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If x > 2 and x < 3, then which of the following is positive?
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28 Mar 2019, 13:25
28 Mar 2019, 13:25
Expert Reply
00:00
Question Stats:
90% (00:49) correct
9% (01:17) wrong based on 22 sessions
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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
Re: If x > 2 and x < 3, then which of the following is positive?
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30 Mar 2019, 11:41
30 Mar 2019, 11:41
1
Expert Reply
So x is between 2 and 3.
X is more than 2, so x – 2 will be positive. X is less than 3, so x – 3 will be negative. (x – 2)(x – 3), then, is a positive times a negative, and is thus negative.
X is more than 2, so 2 – x will be negative. We already know that x – 3 is negative, so (2 – x)(x – 3) is a negative times a negative, and is thus definitely positive.
X is less than 3, so 3 – x will be positive. 2 – x is negative, so (2 – x)(3 – x) is a negative times a positive, which is negative.
We can see then, that only (2 – x)(x – 3) is positive. The answer is choice B, II only.
X is more than 2, so x – 2 will be positive. X is less than 3, so x – 3 will be negative. (x – 2)(x – 3), then, is a positive times a negative, and is thus negative.
X is more than 2, so 2 – x will be negative. We already know that x – 3 is negative, so (2 – x)(x – 3) is a negative times a negative, and is thus definitely positive.
X is less than 3, so 3 – x will be positive. 2 – x is negative, so (2 – x)(3 – x) is a negative times a positive, which is negative.
We can see then, that only (2 – x)(x – 3) is positive. The answer is choice B, II only.
If x > 2 and x < 3, then which of the following is positive?
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Updated on: 31 Jul 2024, 03:11
Updated on: 31 Jul 2024, 03:11
If you plot this in the number line x-3 term is always negative
So options 1 and 2 is not right
only the product of 2-x and 3-x is positive plot this in number line to visualize.
Please correct me if I am wrong
So options 1 and 2 is not right
only the product of 2-x and 3-x is positive plot this in number line to visualize.
Please correct me if I am wrong
Originally posted by defender007 on 31 Jul 2024, 03:02.
Last edited by defender007 on 31 Jul 2024, 03:11, edited 1 time in total.
Last edited by defender007 on 31 Jul 2024, 03:11, edited 1 time in total.
