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.

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.

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