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11 Nov 2022, 04:04
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E
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Difficulty:
25%
(medium)
Question Stats:
91% (01:11) correct
9%
(02:49)
wrong
based on 11
sessions
History
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Time
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Not Attempted Yet
If a, b, and c are positive numbers, is a > b > c ?
(1) a^2 > ab
(2) ac > c^2
(1) a^2 > ab
(2) ac > c^2
11 Nov 2022, 04:22
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Bunuel
We are given that a, b and c are positive. Which means that all the numbers lie to the right of 0 in a number line.
We are asked to find out if the relative order of a , b and c when plotted over a number line is as follows -
---------c---------b---------a---------
Statement 1
\(a^2\) - ab > 0
a(a-b) > 0
We know a positive, so a - b > 0
Hence a > b
We know that a lies to the right of b in a number line. We don't know the position of c. Hence the statement is not sufficient. We can eliminate A and D.
Statement 2
ac > \(c^2\)
ac - \(c^2\) > 0
c (a - c) > 0
We know c > 0, so (a - c ) > 0
a > c
We know that a lies to the right of c in a number line. We don't know the position of b. Hence the statement is not sufficient. We can eliminate B.
Combined
Combined we know that a is right most term, however we don't know the position of b and c with respect to each other.
The ambiguity remains. So combined, the statements give us partial information.
Option E
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