If b is greater than 1, which of the following must be negative?
A. (2 - b)(b - 1)
B. (b - 1)/3b
C. (1 - b)^2
D. (2 - b)/(1 - b)
E. (1 - b^2)/b
The OA is E.
Please, can any expert assist me with this PS question? I'm really confused with it. Thanks in advanced.
If b is greater than 1, which of the following must be...
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Hi LUANDATO,If b is greater than 1, which of the following must be negative?
A. (2 - b)(b - 1)
B. (b - 1)/3b
C. (1 - b)^2
D. (2 - b)/(1 - b)
E. (1 - b^2)/b
The OA is E.
Please, can any expert assist me with this PS question? I'm really confused with it. Thanks in advanced.
Let's take a look at your question.
We will check each option one by one that if b is a number greater than 1, whether the result is negative or positive.
Lets start from Option A.
(2 - b)(b - 1)
Let b = 2
(2-2)(2-1) = zero
We will discard this, since zero is neither positive nor negative.
Option B:
(b - 1)/3b
For b = 2
(2-1)/3(2)=1/6 = POSITIVE
Discard option B.
Option C:
(1 - b)^2
For b = 2
(1-2)^2= (-1)^2 = 1 = POSITIVE
Discard Option C
Option D:
(2 - b)/(1 - b)
For b = 2
(2 - 2)/(1 - 2) = Zero
Discard option D, since zero is neither positive nor negative.
Option E:
(1 - b^2)/b
For b = 2
(1 - 2^2)/2 = (1-4)/2 = -3/2 = NEGATIVE
Therefore, Option E is correct.
Hope it helps.
I am available if you'd like any follow up.
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NOTE: this is one of those questions that require us to check/test each answer choice.LUANDATO wrote:If b is greater than 1, which of the following must be negative?
A. (2 - b)(b - 1)
B. (b - 1)/3b
C. (1 - b)²
D. (2 - b)/(1 - b)
E. (1 - b²)/b
In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.
For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions
So, let's start with E: (1 - b²)/b
Factor the numerator to get: (1 + b)(1 - b)/b [the numerator 1 - b² is a DIFFERENCE OF SQUARES, which can be factored]
Since b > 1, we know that...
(1+b) is POSITIVE
(1-b) is NEGATIVE
b is POSITIVE
So, (1 - b²)/b = (1 + b)(1 - b)/b
= (POSITIVE)(NEGATIVE)/(POSITIVE)
= (NEGATIVE)/(POSITIVE)
= NEGATIVE
Answer: E
Cheers,
Brent