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# If a, b and c are positive, is ac > 5?

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Math Expert
Joined: 02 Sep 2009
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If a, b and c are positive, is ac > 5?  [#permalink]

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14 Aug 2017, 02:02
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55% (hard)

Question Stats:

60% (01:38) correct 40% (01:58) wrong based on 70 sessions

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If a, b and c are positive, is ac > 5?

(1) a + b = 3
(2) 4 = c - b

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If a, b and c are positive, is ac > 5?  [#permalink]

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14 Aug 2017, 02:16
(1) a + b = 3
Without knowing the value of c, we cannot determine if the expression(ac) is greater than 5.
Hence, insufficient
(2) 4 = c - b
Without knowinth the value of a, we cannot determine if the expression(ac) is greater than 5.
Hence, insufficient.

On combining the information from both the statements,
b = 3 - a and b = c - 4
Therefore a + c = 7

Though the sum of a and c is 7, it is possible that the expression (ac) is greater/lesser than 5
Case 1: a = 6.2,c = 0.8. Here ac = 4.96 < 5
Case 2: a = 4, b = 3. Here ac = 12 > 5 (Insufficient)(Option E)
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Re: If a, b and c are positive, is ac > 5?  [#permalink]

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14 Aug 2017, 03:50
a, b, and c are positive.
Ok.

1. a + b = 3 Cant say, without knowing the value of c.

2. 4 = c - b Cant say, without knowing the value of a.

1&2. b = 3 - a, b = c - 4 which gives, a + c = 7.
Now, assume a=1, c=6, ac=6>5.
Now, assume a=0.5, c=6.5, ac=3.25<5.

Not sufficient.
Option E.

I just selected the wrong answer myself.
Re: If a, b and c are positive, is ac > 5?   [#permalink] 14 Aug 2017, 03:50
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