LulaBrazilia wrote:If ~ represents one of the operations +, -, and *, is k~(l+m)=(k~l)+(k~m) for all numbers k, l and m?
1) k~1 is not equal to 1~k for some numbers k.
2) ~ represents subtraction
Target question: Is k~(l+m)=(k~l)+(k~m) for all numbers k, l and m?
Given: ~ represents one of the operations +, -, and *
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Let's replace ~ with each of the three operations to see what happens
~ represents addition: Is it the case that k + (l + m) = (k + l) + (k + m)?
When we simplify, we get k + l + m = 2k + l + m (hmmmm...)
So, when ~ represents addition, it is
not necessarily the case that k~(l+m)=(k~l)+(k~m)
~ represents subtraction: Is it the case that k - (l + m) = (k - l) + (k - m)?
When we simplify, we get k - l - m = 2k - l - m (hmmmm...)
So, when ~ represents subtraction, it is
not necessarily the case that k~(l+m)=(k~l)+(k~m)
~ represents multiplication: Is it the case that k * (l + m) = (k * l) + (k * m)?
When we simplify, we get kl + km = kl + km (PERFECT!)
So, when ~ represents multiplication, it
IS the case that k~(l+m)=(k~l)+(k~m)
So, the
target question is essentially asking "Does ~ represent multiplication?" So, let's rephrase the target question ...
REPHRASED target question: Does ~ represent multiplication?
At this point, it's the statements are relatively easy to analyze.
Statement 1: k~1 is not equal to 1~k for some numbers k.
Check Multiplication
Multiplication: Is k * 1 ≠1 * k for some values of k? No. k*1 ALWAYS equals 1*k
So,
~ definitely does NOT represent multiplication
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: ~ represents subtraction
In other words,
~ does NOT represent multiplication
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
D
Cheers,
