December 2004 LSAT Section 4 Question 20

If Nation Z exports tea and wheat, then which one of the following must be true?

hatemz on February 26, 2020

I thought "only if" introduces necessary conditions

Why can't Y have Soybeans without X? I thought necessary conditions can still exist without sufficient, and "only if" introduced necessary.. For example, why cant this be a solution: X: R O Y: S O Z: T W

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Irina on February 27, 2020

@hatemz,

If and only if is bidirectional.

Nation X exports soybeans if, but only if, Nation Y does also.

We can break it down into two separate statements:

(1) If Y exports soybeans THEN X exports soybeans.

Y -> X

(2) ONLY IF Y exports soybeans THEN X exports soybeans.

X -> Y

~ Nation Y< - > ~ Nation X
Nation X < -> Nation Y

meaning that either both X & Y export soybeans or neither one of them.