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
I struggle with these abstract operations
which operation is represented
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the equation given would only work if the unknown operation were multiplication, so we're really asked whether the unknown operation is multiplication. The solution below is taken from the GMATFix App.
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Target question: Is k~(l+m)=(k~l)+(k~m) for all numbers k, l and m?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
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,