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Asifpirlo
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If a, b, and c are consecutive positive odd integers, not ne 21 Aug 2013, 01:39
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C
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79% (01:26) correct 21% (02:07) wrong based on 218 sessions

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If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following must be true?

I. a + b > c

II. bc > a

III. (a + c)^2 > b

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
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C
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fameatop
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If a, b, and c are consecutive positive odd integers, not ne 21 Aug 2013, 02:02
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Asifpirlo
If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following
must be true?
I. a + b > c
II. bc > a
III. (a + c)^2 > b

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Show more

Lets suppose that a,b,c can take any one of following three value 1,3,5. Most important point is that the options MUST BE TRUE under any condition.
I) a+b>c
Not necessarily true as 1+3<5

II) bc>a
Not necessarily true as 1.3<5

III) We don't need to check option as all the options except C can be discarded.
Thus Answer C
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If a, b, and c are consecutive positive odd integers, not ne 15 May 2014, 10:27
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fameatop
Asifpirlo
If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following
must be true?
I. a + b > c
II. bc > a
III. (a + c)^2 > b

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

Lets suppose that a,b,c can take any one of following three value 1,3,5. Most important point is that the options MUST BE TRUE under any condition.
I) a+b>c
Not necessarily true as 1+3<5

II) bc>a
Not necessarily true as 1.3<5

III) We don't need to check option as all the options except C can be discarded.
Thus Answer C
Show more

I didn't quite get statement 2. We are told that 1,3,5 consecutive odd integers.

Therefore, 3*5=15>1 is always true. What's missing?

Thanks!
Cheers
J :)
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Bunuel
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If a, b, and c are consecutive positive odd integers, not ne 16 May 2014, 01:30
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jlgdr
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Asifpirlo
If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following
must be true?
I. a + b > c
II. bc > a
III. (a + c)^2 > b

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

Lets suppose that a,b,c can take any one of following three value 1,3,5. Most important point is that the options MUST BE TRUE under any condition.
I) a+b>c
Not necessarily true as 1+3<5

II) bc>a
Not necessarily true as 1.3<5

III) We don't need to check option as all the options except C can be discarded.
Thus Answer C

I didn't quite get statement 2. We are told that 1,3,5 consecutive odd integers.

Therefore, 3*5=15>1 is always true. What's missing?

Thanks!
Cheers
J :)
Show more

II says bc > a. Now, if a = 5, b = 1 and c = 3, then bc < a. Hence this option is not necessarily true.
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If a, b, and c are consecutive positive odd integers, not ne 16 May 2014, 20:54
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Asifpirlo
If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following must be true?

I. a + b > c

II. bc > a

III. (a + c)^2 > b

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
Show more

Can someone explain what the highlighted part means?
What are the possibilities that one would need to consider?
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gmatacequants
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If a, b, and c are consecutive positive odd integers, not ne 17 May 2014, 02:50
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shaderon
Asifpirlo
If a, b, and c are consecutive positive odd integers, not necessarily in that order, which of the following must be true?

I. a + b > c

II. bc > a

III. (a + c)^2 > b

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

Can someone explain what the highlighted part means?
What are the possibilities that one would need to consider?
Show more

Hi Shaderon,
The same order would mean that
a < b < c or
being precise : b = a + 2
c = b + 2 = a + 4, where a is a positive odd integer

However as they are not consecutive in the same order so, above inequality a<b<c does not hold true.
i.e., any case is possible : a < b < c or a < c < b or b < a < c or b < c < a or c < a < b or c < b < a

Now,definitely we should consider the boundary case values to find how the inequality behaves.
Boundary case : taking odd numbers 1,3,5

I. a + b > c
put a =1,b=3,c=5 ;does not work

II. bc > a
put b=1,c=3,a=5 ;does not work

III. (a + c)^2 > b
put a=1,c=3,b=5 ; will work

We can reject inequalities I and II.
It is pretty clear, only inequality III is only left which holds true as shown above.
Looking at the answer options, correct option is
Show Spoiler
C


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jlgdr
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If a, b, and c are consecutive positive odd integers, not ne 26 May 2014, 06:58
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Oh cause it says not necessarily in that order. Missed that part, thanks!

Cheers
J
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If a, b, and c are consecutive positive odd integers, not ne 30 Mar 2026, 10:20
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