A manufacturer of a certain type of screw rejects

pretty easy.. i just missed the part about what is accepted so was not focussing on the =

Silly Mistakes :-/

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

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)

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

Bunuel KarishmaB

Answer choice B also always satisfies the inequality. This question then will have 2 correct answers.

I think equal to sign should not be there in answer choice B so that it cannot be correct answer.

Also, it does not seem to be a 700-level ques. May be 700-level for the author of the ques but not for others! Please edit tag, if suitable.

We get daily practice ques basis our level of difficulty. These kind of incorrect tags misleads the right kind of difficulty ques that we deserve. A food for thought.

Please reply.

Acceptable range: (2.5 - 0.03) to (2.5 + 0.03)
So from 2.47 to 2.53.
So if the length lies within a distance of 0.03 from 2.5, it is acceptable. Any less or any more is rejected.
This leads to |k - 2.5| <= 0.03 in absolute value terms.

Note that |x - a| <= b gives the range of all values of x with are at most at a distance of 'b' from 'a'.

What is the range represented by |k — 0.03| <= 2.5?
k is at most at a distance of 2.5 from 0.03.
so acceptable values of k range from is 0.03 - 2.5 to 0.03 + 2.5. The highlighted gives a negative value for k. This is not ok.

Answer (E)

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