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Updated on: 26 Jun 2025, 01:05
Originally posted by Sajjad1994 on 24 Jun 2025, 04:54.
Last edited by Sajjad1994 on 26 Jun 2025, 01:05, edited 1 time in total.
Last edited by Sajjad1994 on 26 Jun 2025, 01:05, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
57% (01:21) correct
42% (02:08) wrong based on 7 sessions
History
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If a and b are negative, and c is positive, which of the following statements are true?
Indicate all such statements.
A. \(a – b < a – c\)
B. If \(a < b,\) then \(\frac{a}{c}<\frac{b}{c}\)
C. \(\frac{1}{b}<\frac{1}{c}\)
Indicate all such statements.
A. \(a – b < a – c\)
B. If \(a < b,\) then \(\frac{a}{c}<\frac{b}{c}\)
C. \(\frac{1}{b}<\frac{1}{c}\)
24 Jun 2025, 23:24
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Given:
To find: The statement(s) that is always true under the given conditions.
Solution:
Statement A: a - b < a - c
Statement A is not always true.
Statement B: If a < b, then a/c < b/c
Statement B is always true.
Statement C: 1/b < 1/c
Statement C is always true.
Correct Answers: B and C only
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
- a < 0, b < 0, c > 0
To find: The statement(s) that is always true under the given conditions.
Solution:
Statement A: a - b < a - c
- This inequality is equivalent to:
- −b < −c ------- [Subtracting a from both sides]
- b > c -----------[Multiplying both sides by -1]
- Since b < 0 and c > 0, b < c. So, b > c can NEVER be true.
- Since b > c is equivalent to the given inequality, we can conclude that Statement A is never true.
Statement A is not always true.
Statement B: If a < b, then a/c < b/c
- Given a < b, if we divide both sides of the inequality by positive number c, we get:
- a/c <b/c
- This is true.
Statement B is always true.
Statement C: 1/b < 1/c
- Given b < 0, we know that 1/b is also negative.
- Similarly, since c > 0, we can infer that 1/c is also positive.
- Therefore, 1/b < 1/c is true.
Statement C is always true.
Correct Answers: B and C only
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
26 Jun 2025, 01:07
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OE
Since b is negative and c is positive, \(b < c ⇒ –b > –c ⇒ a – b > a – c\) (A is false). Since c is positive, dividing by c preserves the inequality. (B is true.) Since b is negative, \(\frac{1}{b}\) is negative, and so is less than , which is positive (C is true).
Answer: B,C
Since b is negative and c is positive, \(b < c ⇒ –b > –c ⇒ a – b > a – c\) (A is false). Since c is positive, dividing by c preserves the inequality. (B is true.) Since b is negative, \(\frac{1}{b}\) is negative, and so is less than , which is positive (C is true).
Answer: B,C
