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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9558
Location: Pune, India
Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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04 Apr 2019, 22:52
AlN 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

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

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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.

Regards,
Rishav
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Joined: 05 Feb 2018
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Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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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 $$55\leq{20}$$
Re: Given the inequalities above, which of the following CANNOT be........   [#permalink] 20 Aug 2019, 09:42

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