If *triangle* denotes one of the arithmetic operations

[nga.kam.lai]

Hi, can someone please offer some insight on my line of reasoning for the below question?

If *triangle* denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 *triangle* 2 ?

(1) n *triangle* 0 = n for all integers n.
(2) n *triangle* n = 0 for all integers n.

The answer is B.

My reasoning was:

(1) n + 0 = n so Yes
n - 0 = n so Yes
so therefore (1) is insufficient

(2) n - n = 0 so Yes
n n n = n ^ 2 - appears No however when n = 0, n x n = 0
so therefore I thought that (2) was insufficient as well. Is my reasoning above incorrect? Is 0 not an integer?

thanks,
Jen

[rohit801]

Jen,
Let's look at #2:

(2) n *triangle* n = 0 for all integers n.
Now, *triangle* denotes one of the four arithmetic operations addition, subtraction, multiplication and division. So, we need to find out which of these operations would make the statement true FOR ALL N.

1. Addition: if n=0, then it works BUT for all non zero n, #2 doesn't hold true. So, Addition is OUT

2. Multipication: if n=0, then it works BUT for all non zero n, #2 doesn't hold true. So, Multipication is OUT

3. Division: Since division by zero is nor defined, *triangle* can't be the division operation.

4. Subtraction: n-n wil be 0 FOR ALL n. So, Subtraction is the only operator which will SATISFY the conditions of #2.

The questions is: what is the value of 1 *triangle* 2

So, our task to find a DEFINITE value of*triangle* that works for all cases, all the time. You can see that in Statement #1:

(1) n *triangle* 0 = n for all integers n.
The operations "Addition" and "Subtraction" Work for ALL THE CASES, hence it is Insufficient.

Hope that helps....

[RonPurewal]

Jen,
Let's look at #2:

(2) n *triangle* n = 0 for all integers n.
Now, *triangle* denotes one of the four arithmetic operations addition, subtraction, multiplication and division. So, we need to find out which of these operations would make the statement true FOR ALL N.

1. Addition: if n=0, then it works BUT for all non zero n, #2 doesn't hold true. So, Addition is OUT

2. Multipication: if n=0, then it works BUT for all non zero n, #2 doesn't hold true. So, Multipication is OUT

3. Division: Since division by zero is nor defined, *triangle* can't be the division operation.

4. Subtraction: n-n wil be 0 FOR ALL n. So, Subtraction is the only operator which will SATISFY the conditions of #2.

The questions is: what is the value of 1 *triangle* 2

So, our task to find a DEFINITE value of*triangle* that works for all cases, all the time. You can see that in Statement #1:

(1) n *triangle* 0 = n for all integers n.
The operations "Addition" and "Subtraction" Work for ALL THE CASES, hence it is Insufficient.

Hope that helps....

this is not a bad analysis, but there's one problem with it: namely, you're neglecting the fact that you have to answer the question in the problem.

for instance, if the problem had asked for 3 Δ 0, instead of 1 Δ 2, then statement 1 would be sufficient, even though it allows two operations!
viz., statement 1 allows both addition and subtraction. however, if the problem asked for 3 Δ 0, both of these values would be 3, so the statement would be sufficient.

in this problem, if you just think in terms of "find the operation that Δ represents", then you get lucky, because the four different operations give four different values for 1 and 2.