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2s>8 and 3t<9

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by GMATGuruNY » Wed Sep 28, 2016 9:24 am
Needgmat wrote:If 2s>8 and 3t<9, which of the following could be the value of s-t?

1) -1

2) 0

3) 1

A) None

B) 1 only

C) 2 only

D) 3 only

E) 2 and 3


OAA
2s>8
s>4.

3t<9
t<3.

If s=4 and t=3, then s-t = 4-3 = 1.
Since s is actually GREATER THAN 4, and t is actually LESS THAN 3, the distance between s and t cannot actually be 1 but must be GREATER THAN 1.
Thus, none of the listed differences is possible.

The correct answer is A.
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by Brent@GMATPrepNow » Wed Sep 28, 2016 9:42 am
Needgmat 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

OAA
Here's another approach:

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

RELATED VIDEOS
- Inequalities - Part I: https://www.gmatprepnow.com/module/gmat ... /video/979
- Inequalities - Part II: https://www.gmatprepnow.com/module/gmat ... /video/982
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by Matt@VeritasPrep » Thu Sep 29, 2016 6:39 pm
s > 4
3 > t

so

s > 4 > 3 > t

and s - t > 0. That means it's either (III) or nothing. But s - t = 1 is impossible, since s > 4 > 3 > t implies that the gap between s and t is greater than the gap between 4 and 3! So s - t > 4 - 3, and there are no solutions listed.
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by Jeff@TargetTestPrep » Mon Feb 12, 2018 4:20 pm
Needgmat wrote:If 2s>8 and 3t<9, which of the following could be the value of s-t?

1) -1

2) 0

3) 1

A) None

B) 1 only

C) 2 only

D) 3 only

E) 2 and 3
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, paying attention 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 is greater than 1.

Answer: A

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