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

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by Jay@ManhattanReview » Fri Jul 19, 2019 11:58 pm
BTGmoderatorDC 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

OA A

Source: GMAT Prep
Given 2s > 8 and 3t < 9, we find that s > 4 and t < 3. So, s - t would be greater than 1. Thus, none of the values -1, 0, and 1 can be correct for it.

The correct answer: A

Hope this helps!

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by deloitte247 » Sun Jul 21, 2019 12:48 am
$$2s>8$$
$$s>\frac{8}{2}$$
$$s>4\ -----\ \left(i\right)$$

$$3t<9$$
$$t<\frac{9}{3}$$
$$t<3$$ $$t<3\ -----\ \left(ii\right)$$

Multiply eqn (ii) by -1, we have
$$-t>-3\ \ \ ----\left(iii\right)$$
Add up eqn (1i) and eqn (iii), we have
$$s-t>4-3$$
$$s-t>1$$
Therefore, none of i, ii, iii is > 1. Hence, the correct answer is option A
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by Scott@TargetTestPrep » Tue Jul 30, 2019 8:42 am
BTGmoderatorDC 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

OA A

Source: GMAT Prep

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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