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# If a, b, and c are consecutive integers such that a < b < c and a is

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
If a, b, and c are consecutive integers such that a < b < c and a is  [#permalink]

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13 Apr 2016, 04:31
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Difficulty:

15% (low)

Question Stats:

84% (01:18) correct 16% (01:11) wrong based on 105 sessions

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If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?

I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc

A. I only
B. II only
C. III only
D. II and III
E. I, II, and III

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Re: If a, b, and c are consecutive integers such that a < b < c and a is  [#permalink]

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13 Apr 2016, 06:04
Only 'B' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4

Putting the values in the answers only 'B' seems valid.
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Re: If a, b, and c are consecutive integers such that a < b < c and a is  [#permalink]

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13 Apr 2016, 06:24
Given:
1) a is even prime. The only even prime number known is 2, so a must be equal to 2.
2) a,b,c are consecutive such that a<b<c. So, b must be 3 and c must be 4.

So, we know that a=2, b=3 and c=4.

Substituting the above values in the three equations,
I. abc<a^3
which simplifies to 24<8. False.
II. a+b+c>a^3
which simplifies to 9>8. True.
III. 5b<bc
which simplifies to 15<12. False.

The only option correct is II, so the answer is B.
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If a, b, and c are consecutive integers such that a < b < c and a is  [#permalink]

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18 Apr 2017, 03:08
Bunuel wrote:
If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?

I. a × b × c < a^3
II. a + b + c > a^3
III. 5b < bc

A. I only
B. II only
C. III only
D. II and III
E. I, II, and III

Here we go
only even prime is 2
so as per requirement
a<b<c
2 3 4
Now we just have to put values
24<8--False
9>8--True
15<12--False
Choice:B
Time Taken: 59 seconds
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If a, b, and c are consecutive integers such that a < b < c and a is &nbs [#permalink] 18 Apr 2017, 03:08
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