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

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29 Nov 2012, 10:32

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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

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: \(-0.03\leq{k-2.5}\leq{0.03}\) --> \(|k-2.5|\leq{0.03}\).

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.

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

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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

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

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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

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

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06 Nov 2014, 22:21

Hello from the GMAT Club BumpBot!

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

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25 Nov 2015, 10:14

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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

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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01 Jan 2017, 12:24

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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