If x is a positive integer, find the value of x? 1) sum of x consecut

Question

If x is a positive integer, find the value of x? 1) sum of x consecutive integers is x+1 2) Product of x consecutive integers is x Source: http://www.GMATinsight.com

gmatophobia · Answer

Statement 1

1) sum of x consecutive integers is x

The smallest number in the set = a

a + a+1 + a+2 + ... a + (x-1) = x

ax +\frac{ x(x-1)}{2} = x

\frac{2ax + x(x-1)}{2} = x

As x is positive, we can divide both sides by x

\frac{2a + (x-1)}{2} = 1

2a + x - 1 = 2

2a + x = 3

As a and x are positive numbers, the equation holds true x = 2 and a = 1

We have a definite value of x. Hence, the statement alone is sufficient.

Statement 2

2) Product of x consecutive integers is x

As x represents the number of consecutive integers, x the minimum value of x should be two.

a * (a+1) * (a+2) .. * (a + x-1) = x

The only value of x that's possible is 2 and the product is

1 * 2 = 2

IMO D

gmatophobia · Answer

GMATinsight  - Can you share OE to this question.

ankitgoswami · Answer

The question, maybe, needs a relook.

Statement 1 - sum of x consecutive integers is x

sum of 3 consecutive integers is 3
0,1,2

sum of 5 consecutive integers is 5
-1,0,1,2,3

sum of 7 consecutive integers is 7
-2,-1,0,1,2,3,4

Etc...

Insufficient

Statement 2 - Product of x consecutive integers is x

Here we can not include negative integers. Because it's the product of consecutive integers and 0 will make the product 0.

So only possibility is

Product of 2 consecutive integers is 2
1,2

So B may seem to be the ans, but Statement 1 doesn't seem to compliment Statement 2, rather seems to be in contradiction as sum of 2 consecutive integers can never be 2.

Posted from my mobile device

GMATinsight · Answer

Question x = ?

Statement 1 : sum of x consecutive integers is x+1 
Example 1: For the set {1,2}, x = 2 and sum = 3
Example 2: For the set {2}, x = 1 and sum = 2
i.e. x maybe 1 or 2 hence 
 NOT SUFFICIENT

Statement 2 : Product of x consecutive integers is x 
when x = 2 and the numbers are {1, 2}
when x = 1 and the numbers are {1}
 NOT SUFFICIENT

After combining we have, x = 1 or 2

NOT SUFFICIENT

Answer: option E

GMATinsight · Answer

Due to some error, I have made a small change in statement 1 and in answer as well.

Regret for inconvenience and delay

gmatophobia · Answer

Hi GMATinsight , I have a question on the highlighted part of the explanation. x denotes the number of integers. If the statement mentions that x numbers are consecutive, can x be equal to 1? IMO if we have a single number we can't term it to be consecutive to itself (shouldn't we need at least two terms in this case). The dictionary definition* of consecutive is " Consecutive events, numbers, etc. follow one after another without an interruption ". For a single number, we don't have any number that either precedes or succeeds the number. Hence, I think nothing is consecutive in that case (put otherwise the definition of consecutive doesn't apply to a single number). Can you share an official example in which the use of a single integer is used in reference to consecutive integers? *Source: https://dictionary.cambridge.org/dictio ... onsecutive Bunuel / IanStewart - Request your thoughts on the same. Can a single integer be consecutive to itself or in this context can we take x = 1 as a valid value?

Archit3110 · Answer

given that x is a +ve integer
target find value of x
#1
sum of x consecutive integers is x+1
1/2 * x*(x+1) = x+1
supposedly if value of x is 1 then LHS = RHS ; 2
or if x is 2 LHS = RHS = 3

x can be 1,2
insufficient
#2
Product of x consecutive integers is x
let consecutive integers be
(x-1) (x) ( x+1) = x
where LHS is nothing but count of consecutive integers so we can have
case 1
x = 1 then LHS = RHS=1
case 2
x= 2
(2-1) (2) = 2
LHS= RHS = 2
x can be 1,2
insufficient
from 1 &2
x can be +1,+2
insufficient
option E

GMATinsight ; great question sir...

GMATinsight

If x is a positive integer, find the value of x?

1) sum of x consecutive integers is x+1
2) Product of x consecutive integers is x

Source: http://www.GMATinsight.com

IanStewart · Answer

Technically, in math I think the answer is yes, even if that doesn't appear to make much sense when you think of the traditional definition of 'consecutive' (I can remember seeing some more advanced math questions, outside of the GMAT, that talk about "one or more consecutive integers", for example). But the GMAT will literally never test a situation where you were asked to think about whether you can have "one consecutive integer", because the GMAT doesn't test technicalities like that, ones which don't test your ability but rather whether you've guessed correctly what meaning they intend by certain ambiguous words.

There's a more serious issue with the wording of the question, though. In math, if we say something like "the sum of the first n positive integers is n(n+1)/2", we do  not  mean "there is  some  value of n for which the sum of the first n positive integers is n(n+1)/2". That sentence expresses a general fact about n, one that is always true. So Statement 1 here ("sum of x consecutive integers is x+1"), interpreted as we interpret any similar sentence in math, means "when we add any x consecutive integers, we get a sum of x+1". This is clearly not the intended meaning, because it can't be true; the question is trying to say "there exists a set of x consecutive integers that has a sum of x+1". But I had to reread the question a couple of times to just figure out what it was trying to say.

If x is a positive integer, find the value of x? 1) sum of x consecut

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If x is a positive integer, find the value of x? 1) sum of x consecut

Prep Toolkit

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