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A manufacturer of a certain type of screw rejects

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A manufacturer of a certain type of screw rejects  [#permalink]

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New post 29 Nov 2012, 10:32
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62% (01:57) correct 38% (02:09) wrong based on 349 sessions

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A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

A. |k + 0.03| > 2.5
B. |k — 0.03| <= 2.5
C. |k — 2.5| > 0.03
D. |k — 2.5| >= 0.06
E. |k — 2.5| <= 0.03
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 29 Nov 2012, 10:47
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ritumaheshwari02 wrote:
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

A. lk + 0.03| > 2.5
B. lk — 0.03| <= 2.5
C. lk — 2.5| > 0.03
D. lk — 2.5| >= 0.06
E. lk — 2.5| <= 0.03


Given that \(2.5-0.03\leq{k}\leq{2.5+0.03}\). Subtract 2.5 from all parts: \(-0.03\leq{k-2.5}\leq{0.03}\) --> \(|k-2.5|\leq{0.03}\).

Answer: E.
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 04 Dec 2012, 20:28
GMATClub Forum has been such a great teacher and tutor. Kudos!

(1) Simply get the center of the range value of k ==> 2.5
(2) Flip the sign and append to k ==> | k - 2.5 |
(3) Get the distance of the center from one far end: Distance = (2.5 + 0.03) - Center = 2.5 + 0.03 - 2.5 = 0.03 (Just to illustrate a point)
(4) Now we select an inequality sign. We are concerned with the values of k within the range.
- If within, select "<"
- If outside range, select ">"
- If inclusive, include "=" sign

Answer: |k - 2.5| <= 0.03
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 18 Jun 2013, 08:28
pretty easy.. i just missed the part about what is accepted so was not focussing on the =

Silly Mistakes :-/
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 18 Jun 2013, 21:04
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ritumaheshwari02 wrote:
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

A. |k + 0.03| > 2.5
B. |k — 0.03| <= 2.5
C. |k — 2.5| > 0.03
D. |k — 2.5| >= 0.06
E. |k — 2.5| <= 0.03



Using the distance concept of mod, we are given that k is a point lying within .03 cms from 2.5.

This gives us |k — 2.5| <= 0.03

For a discussion of the distance concept, check out this link: http://www.veritasprep.com/blog/2011/01 ... edore-did/
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 01 Jul 2013, 09:04
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

A. |k + 0.03| > 2.5
B. |k — 0.03| <= 2.5
C. |k — 2.5| > 0.03
D. |k — 2.5| >= 0.06
E. |k — 2.5| <= 0.03

So, let's go through this step by step:

"rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters."

In other words, any screw that is less than: 2.50 - 0.03 = 2.47 or greater than 2.50 + 0.03 = 2.53 will be rejected.

If k represents the length of a screw

In other words, "K" is an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:
2.47 ≤ K ≤ 2.53

You can rule out answers with < or > as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.

Let's look at (E):

|k — 2.5| <= 0.03

For the positive case: k - 2.5 ≤ 0.03 ===> k ≤ 2.53
For the negative case: -(k - 2.5) ≤ 0.03 ===> -k +2.5 ≤ 0.03 ===> - k ≤ -2.47 ===> k ≥ 2.47

2.47 ≤ k ≤ 2.53

(E)
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 26 Nov 2015, 02:14
ritumaheshwari02 wrote:
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.5 — 0.03 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?

A. |k + 0.03| > 2.5
B. |k — 0.03| <= 2.5
C. |k — 2.5| > 0.03
D. |k — 2.5| >= 0.06
E. |k — 2.5| <= 0.03


Given:
Length = k

\({2.5 - 0.03} \leq k \leq {2.5 + 0.03}\)
\({-0.03} \leq k - 2.5 \leq {0.03}\)

Or simply
\(|k - 2.5| \leq 0.03\)
Option E
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Re: A manufacturer of a certain type of screw rejects  [#permalink]

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New post 18 Mar 2019, 03:07
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Re: A manufacturer of a certain type of screw rejects   [#permalink] 18 Mar 2019, 03:07
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