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 and 3t<9
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2s>8Needgmat 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
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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Here's another approach: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
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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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.
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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We see that s > 4 and that t < 3. Since s is always greater than t, the difference cannot be -1 or zero.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
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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