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The location of points a and b is shown on the number line above. c is
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03 Jul 2023, 01:18

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The location of points a and b is shown on the number line above. c is the middle point of a and b. Which of the following must be true?

A. \(c – b > 0\)

B. \(abc > 0\)

C. \(a^3 × b^2 × c^3 < 0\)

D. \(a^3 × b^3 × c > 0\)

Post A Detailed Correct Solution For The Above Questions And Get Kudos.

Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos

\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge

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Re: The location of points a and b is shown on the number line above. c is
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07 Aug 2023, 09:16

Expert Reply

OE

Number line is always drawn to scale. So, numbers on number line are exactly as they appear.

Since 𝑐 is the middle point of 𝑎 and 𝑏 on the number line where 𝑎 is positive (and less distant from 0 as compared to b) and 𝑏 is negative, hence 𝑐 has to be negative.

(A) 𝑐 − 𝑏 > 0 𝑂𝑟 𝑐 > 𝑏 {Definitely true as 𝑐 is to the right of 𝑏 on the number line}

(B) 𝑎𝑏𝑐 > 0 {Definitely true as 𝑎 is positive, 𝑏 is negative and 𝑐 is negative}

(C) 𝑎^3 × 𝑏^2 × 𝑐^3 < 0 {Definitely true as 𝑎^3 is positive, 𝑏^2 is positive and 𝑐^3 is negative}

(D) 𝑎^3 × 𝑏^3 × 𝑐 > 0 {Definitely true as 𝑎^3 is positive, 𝑏^3 is negative and 𝑐 is negative}

Ans. (A, B, C, D)

_________________

Number line is always drawn to scale. So, numbers on number line are exactly as they appear.

Since 𝑐 is the middle point of 𝑎 and 𝑏 on the number line where 𝑎 is positive (and less distant from 0 as compared to b) and 𝑏 is negative, hence 𝑐 has to be negative.

(A) 𝑐 − 𝑏 > 0 𝑂𝑟 𝑐 > 𝑏 {Definitely true as 𝑐 is to the right of 𝑏 on the number line}

(B) 𝑎𝑏𝑐 > 0 {Definitely true as 𝑎 is positive, 𝑏 is negative and 𝑐 is negative}

(C) 𝑎^3 × 𝑏^2 × 𝑐^3 < 0 {Definitely true as 𝑎^3 is positive, 𝑏^2 is positive and 𝑐^3 is negative}

(D) 𝑎^3 × 𝑏^3 × 𝑐 > 0 {Definitely true as 𝑎^3 is positive, 𝑏^3 is negative and 𝑐 is negative}

Ans. (A, B, C, D)

_________________

gmatclubot

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