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Updated on: 25 Sep 2025, 08:40
Originally posted by Sajjad1994 on 25 Sep 2025, 08:37.
Last edited by Sajjad1994 on 25 Sep 2025, 08:40, edited 1 time in total.
Last edited by Sajjad1994 on 25 Sep 2025, 08:40, edited 1 time in total.
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Difficulty:
25%
(medium)
Question Stats:
66% (00:59) correct
33% (01:01) wrong based on 9 sessions
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Eight less than the square of x is less than eight. Which of the following expresses all possible values of x?
A. \(x < 8\)
B. \(x < 4\)
C. \(x < 0\)
D. \(–4 < x < 4\)
E. \(x > 4 \) or \(x < –4\)
A. \(x < 8\)
B. \(x < 4\)
C. \(x < 0\)
D. \(–4 < x < 4\)
E. \(x > 4 \) or \(x < –4\)
25 Sep 2025, 09:30
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Eight less than the square of x is less than eight. Which of the following expresses all possible values of x?
x^2 -8 <8
x^2 <16
Taking square root
-4<x<+4
D
x^2 -8 <8
x^2 <16
Taking square root
-4<x<+4
D
29 Sep 2025, 07:39
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Official Explanation
Translate the words into math symbols, noting that eight less than the square of \(x\) translates into x-squared minus 8, so \(x^2 – 8 < 8\). Add 8 to both sides, and \(x^2 < 16.\) Avoid carelessly taking the square-root of each side to obtain x < 4, (B), because this approach neglects consideration of negative values. Negative numbers that are more than 4 units from 0 will become positive and greater than 16 when squared, failing to satisfy the inequality. All numbers less than 4 units from 0 in either direction will be less than 16 when squared: The values of x within the shaded region, \(–4 < x < 4, (D),\) satisfy the inequality.
Answer: D
GMAT-Club-Forum-ywmvf5el.png [ 23 KiB | Viewed 224 times ]
Translate the words into math symbols, noting that eight less than the square of \(x\) translates into x-squared minus 8, so \(x^2 – 8 < 8\). Add 8 to both sides, and \(x^2 < 16.\) Avoid carelessly taking the square-root of each side to obtain x < 4, (B), because this approach neglects consideration of negative values. Negative numbers that are more than 4 units from 0 will become positive and greater than 16 when squared, failing to satisfy the inequality. All numbers less than 4 units from 0 in either direction will be less than 16 when squared: The values of x within the shaded region, \(–4 < x < 4, (D),\) satisfy the inequality.
Answer: D
Attachment:
GMAT-Club-Forum-ywmvf5el.png [ 23 KiB | Viewed 224 times ]
