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

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

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

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