If X is a positive integer, is X even? (1) X is the sum of 7 consecut

Question

If X is a positive integer, is X even?

(1) X is the sum of 7 consecutive integers.

(2) X < 12.

pushpitkc · Answer

1. If X is the sum of the first 7 positive integers, the sum is 21(which is ODD)
If X is the sum of the 7 integers starting from -1, the sum is 14(which is EVEN)  (Insufficient)

2. If X < 12, two possibilities are 1(ODD) or 2(EVEN)  (Insufficient)

Combining the information in both the sentences, 
X can only take a value of 7(starting from -2 to 4) since X is positive and X < 12  (Sufficient - Option C)

FillFM · Answer

Option C.

(1) X is the sum of 7 consecutive integers. - Not Sufficient

X = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 - even
X = 2 + 3 + 4 + 5 + 6 + 7 + 8 = 35 - odd

(2) X < 12 - Not Sufficient

X = 4
X = 5

(1) + (2) - Sufficient

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) < 12
7x + 21 < 12

x <  \frac{-9}{7}

(-2) + (-1) + 0 + 1 + 2 + 3 + 4 =7 - odd
(-3) + (-2) + (-1) + 0 + 1 + 2 + 3 = 0 (but X have to be a positive integer)

X = 7 >  Option C

u1983 · Answer

X is a positive integer ==> x=1,2,3,......etc (1) X is the sum of 7 consecutive integers. Thus if The 1st number is even, then 7th will be even. The set consists 4 even and 3 odd numbers and thus their sum(X) is odd. or else if The 1st number is odd, then 7th will be odd. The set consists 4 odd and 3 even numbers and thus their sum(X) is even. ....(NS) (2) X < 12 ==> X = 1, 2,....,10,11.............(NS) (1)+(2) ==> Case 01: (-3)+(-2)+(-1)+(-0)+1+2+3 = 0 =X ... not a valid case as X is a positive integer Case 02: (-2)+(-1)+(-0)+1+2+3+4 = 7 =X ... X is odd ==>valid case Case 03: (-1)+(-0)+1+2+3+4+5 = 12 =X ... not a valid case as X < 12 So for the only valid case X is odd........................(Sufficient) Thus I would go for option C .

amandeep0306 · Answer

Statement1 :- X is the sum of 7 consecutive integers,

Assume the numbers be a-3,a-2,a-1,a,a+1,1+2,a+3
Sum of 7 consecutive integers = 7a

so x can be a multiple of 7 it means x can be 7,14,21,...
 (Not Sufficient)

Statement2 :- X <12
 (Not sufficient)

Statement 1 &2 together

x=7,14,21.....
X<12

So there is only one case possible in which x=7

Hence option :- C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If X is a positive integer, is X even? (1) X is the sum of 7 consecut

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards