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Given the inequalities above, which of the following CANNOT be........

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Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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New post 04 Apr 2019, 22:52
AlN wrote:
VeritasKarishma wrote:
nalinnair wrote:
\(3r\leq{4s + 5}\)
\(|s|\leq{5}\)

Given the inequalities above, which of the following CANNOT be the value of r?

A. –20
B. –5
C. 0
D. 5
E. 20


To get the range of r, we need the value of s.
But what we have is the range for s. Let's evaluate it:

\(|s|\leq{5}\)
This means \(-5 \leq s \leq 5\)

Check at the extremes.
s = -5 gives \(3r\leq{4*-5 + 5}\) so we get \(r\leq{-5}\)
s = 5 gives \(3r\leq{4*5 + 5}\) so we get \(r\leq{8.33}\)

Note that any intermediate value of s will ensure that r is less than 8.33. The maximum value that s can take is 5 and corresponding to that, the max value r can take is 8.33.
Hence r can never be 20
Answer (E)



I am not able to understand the highlighted part . isnt r>=-5


Assuming s= -5, we get
\(r\leq{-5}\)

From where do you get \(r\geq{-5}\)?
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Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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New post 05 Aug 2019, 09:44
Simplest way to solve this:

Given | s | <= 5
=> -5 <= s <= 5
=> -20 <= 4s <= 20 ( Sign remains unchanged if the inequalities divided/multiplied/added or subtracted by SAME +VE NUMBER)
=> -15 <= 4s + 5 <= 25
=> -5 <= (4s + 5)/3 <= 8.33

Now we know that r <= (4s+5)/3
so r's range can be r <= -5, -5 <=r <= (4s+5)/3 <=8.33

Now we know that r can NEVER exceed 8.33 -> 20 is our ANSWER.

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Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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New post 20 Aug 2019, 09:42
nalinnair wrote:
\(3r\leq{4s + 5}\)
\(|s|\leq{5}\)

Given the inequalities above, which of the following CANNOT be the value of r?

A. –20
B. –5
C. 0
D. 5
E. 20


\(3r\leq{4s + 5}\) --> \(3r-5\leq{4s}\)

\(|s|\leq{5}\) --> \({-5}\leq s\leq{5}\)

MAX S = 5, so \(3r-5\leq{20}\)
Testing E, r = 20 gives us a false statement \(55\leq{20}\)
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Re: Given the inequalities above, which of the following CANNOT be........   [#permalink] 20 Aug 2019, 09:42

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