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Three even integers

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Three even integers

by sidimo84 » Sun Oct 17, 2010 9:56 am
Hi,

Consider this data sufficiency excercice:

A, B, and C are three consecutive even
integers (not necessarily in order). Which
has the greatest value?
(1) A + B = C
(2) C is a positive number.

I found this in a gmat book and i think the solution that they give are wrong.

Could you please try to fix and then i will put the solution they give.
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by limestone » Sun Oct 17, 2010 10:49 am
IMO: C

My approach:
take the values for those three consecutive integer as: x, x+1, x+2

1. A + B = C,
I'll plug in above values into C, then solve for x. If I can find the value of x, then that case is acceptable.

If C = x, then
x+1+x+2 = x, or 2x+3 = x, or x =-3. The three consecutive integers are: -3,-2,-1. C has not got the greatest value.

If C = x+1, then
x+2+x = x+1, or 2x+2 = x+1, or x = -1. The three consecutive integers are: -1,0,1. C has not got the greatest value.

If C = x+2, then
x+1+x = x+2, or 2x+1 = x+2, or x = 1. The three consecutive integers are:1,2,3. C has the greatest value.

So with the given information in 1, C can either have or have not got the greatest value. Thus, 1 is INSUFFICIENT.

2. C is positive, and without any other relationship among A,B,C. Thus INSUFFICIENT too.

1&2.
C can take 3 values as I listed above in 1.
The condition that C is a positive number eliminates the first two cases where C is -3 and 0, and is not the greatest number.
The last case, where C is positive and is the greatest number, is the only remained set of number.
Thus, 1&2 is SUFFICIENT.

Pick C.
Last edited by limestone on Sun Oct 17, 2010 10:52 am, edited 1 time in total.
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by shovan85 » Sun Oct 17, 2010 10:52 am
sidimo84 wrote:Hi,

Consider this data sufficiency excercice:

A, B, and C are three consecutive even
integers (not necessarily in order). Which
has the greatest value?
(1) A + B = C
(2) C is a positive number.

I found this in a gmat book and i think the solution that they give are wrong.

Could you please try to fix and then i will put the solution they give.
IMO C

Consecutive Even Integers A B C (not in order)

1: A+B = C

So possible cases
-2 -4 -6: If A and B are -2 and -4 then C = -6 but C is lowest
2 4 6: If A and B are 2 and 4 then C = 6 thus C is greatest
-2 0 2: If A and B are -2 and 2 then C = 0 but the middle value

1 is not sufficient.

2: C is a positive integer.
2 4 6: But as A,B and C are not in order C can be 2 or 4 or 6.

2 is insufficient.

Combine 1 and 2,

-2 0 2 fails as C is +ve not zero.
-2 -4 -6 fails as C is -ve.
2 4 6 passes as C is +ve.So we got a concrete answer here C is greatest. (Sufficient)

Hope I did not miss anything. Please let us know what is this book and what solution they are providing?
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by limestone » Sun Oct 17, 2010 10:55 am
My mistake that I didn't see that A,B,C are three consecutive even integers. However, the approach is the same. And shovan85 has done this well.
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by sidimo84 » Sun Oct 17, 2010 12:30 pm
shovan85 wrote:
sidimo84 wrote:Hi,

Consider this data sufficiency excercice:

A, B, and C are three consecutive even
integers (not necessarily in order). Which
has the greatest value?
(1) A + B = C
(2) C is a positive number.

I found this in a gmat book and i think the solution that they give are wrong.

Could you please try to fix and then i will put the solution they give.
IMO C

Consecutive Even Integers A B C (not in order)

1: A+B = C

So possible cases
-2 -4 -6: If A and B are -2 and -4 then C = -6 but C is lowest
2 4 6: If A and B are 2 and 4 then C = 6 thus C is greatest
-2 0 2: If A and B are -2 and 2 then C = 0 but the middle value

1 is not sufficient.

2: C is a positive integer.
2 4 6: But as A,B and C are not in order C can be 2 or 4 or 6.

2 is insufficient.

Combine 1 and 2,

-2 0 2 fails as C is +ve not zero.
-2 -4 -6 fails as C is -ve.
2 4 6 passes as C is +ve.So we got a concrete answer here C is greatest. (Sufficient)

Hope I did not miss anything. Please let us know what is this book and what solution they are providing?
The solution given is like yours:

The correct answer is (C). There are
three possible combinations fulfilling (1):
-2 + (-4) = (-6); -2 + 2 = 0; and 2 + 4 = 6.
Only the last satisfies property (2).

But what about this combination:
-4+6=2, it fulfill (1) and (2). But does it help to answer the question.
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by shovan85 » Sun Oct 17, 2010 12:46 pm
sidimo84 wrote: But what about this combination:
-4+6=2, it fulfill (1) and (2). But does it help to answer the question.
-4, 2, and 6 are not consecutive even integers
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by fskilnik@GMATH » Sun Oct 17, 2010 4:21 pm
sidimo84 wrote:A, B, and C are three consecutive even
integers (not necessarily in order). Which
has the greatest value?
(1) A + B = C
(2) C is a positive number.
Hi sidimo84, the answer is really C. Let us justify this completely, ok?

(1) Insufficient:

> Take A =2 , B = 4 and C = 6 therefore C is the greatest
> Take A = -2, B = 2 and C = 0 therefore B is the greatest

(2) Insufficient:

> Take A = 2, B = 4 and C = 6 therefore C is the greatest
> Take A = 6, B = 4 and C = 2 therefore A is the greatest


(1+2) Sufficient:

Let A, B, C be equal to 2x-2, 2x and 2x+2, not necessarily in that order.

> If C = 2x-2, then A+B = 4x+2 then 4x+2 = 2x-2 implies C negative (check that), impossible.
> If C = 2x, then A+B = 4x then 4x = 2x implies C zero (check that), impossible.

Finally the only option for C is 2x+2, that means that C is greater than A and than B (because they are 2x-2 and 2x, in some order.)

Hope you like it.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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