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One out of every 1000 computer chips is defective. If 2 out of every 3

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One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 07 Jan 2015, 06:32
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Tough and Tricky questions: Word Problems.



One out of every 1000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?

A. 450
B. 900
C. 90,000
D. 450,000
E. 900,000

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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 07 Jan 2015, 10:38
Bunuel wrote:

Tough and Tricky questions: Word Problems.



One out of every 1000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?

A. 450
B. 900
C. 90,000
D. 450,000
E. 900,000

Kudos for a correct solution.

1 defective Chip per 1000
2 out of 30 defective chips have defective processors

Defective processors in first batch = 30
Defective chips in first batch = 30 * 30 / 2= 450

1 defective Chip per 1000, so total chips = 450 * 1000 = 450000

Ans D
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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 07 Jan 2015, 22:10
1
Answer = D. 450,000

Equation setup would be as follows:

\(\frac{30}{2} * 30 * 1000 = 450000\)

(Defective processor) * (Defective chips) * (Number of chips) = Total chips

Another way

................... Chips ......................... Defective .....................................

..................... 1000 ........................... 1 ....................................

.................... 1000*30 ...................... 30 .......... (To produce 30 defective chips, 30000 regular chips are to be made)

.................... 30000 .......................... 30 .................... 2 (Defective processor) ...........

..................... 30000*15 ...................... 30*15 ............. 30 (Multiplication factor is 15 to produce 30 defective processors)

Chips = 15 * 30000 = 450000
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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 08 Jan 2015, 01:17
1
Here we go -

2 out of every 30 defective chips have defective processors

1 out of every 15 defective chips has defective processor

30 out of every 450 defective chips have defective processors

**************************************************************

1 out of every 1000 computer chips is defective

450 out of every 450,000 computer chips are defective

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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 09 Jan 2015, 05:54
Bunuel wrote:

Tough and Tricky questions: Word Problems.



One out of every 1000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?

A. 450
B. 900
C. 90,000
D. 450,000
E. 900,000

Kudos for a correct solution.


OFFICIAL SOLUTION:

(D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 1000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/1000 = 450/y. Solve for y and you will get the total number of chips in the batch: 450,000.

The answer is (D).
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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 03 Jun 2017, 07:22
Bunuel wrote:

Tough and Tricky questions: Word Problems.



One out of every 1000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?

A. 450
B. 900
C. 90,000
D. 450,000
E. 900,000

Kudos for a correct solution.


Chips = 1000 , Defective Chips = 1
Chips = 30000 , Defective Chips = 30

Quote:
If 2 out of every 30 defective chips have defective processors


Chips = 30000 , Defective Chips = 30 , Defective Processors = 2

Quote:
there are 30 defective processors in the first batch, how many computer chips are there in the first batch?


When there are 2 Defective processors there are 30,000 chips
When there is 1 Defective processors there are 30,000/2 chips
When there are 30 Defective processors there are 30,000/2*30 chips = 45,000 Chips..

Thus, answer must be (D) 450,000
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One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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New post 03 Jun 2017, 07:36
Bunuel wrote:

Tough and Tricky questions: Word Problems.



One out of every 1000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?

A. 450
B. 900
C. 90,000
D. 450,000
E. 900,000

Kudos for a correct solution.

I thought of this question as a set within a set, which prevented me from choosing trap answer A.

Let D = number of defective parts generally

Let P = number of defective parts with bad processors (P is a subset of D)

Let T be total number of chips
Quote:
One out of every 1000 computer chips is defective.

\(\frac{D}{T}=\frac{1}{1000}\)
Quote:
If 2 out of every 30 defective chips have defective processors

\(\frac{2}{30}\) or\(\frac{1}{15}\)D are P, or P = \(\frac{1}{15}\)D
Quote:
there are 30 defective PROCESSORS in the first batch

P = 30, substitute that value:

30 = \(\frac{1}{15}\)D

D = 450 in the first batch
Quote:
how many computer chips are there in the first batch?

\(\frac{D}{T}=\frac{1}{1000}\)

\(\frac{450}{T}=\frac{1}{1000}\)

T = 450,000
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Re: One out of every 1000 computer chips is defective. If 2 out of every 3  [#permalink]

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