X and Y are both positive integers whose combined factors include 3 an

Question

X and Y are both positive integers whose combined factors include 3 and 7. Is the sum X + Y + 1 an odd integer?

(1) Both X and Y are divisible by 2

(2) X + 2 = Y

Source:   Platinum GMAT  
Difficulty Level:   700

ShashankDave · Answer

What do you mean by combined factors? please elaborate

Sajjad1994 · Answer

Factors are numbers we can multiply together to get another number:
Like 2 and 3 both are combined factor of 6 
3 and 4 are combines factor of 12
3 and 5 are combined factor of 15

coolkl · Answer

Infer : X+Y+1 = Odd means X+Y = Odd - 1 = Even. Means we have to prove either 
X, Y are Even or both are odd. In simple words find the parity of X & Y

S-1) Both X and Y are even. Sufficient to prove X+Y+1 odd

S-2) X+2 = Y means X-Y = Even. So either both X,Y are even or odd. Sufficient to prove X+Y is even and X+Y+1 is odd

Answer is D.

shakun · Answer

Is the question (statement-2) correct? 
Since 3 and 7 are combined factors of both X and Y, both of these numbers are multiples of 21.
Then X=21p and Y=21q. Using statement-2, 21p+2 = 21q, this is not possible for any integer p and q.

adityapareshshah · Answer

The Statement that X and Y are positive integers whose combined factors include 3 and 7 was not useful to solve this question.I could confidently choose D without considering that statement. Seems like the question is incomplete.

LevanKhukhunashvili · Answer

Seems like it's a trap to waste precious time, otherwise from stem X+Y+1 and 2) stat- X+2=Y. we can arrive to X+X+2+1 is odd or not? It doesn't matter the even/odd nature of X, the answer is Yes it's odd in any case

aserghe1 · Answer

Is the sum X + Y + 1 an odd integer?
Equivalently, is the sum of X + Y an even integer?
This will be true if both X and Y are odd or if both X and Y are even.

Statement 1
Both X and Y are even.
Sufficient

Statement 2
Y = X + 2
Since we need to find if X + Y is even, the question becomes is X + (X + 2) even?
Simplified, is 2X + 2 even. Yes, it's even.
Sufficient

Answer: D

X and Y are both positive integers whose combined factors include 3 an

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