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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: 9866
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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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 $$55\leq{20}$$
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Joined: 18 Aug 2019
Posts: 6
Re: Given the inequalities above, which of the following CANNOT be........  [#permalink]

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01 Dec 2019, 00:45
generis wrote:
Quote:
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

Saumya2403 wrote:
Hi,

We have to find which answer choice does not satisfy whatever solution, or range of solutions, that we find for $$r$$.

The first inequality defines the solutions or ranges of solutions for $$r$$ in terms of $$s$$. The second inequality defines the solutions for $$s$$. So we should find out what to "plug in" for $$s$$ first, i.e. find out what $$s$$ might be in order to plug it into the first inequality.

1) $$|s|\leq{5}$$

Remove the absolute value bars, and the expression translates to the compound expression

$$-5\leq{s}\leq{5}$$

$$s$$ lies between -5 and 5, inclusive. Breaking it down further

Case One: $$s\geq {-5}$$, so we will plug in -5 for $$s$$ in the first inequality to test the limits of the possible solutions for $$r$$

Case Two: $$s\leq {5}$$, so we will plug in 5 for $$s$$

2) Back to the first inequality: $$3r\leq{4s + 5}$$

The solutions for $$r$$ depend on the solutions for $$s$$ that we just found.

Case One: if $$s\geq {-5}$$, then

$$3r\leq{4*(-5) + 5}$$

$$3r\leq {-15}$$

$$r\leq{-5}$$

That's one possible range of solutions for $$r$$.
<------------(-5)

Case Two: if $$s\leq {5}$$, then

$$3r\leq{4(5) + 5}$$

$$3r\leq{25}$$

$$r\leq{\frac{25}{3}}$$, or $$r\leq{8.33}$$

That's another range of solutions for $$r$$
<-------------0-------------8.33

So the second range of solutions covers the first:

< ----(-5)----0-------------(8.33)

3) Which answer choice does not lie in that range of solutions?

A) –20: that works. -20 is less than 8.33. KEEP

B) –5: that works. -5 is less than 8.33. KEEP

C) 0: that works. 0 is less than 8.33. KEEP

D) 5: that works. 5 is less than 8. KEEP

E) 20: that DOES NOT WORK. 20 is greater than 8.33. $$r$$ must be LESS than or equal to 8.33. On the number line, 20 lies to the right of where we have defined the solutions for $$r$$. 20 CANNOT be the value of $$r$$. It's too large. REJECT

Does that make sense?

Why cant we insert value of S in 3r<=4s+5 equation and check if s is between -5 and 5? when i do this, i got 13.75<=s for (a). Which I thought that was the answer
Re: Given the inequalities above, which of the following CANNOT be........   [#permalink] 01 Dec 2019, 00:45

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