are exactly three steps—Steps 1, 2, and 3, in that order—used to assemble light bulbs at a particular factory.

A sequence of three steps to assemble light bulbs at a factory.

Some of the bulbs fail to make it through every step in the assembly process; if a bulb fails a given step, it will not proceed to the next step.

Some bulbs do not go through every step. If a bulb fails a given step, it does not go to the next step.

Essentially, some bulbs can be discarded during this process of assembling at any step.

For the most recent month, the factory manager knows the number of bulbs that were started as well as each of the following:

For the last month, the manager knows the bulbs that were started and the following pieces of information.

A = the number of bulbs making it through Step 1 only;

A  essentially depicts the number of bulbs that were discarded after going through step one, so these bulbs do not go through step two and step three.

B = the number of bulbs making it through at least Step 2;

B  is the number of bulbs that definitely go through step two and may go through step three also.

It's important to understand that these bulbs are different from the bulbs counted as  A . Those  A  bulbs do not even go through step two. So if you are looking at the total number of bulbs, that would be  A + B  + those bulbs which failed to go through even step one.

It is also important to understand that these  B  bulbs include the bulbs that are going through all three steps and the bulbs that are stopping after going through step two.

C = the number of bulbs making it through all three steps.

C  is the number of bulbs that go through all three steps. So, if I try to put things together, I can understand that  B minus C  would be the number of bulbs that are taken out after going through step 2.

Question Analysis

The manager wishes to know the fraction of the bulbs that made it through Step 1 that also made it through all three steps.

Here the  fraction  consists of the  denominator , which is the number of bulbs going through step one.

What would this number be? This would be  A + B . Here  A  depicts those bulbs which stop after step 1, and  B  depicts all the bulbs that also go through other steps. So  A + B  is the number of all the bulbs that go through step one.

The  numerator  will be the bulbs that are making it through all three steps, which we are given as  C .

Therefore, the fraction is  C / (A + B) .

There are exactly three stepsSteps 1, 2, and 3, in that orderused to

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