carcass wrote:
Is \(xm < ym\) ?
(1) \(x > y\)
(2) \(m < 0\)
Target question: Is xm < ym?Another approach is to
rephrase the target question.
Take the inequality and subtract ym from both sides to get:
xm - ym < 0Factor out the m to get
m(x - y) < 0In other words....
REPHRASED target question: Is m(x - y) a NEGATIVE value? Statement 1: x > y Subtract y from both sides to get: x - y > 0
So, x - y is a POSITIVE value
Does this provide enough information to determine whether or not
m(x - y) a NEGATIVE value?No. We still don't know anything about the value of m
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: m < 0 In other words, m is NEGATIVE
Does this provide enough information to determine whether or not
m(x - y) a NEGATIVE value?No. We don't know anything about the value of (x - y)
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x - y is a POSITIVE value
Statement 2 tells us that m is a NEGATIVE value
So, m(x - y) = (NEGATIVE)(POSITIVE) = some NEGATIVE VALUE
In other words,
m(x - y) is definitely a NEGATIVE valueSince we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer:
RELATED VIDEO FROM OUR COURSE
In this case, we can subtract ym from both sides even though we don't know their signs?