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07 Oct 2025, 00:14
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
89% (01:04) correct
11%
(01:18)
wrong
based on 161
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Not Attempted Yet
If \(x > 2\) and \(x < 3\), then which of the following is positive?
I. \((x – 2)(x – 3)\)
II. \((2 – x)(x – 3)\)
III. \((2 – x)(3 – x)\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
I. \((x – 2)(x – 3)\)
II. \((2 – x)(x – 3)\)
III. \((2 – x)(3 – x)\)
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
07 Oct 2025, 00:47
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Let's analyze each expression for 2 < x < 3:
I. (x - 2)(x - 3)
x - 2 > 0 (positive)
x - 3 < 0 (negative)
Product: positive * negative = negative
II. (2 - x)(x - 3)
2 - x < 0 (negative)
x - 3 < 0 (negative)
Product: negative * negative = positive
III. (2 - x)(3 - x)
2 - x < 0 (negative)
3 - x > 0 (positive)
Product: negative * positive = negative
Final answer: II only
So, the correct answer is option B.
I. (x - 2)(x - 3)
x - 2 > 0 (positive)
x - 3 < 0 (negative)
Product: positive * negative = negative
II. (2 - x)(x - 3)
2 - x < 0 (negative)
x - 3 < 0 (negative)
Product: negative * negative = positive
III. (2 - x)(3 - x)
2 - x < 0 (negative)
3 - x > 0 (positive)
Product: negative * positive = negative
Final answer: II only
So, the correct answer is option B.
07 Oct 2025, 06:53
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Bunuel
When x is greater than 2 and less than 3. Let’s assume the value of x = 2.5
Let’s navigate through each of the options to see which are positive and which are not positive.
I. \((x – 2)(x – 3)\)
substitute the value of x = 2.5 in the above equation, we get
(+ve) ( -ve) = -ve
Hence, False.
II. \((2 – x)(x – 3)\)
substitute the value of x = 2.5 in the above equation, we get
(-ve) (-ve) = +ve
Hence, True.
III. \((2 – x)(3 – x)\)
substitute the value of x = 2.5 in the above equation, we get
(- ve) (+ve) = -ve .
Hence, False.
II only.
Option B
