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If 2s > 8 and 3t < 9, which of the following could be the va

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If 2s > 8 and 3t < 9, which of the following could be the va [#permalink] New post 29 Jul 2020, 10:45
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If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III


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[Reveal] Spoiler: OA

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Re: If 2s > 8 and 3t < 9, which of the following could be the va [#permalink] New post 29 Jul 2020, 11:08
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Carcass wrote:
If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. II and III


Kudos for the right answer and explanation


Given: 2s > 8
Divide both sides by 2 to get: s > 4

Given: 3t < 9
Divide both sides by 3 to get: t < 3

NOTE: If we have two inequalities with the inequality symbols facing in the same direction, we can add the inequalities to learn something new.

So, take t < 3 and multiply both sides by -1 to get: -t > -3 [aside: when we divide or multiply both sides of an inequality by a NEGATIVE value, we mist REVERSE the symbol]

We now have:
s > 4
-t > -3

When we ADD these two inequalities, we get:
s - t > 1

If s - t > 1, then:
I) s - t CANNOT equal -1
II) s - t CANNOT equal 0
III) s - t CANNOT equal 1

Answer: A
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Re: If 2s > 8 and 3t < 9, which of the following could be the va [#permalink] New post 29 Jul 2020, 11:13
So, 2s > 8 => s > 4
and, 3t < 9 => t < 3 => -t > -3

Adding these two we get,
s - t > 4 - 3
=> s-t > 1

So, the answer is A.
Re: If 2s > 8 and 3t < 9, which of the following could be the va   [#permalink] 29 Jul 2020, 11:13
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If 2s > 8 and 3t < 9, which of the following could be the va

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