Question

Of the numbers r + s, r – s, r × s, and r/s,which is greast?(1) r = s = 1(2) r – s is the least of the numbers.a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d. EACH statement ALONE is sufficient.e. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer 1

a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b

Explanation:

Lets talk about propositions in general. If you have the propositions "p,q" When we say that "p" is sufficient, that's an other way to say that,

p⇒q

Let me give you an other brief example, lets say you have the propositions "x,y", when we say that "x" is sufficient, that means that

x⇒y

IMPORTANT.

Notice that if I say that "p" is sufficient, that does not imply that "q" is sufficient, in other words, If I know that

p⇒q

NOT NECESARILLY

q⇒p

Lets work on the problem.

Step 1.

When you say that (1) is sufficient it means that

(1)⇒(2)

In other words

"If r = s = 1 then r – s is the least of the numbers"

That's true because, if r=s=1 , then, r+s = 2, r-s = 0, and r × s = 1, r/s = 1, so, in fact, r-s = 0 is the least of the numbers.

Step 2.

Notice that (2) is NOT sufficient.

(2) DOES NOT imply (1)

You just have to give a counter example.

For example r=s=2, r+s = 4, r × s = 4, r/s = 1 and r-s = 0, so, in fact, r-s is the least of the numbers, but is NOT true that r=s=1.