gmat1220 wrote:
I have a similar question from OG12 wherein the values are contradicting the question stem. Pls take a look at this OG12 #125. While evaluating second statement, I can assume k,l,m to be all zero since the stem uses "all" - for all the number k,l,m. Lets analyze statement 2)
125. 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.
From 2)
When k = l = m = 0 then the answer is YES
op = "minus"
k op (l + m) = (k op l) + (k op m) = 0
LHS = 0 = RHS.
However when k,l and m are non zero then the answer is NO. I have a YES and NO. So the answer should be E. But the official answer is D. Is there is problem with my analysis? Pls weigh in.
125. 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.
Question: Is k ° (l + m) = (k ° l ) + (k ° m) for all numbers k, l, and m?
(1) We understand that had ° been '+' or '*', k ° 1 = 1° k for ALL values of k. Hence ° must be subtraction '-'
Ques: Is k - (l + m) = (k - l ) + (k - m) for all numbers k, l, and m?
Ans: Definitely No. This equation does not hold for ALL numbers.
For some numbers the equation holds (e.g. when k = 0, l= 0, m = 0), for others it doesn't (e.g. k = 1, m = 0, l = 2).
(2) ° represents subtraction.
Ques: Is k - (l + m) = (k - l ) + (k - m) for all numbers k, l, and m?
Ans: Definitely No. This equation does not hold for ALL numbers.
For some numbers the equation holds (e.g. when k = 0, l= 0, m = 0), for others it doesn't (e.g. k = 1, m = 0, l = 2).
Both statements alone are sufficient to give us a definite answer to the question. The question explicitly says "Is it true for all numbers?" You answer with "No. It is not true for ALL numbers. For some numbers it is true, for others it is not." Valid and clear answer. Answer (D)
(Tip: Focus on what the question is asking. The question didn't ask you - "Is it true?" It asked you - "Is it true for all numbers?"