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,