dave13
mau5
tulsa
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
s>4
t<3 (multiply by -1) --> -t>-3
Add both of them
Thus s-t >4-3
or s-t>1. As none of the options given are greater than 1, the answer is none.
A.
pushpitkc any idea why do we multiply t<3 by -1 and s>4 leave as it is ?
thank you
Hi
dave13 - I hope you have been slaying Quant dragons. At the least, dump some water on their heads.
I'm going to expand a little on
pushpitkc 's good answer. BTW, I have to add little dots at times to get terms to line up.
We multiply one of the inequalities by -1 because they have signs that point in different directions. The rule: you cannot add inequalities unless their signs point in the SAME direction.
Another rule: multiplying an inequality by any negative number changes the direction of the sign.
Another rule: Multiplying by -1 changes the sign but leaves the numbers and variables the same except with opposite signs.
We are asked to find \(s-t\). If we multiply \((t<3)\)by \(-1,\) we can make \(t\) negative (hang on) AND flip its sign so it points the same way as that of \(s\)
We've isolated \(s\) and \(t\) to get: \(s>4\) and \(t<3\)
One sign MUST change so we can add. We change the \(t\) inequality because we will get a sign flip AND a MINUS \(t\)
\(s\) +
\((-t)\)? Is \((s-t)\)
Mulitply \((t<3)\) by (-1). SIGN flips.
\((-1*t)>(-1*3)\)
\(-t > -3\)
Now add the two inequalities
··\((s > 4)\)
+\((-t>-3)\)
------------------
\(s - t> 1\)
Horizontally:
\(s + (-t) = (s-t)\)
\(4 + (-3) = (4-3) = 1\)
The > sign is between, thus \(s - t> 1\)
No answer choices are greater than 1. The answer is A. Hope that helps.
Technically, we can subtract (NOT add) inequalities with different signs. The sign on top controls.
··\((t<3)\)
-\((s>4)\)
============
\(t-s<-1\) ....Oh yay. Now we get to multiply by -1. We need (s-t), not (t-s).
\((-1*t)-(-1*s)<(-1*-1)\)
\(-t + s>1\)
\(s-t>1.\) Trust me. ADD.