Data Sufficiency

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Aman verma wrote:Q: X is a Set of 50 consequtive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

Let the first integer be P and the 50th integer be Q.


St 1:-It means that smallest is -25 and biggest is +25.
Sufficient.
St2:-Also sufficient.
Biggest 32
Smallest = 32-50 =-18
Hence ,IMO D.

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Aman verma wrote:

harsh.champ wrote:

Aman verma wrote:Q: X is a Set of 50 consequtive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

Let the first integer be P and the 50th integer be Q.


St 1:-It means that smallest is -25 and biggest is +25.
Sufficient.
St2:-Also sufficient.
Biggest 32
Smallest = 32-50 =-18
Hence ,IMO D.

But you are forgetting 0 ( zero) which is also an integer and comes in between other integers. If the largest integer is 25 ,the smallest integer will be -24 and not -25

OIC,thanks for pointing it out.
But I can't seem to find any other case when the sum (P + Q) will be zero.
Both P and Q should be equidistant from the number line in opposite directions
Also we are considering consecutive integers.
Is something wrong in the question??-Statement 1 is mathematically impossible.

Aman verma wrote:Q: X is a Set of 50 consequtive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

St.I) If sum of greatest and smallest = 0 so obviously each there are all same +ve and -ve no. in between i.e. from -25 to 25 but total no. has to be odd in that case including 0 ..so it is not possible...insuff..
St.II ) greatest integer is 32 so we have nos. from -17 to 32
so sum = 18 +19+20 +21+..........32 >100 suff. so ans B

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Aman verma wrote:

shashank.ism wrote:

Aman verma wrote:Q: X is a Set of 50 consequtive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

St.I) If sum of greatest and smallest = 0 so obviously each there are all same +ve and -ve no. in between i.e. from -25 to 25 but total no. has to be odd in that case including 0 ..so it is not possible...insuff..
St.II ) greatest integer is 32 so we have nos. from -17 to 32
so sum = 18 +19+20 +21+..........32 >100 suff. so ans B

Now I have one question regarding statement I : should consequtive statements be considered as consequtive integers with a difference of 1. Can't we consider consequtive odd numbers because in that case we can get 25 consequtive numbers on either side of the number. Now I may be wrong but I am asking about the general position regarding GMAT. Does consequtive number means only numbers with difference of one or can we consider consequtive odd/even numbers under the general definition of the term Consequtive on the GMAT. I will like to have other students and experts views in this regard. If it is not mentioned in the question specifically that it is consequtive odd/even number should that necessarily mean consequtive numbers with a difference of one only , on the GMAT.

Well,in GMAT unless otherwise given you have to consider the numbers with a difference of 1 only.
I have highlighted the blue part-corect.
red part-incorrect

Aman verma wrote:
Now I have one question regarding statement I : should consequtive statements be considered as consequtive integers with a difference of 1. Can't we consider consequtive odd numbers because in that case we can get 25 consequtive numbers on either side of the number. Now I may be wrong but I am asking about the general position regarding GMAT. Does consequtive number means only numbers with difference of one or can we consider consequtive odd/even numbers under the general definition of the term Consequtive on the GMAT. I will like to have other students and experts views in this regard. If it is not mentioned in the question specifically that it is consequtive odd/even number should that necessarily mean consequtive numbers with a difference of one only , on the GMAT.

Aman you have put forward a very good question..so first i would like to explain you the definition of consecutive number...
DEf.: following one after the other in order
now consecutive number means :numbers following one after the other in order
consecutive integer means :integers following one after the other in order

it means integer beside each other like 3and 4 are consecutive integers

Now if it is written that consecutive odd nos. = odd numbers following one after the other in order
if it is written that consecutive even nos. = even numbers following one after the other in order

if u say consecutive numbers leaving 2 nos in between it means 1,4,7,/.......so it all depends on what is written
well for consecutive nos. it is ............3,4,5...............

Aman verma wrote:Q: X is a Set of 50 consecutive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

1) is Sufficient

2) is also sufficient (the sum = 25*(-17+32) = 25*15=375

D

[in case people are wondering why 1 is sufficient; I assume 1 to be true even if it is not possible and sum of an AP = n/2(first term and last term) - Never question the question maker]

+1 for D

what's the OA?

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The first hint is a fallacy. 50 consecutive numbers cannot have total of 0. Is it not better to say the condition is Insufficient.
The seecond hint that the greatest no is 38 , least no is -18 so Total of 50 nos. > 100. Sufficient
IMO B

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Aman verma wrote:Q: X is a Set of 50 consequtive integers.Is the sum of integers of the Set X greater than 100 ?

I. The sum of the greatest and the smallest integer in the set is Zero

II. The greatest integer in the Set X is 32

This is an impossible question for 2 reasons:

1) statement (I) is impossible to satisfy, since there is no set of 50 consecutive integers that sum to 0.

The fact that a statement is impossible doesn't make it insufficient; rather, it invalidates the entire question. On the actual GMAT, this will NEVER happen (or if it does, someone in quality control will lose his or her job).

2) even if we ignore the fact that (I) is impossible and pretend that it gives a "no" answer (let's assume there are 51 integers instead of 50 and therefore the sum of the series is 0), statement (2) gives a "yes" answer to the question).

At an even more basic level, statements (1) and (2) are satisfied by different strings of consecutive integers; another contradiction.

On the actual GMAT, the two statements will never contradict each other.

So, the answer to this question is (F): whoever designed this question did a horrible job.

What's the source?

Aman verma wrote:I was just asking the official position on the GMAT.Whether we can include consequtive odd/even number under the general term of consequtive on the GMAT.Should that term odd/even will always be mentioned with consequtive on the GMAT if that is required.

The official position of the GMAT is the same as normal mathematical convention:

the word "consecutive" in a vaccuum is ambiguous. On the GMAT, it will always be accompanied by a modifier.

"consecutive integers" means integers in a row, e.g. {5, 6, 7, 8} or {-3, -2, -1, 0, 1}
"consecutive even integers" means even integers in a row, e.g. {-2, 0, 2, 4, 6}
"consecutive odd integers" means odd integers in a row, e.g. {3, 5, 7, 9, 11, 13}
"consecutive multiples of 4" means multiples of 4 in a row, e.g. {8, 12, 16, 20}
"consecutive perfect squares" means perfect squares in a row, e.g. {9, 16, 25, 36}

You can have pretty much any modifier when you're talking about consecutives.