If gh < 0 < gk, is g < 0?
1) k < h
2) 0 < h
OA D
Source: EMPOWERgmat
If gh < 0 < gk, is g < 0?
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When we have variables with inequalities, we have to make sure that we don't make assumptions about the SIGN, i.e. whether it's positive or negative.
If gh < 0 < gk, is g < 0?
We definitely can't divide through by g to get h < 0 < k, because if g were negative, the signs would flip to h > 0 > k. There are 2 possible scenarios:
1. g is positive, h is negative, and k is positive
2. g is negative, h is positive, and k is negative
If we're wondering whether g is negative, we could rephrase the question as: is h > 0 > k ?
1) k < h
We know from the question stem that h & k must have opposite signs (one positive, one negative). If k is less than h, then k must be negative, so we have scenario #2: g is negative, h is positive, and k is negative.
This is sufficient to answer the question.
2) 0 < h
Again, we know from the question stem that h & k must have opposite signs (one positive, one negative). If h > 0, then h must be positive, so we have scenario #2: g is negative, h is positive, and k is negative.
This is sufficient to answer the question.
The answer is D.
If gh < 0 < gk, is g < 0?
We definitely can't divide through by g to get h < 0 < k, because if g were negative, the signs would flip to h > 0 > k. There are 2 possible scenarios:
1. g is positive, h is negative, and k is positive
2. g is negative, h is positive, and k is negative
If we're wondering whether g is negative, we could rephrase the question as: is h > 0 > k ?
1) k < h
We know from the question stem that h & k must have opposite signs (one positive, one negative). If k is less than h, then k must be negative, so we have scenario #2: g is negative, h is positive, and k is negative.
This is sufficient to answer the question.
2) 0 < h
Again, we know from the question stem that h & k must have opposite signs (one positive, one negative). If h > 0, then h must be positive, so we have scenario #2: g is negative, h is positive, and k is negative.
This is sufficient to answer the question.
The answer is D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education