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16 Mar 2020, 03:04
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (02:10) correct
35%
(02:21)
wrong
based on 166
sessions
History
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Not Attempted Yet
If a < b and c < b, is abc < a ?
(1) ab < 0
(2) ac > 0
Are You Up For the Challenge: 700 Level Questions
(1) ab < 0
(2) ac > 0
Are You Up For the Challenge: 700 Level Questions
16 Mar 2020, 04:11
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Bunuel
Question: is abc < a ?
Question: is abc-a < 0 ?
Question: is a(bc-1) < 0 ?
Given: b > a and c
Statement 1: ab < 0
i.e. a is negative and b is positive
but sign of bc-1 is unknown hence
NOT SUFFICIENT
Statement 2: ac > 0
i.e. a and c are both negative or both positive
but sign of bc-1 is unknown hence
NOT SUFFICIENT
Combining statements
ac > 0, ab < 0
i.e. a and c are negative while b is positive
i.e. a and (bc-1) are both negative i.e. product is positive
SUFFICIENT
Answer: Option C
Updated on: 16 Mar 2020, 05:14
Originally posted by CareerGeek on 16 Mar 2020, 04:44.
Last edited by CareerGeek on 16 Mar 2020, 05:14, edited 1 time in total.
Last edited by CareerGeek on 16 Mar 2020, 05:14, edited 1 time in total.
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Bunuel
a < b and c < b or b > c
--> a < c < b
Question: Is abc < a ?
--> Is abc - a < 0
--> Is a(bc - 1) < 0
(1) ab < 0
For product to be negative, both should have opposite signs
--> Since a < b
a < 0 & b > 0.
Nothing can be said about 'c' --> c can be >0 or <0
To Find: If a(bc - 1) < 0 or not
Since a < 0, bc - 1 should be greater than 1
We do not know anything about the values of c. Eg: b = 1/2 & c = -1, bc = 1/2 (<1) --> a(bc - 1) < 0
If b = 2 & c = 1, bc = 2 (>1) --> a(bc - 1) > 0
No Definite answer --> Insufficient
(2) ac > 0
--> a > 0 & c > 0 or a < 0 & c < 0
Case 1: a > 0 & c > 0: --> b > 0
To Find: If a(bc - 1) < 0 or not
If a > 0, bc - 1 should be less than 0
We do not know anything about the values of b & c. Eg: b = 1/2 & c = 1, bc = 1/2 (<1); or if b = 2 & c = 3, bc = 6 (>1) --> Insufficient
Case 2: a < 0 & c < 0: --> b <0 or >0
No Definite answer --> Insufficient
Combining (1) & (2),
a < 0 & b > 0; --> c < 0 Only
To find: If a(bc - 1) < 0 or not
Since a < 0 and bc < 0 (b > 0 & c < 0), bc - 1 < 0
--> a(bc - 1) > 0 ALWAYS
A Definite value --> Sufficient
Option C
