Data Sufficiency

If r,s, and t are non zero integers, is (r^5)(S^3)(t^4) negative

1) rt is negative
2) s is negative

Hey mate,

To know whether (r^5)(S^3)(t^4) is negative, we need to know what kind of numbers 's' and 'r' are. 't' doesn't matter since it is to the power 4 and hence it is always positive.

Statement 1 says 'rt' is negative. It implies either 'r' or 't' is negative. As we don't know which one of them is negative and what kind of an integer 's' is, we can't decide upon the stem. Hence INSUFFICIENT

Statement 2 says s is negative. No clue on what 'r' & 't' are. Hence INSUFFICIENT.

Combining, we have rt is negative and s is negative.
If we assume r is negative, then the whole stem would turn positive as 's' is already negative.
If we assume 't' is negative, the stem would then be negative.

Hence, INSUFFICIENT.

IMO E

[email protected] wrote:If r,s, and t are non zero integers, is (r^5)(S^3)(t^4) negative

1) rt is negative
2) s is negative

The following combinations satisfy both statements.

Case 1: r=1, s=-1, t=-1
Here, r�s³t� = 1�(-1)³(-1)� = (1)(-1)(1) = -1.
In this case, r�s³t� < 0.

Case 2: r=-1, s=-1, t=1
Here, r�s³t� = (-1)�(-1)³(1)� = (-1)(-1)(1) = 1.
In this case, r�s³t� > 0.

Since the first case r�s³t� < 0, and in the second case r�s³t� > 0, the two statements combined are INSUFFICIENT.

The correct answer is E.