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
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If 2s > 8 and 3t < 9, which of the following could be
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BTGmoderatorDC
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Jay@ManhattanReview
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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.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
The correct answer: A
Hope this helps!
-Jay
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deloitte247
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$$2s>8$$
$$s>\frac{8}{2}$$
$$s>4\ -----\ \left(i\right)$$
$$3t<9$$
$$t<\frac{9}{3}$$
$$t<3$$ $$t<3\ -----\ \left(ii\right)$$
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
$$s>\frac{8}{2}$$
$$s>4\ -----\ \left(i\right)$$
$$3t<9$$
$$t<\frac{9}{3}$$
$$t<3$$ $$t<3\ -----\ \left(ii\right)$$
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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Scott@TargetTestPrep
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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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