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

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SVP
Status: Preparing GMAT
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X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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Updated on: 21 Oct 2018, 07:52
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00:00

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(N/A)

Question Stats:

66% (01:22) correct 34% (01:15) wrong based on 131 sessions

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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: Hard

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Last edited by SajjadAhmad on 21 Oct 2018, 07:52, edited 2 times in total.
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GMAT 1: 740 Q50 V41
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Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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10 Mar 2017, 23:42
Source: platinum GMAT

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

What do you mean by combined factors? please elaborate
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SVP
Status: Preparing GMAT
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Posts: 2032
Location: Pakistan
GPA: 3.39
Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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12 Mar 2017, 11:47
ShashankDave wrote:
Source: platinum GMAT

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

What do you mean by combined factors? please elaborate

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
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Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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16 Mar 2017, 16:08
1
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

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Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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27 Apr 2017, 13:37
Source: platinum GMAT

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

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.
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Joined: 17 Apr 2016
Posts: 88
Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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27 Apr 2017, 18:03
1
shakun wrote:
Source: platinum GMAT

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

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.

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.
Manager
Joined: 13 Feb 2018
Posts: 146
Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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29 Mar 2018, 12:00
shakun wrote:
Source: platinum GMAT

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

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.

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.

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
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Joined: 30 Mar 2017
Posts: 134
GMAT 1: 200 Q1 V1
Re: X and Y are both positive integers whose combined factors include 3 an  [#permalink]

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09 Jun 2018, 05:44
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

Re: X and Y are both positive integers whose combined factors include 3 an &nbs [#permalink] 09 Jun 2018, 05:44
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