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

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Re: If 2s > 8 and 3t < 9, which of the following could be the value of s-t?

by Brent@GMATPrepNow » Sat Apr 04, 2020 2:35 pm
BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:30 am
 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

Answer: A
Source: GMATPrep test
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 value of s-t?

by Scott@TargetTestPrep » Mon Apr 27, 2020 3:45 am
BTGModeratorVI wrote: ↑
Fri Apr 03, 2020 9:30 am
 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

Answer: A
Source: GMATPrep test
Solution:

We see that s > 4 and that t < 3. Since s is always greater than t, the difference cannot be -1 or zero.

Furthermore, since s > 4 and t < 3, we see that s and t are more than 1 unit apart, so the difference cannot be 1.

Alternate Solution:

Let’s divide each side of 2s > 8 by 2: s > 4

Let’s divide each side of 3t < 9 by -3, being sure to change the direction of the inequality since we are dividing by a negative number: -t > -3

Let’s add the two inequalities together: s - t > 1

We see that none of the provided numbers are greater than 1.

Answer: A

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