It is currently 20 Nov 2017, 14:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and y are positive integers, is x a prime number?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 12 Dec 2013
Posts: 25

Kudos [?]: 26 [4], given: 22

If x and y are positive integers, is x a prime number? [#permalink]

### Show Tags

22 May 2014, 17:42
4
KUDOS
17
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

38% (01:54) correct 62% (01:55) wrong based on 465 sessions

### HideShow timer Statistics

If x and y are positive integers, is x a prime number? [M28-58]

(1) |x−2|<2−y.

(2) x+y−3=|1−y|
[Reveal] Spoiler: OA

_________________

Please +1 KUDOS if my post helps. Thank you.

Kudos [?]: 26 [4], given: 22

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7738

Kudos [?]: 17819 [11], given: 235

Location: Pune, India
Re: If x and y are positive integers, is x a prime number? [#permalink]

### Show Tags

22 May 2014, 21:48
11
KUDOS
Expert's post
4
This post was
BOOKMARKED
bekerman wrote:
If x and y are positive integers, is x a prime number? [M28-58]

(1) |x−2|<2−y.

(2) x+y−3=|1−y|

"If x and y are positive integers" implies x and y are 1/2/3/4... etc

(1) |x−2|<2−y
Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer)

|x−2| = 0 means x = 2 (prime number)
This statement alone is sufficient.

(2) x+y−3=|1−y|
x = |1−y| - y + 3

If y = 1, x = 0 - 1 + 3 = 2
If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1
So x = y - 1 - y + 3 = 2

So for all cases, x must be 2. This statement alone is sufficient.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17819 [11], given: 235 Intern Joined: 20 May 2014 Posts: 37 Kudos [?]: 40 [3], given: 16 Location: India Schools: IIMC GMAT 1: 700 Q51 V32 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 22 May 2014, 23:00 3 This post received KUDOS 1 This post was BOOKMARKED Another way to solve it: Positive integers are: 1, 2,3, etc 1) |x−2|<2−y RHS should be greater than 0 as LHS is MOD Therefore, 2-y > 0 or y<2 or $$y = 1$$ (As y is a +ve integer) Hence, |x−2| <2−y or |x−2|<1 or |x−2|= 0 (As LHS cannot be negative) x = 2 Hence, Statement 1) is alone sufficient 2) x+y−3=|1−y| Can be written as: x+y-3 =|y−1| (Same as it is modulus) or x - 2 + (y -1) = |y−1| Using, X + Y = |Y| Where x-2 = X (Can have Values: -1, 0, 1, 2, etc) And y -1 = Y (Can have Values: 0, 1, 2, 3, etc) As Y is always positive, we have X + Y = Y or X = 0 or x - 2 = 0 or x = 2 Hence, Statement 2) is alone sufficient Answer (D) Rgds, Rajat _________________ If you liked the post, please press the'Kudos' button on the left Kudos [?]: 40 [3], given: 16 Math Expert Joined: 02 Sep 2009 Posts: 42269 Kudos [?]: 132827 [0], given: 12378 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 23 May 2014, 01:53 Expert's post 1 This post was BOOKMARKED bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| This question is discussed here: new-set-number-properties-149775.html If x and y are positive integers, is x a prime number? (1) |x - 2| < 2 - y . The left hand side of the inequality is an absolute value, so the least value of LHS is zero, thus 0 < 2 - y, thus y < 2 (if y is more than or equal to 2, then $$y-2\leq{0}$$ and it cannot be greater than |x - 2|). Next, since given that y is a positive integer, then y=1. So, we have that: $$|x - 2| < 1$$, which implies that $$-1 < x-2 < 1$$, or $$1 < x < 3$$, thus $$x=2=prime$$. Sufficient. (2) x + y - 3 = |1-y|. Since y is a positive integer, then $$1-y\leq{0}$$, thus $$|1-y|=-(1-y)$$. So, we have that $$x + y - 3 = -(1-y)$$, which gives $$x=2=prime$$. Sufficient. Answer: D. _________________ Kudos [?]: 132827 [0], given: 12378 Current Student Joined: 20 Jan 2014 Posts: 175 Kudos [?]: 72 [2], given: 120 Location: India Concentration: Technology, Marketing Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 05 Jul 2014, 07:23 2 This post received KUDOS This is one of the classic question. (1). |x−2|<2−y. The left hand side of the inequality is an absolute value, so the least value of LHS is zero, thus ,2-y>0 thus y<2 . Next, since given that is a positive integer, then y=1. So, we have that:|x-2|<1 , which implies that ,-1<x-2>1 thus x=2. Sufficient. (2).x+y-3 = |1-y| we can write this in two form , considering positive & negative (a) x+y-3 = 1-y x=1-y-y+3 => x= 1-2y+3 => x= 2(2-y) Since x is positive integer so y can be greater than 2 so y has to be 1. So x=2 (b) x+y-3 = y-1 x=2. So by both ways X=2. Each statement is sufficient _________________ Consider +1 Kudos Please Kudos [?]: 72 [2], given: 120 Intern Joined: 05 May 2014 Posts: 4 Kudos [?]: 1 [0], given: 11 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 21 Aug 2014, 23:23 Hi Isn't 0 a positive interger. If isn't whenever the question mentions positive or negative intergers we do not take 0...right what about non-negative integers which include...0.1..2...... VeritasPrepKarishma wrote: bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| "If x and y are positive integers" implies x and y are 1/2/3/4... etc (1) |x−2|<2−y Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer) |x−2| = 0 means x = 2 (prime number) This statement alone is sufficient. (2) x+y−3=|1−y| x = |1−y| - y + 3 If y = 1, x = 0 - 1 + 3 = 2 If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1 So x = y - 1 - y + 3 = 2 So for all cases, x must be 2. This statement alone is sufficient. Answer (D) Kudos [?]: 1 [0], given: 11 Math Expert Joined: 02 Sep 2009 Posts: 42269 Kudos [?]: 132827 [0], given: 12378 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 22 Aug 2014, 04:01 akshaybansal991 wrote: Hi Isn't 0 a positive interger. If isn't whenever the question mentions positive or negative intergers we do not take 0...right what about non-negative integers which include...0.1..2...... VeritasPrepKarishma wrote: bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| "If x and y are positive integers" implies x and y are 1/2/3/4... etc (1) |x−2|<2−y Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer) |x−2| = 0 means x = 2 (prime number) This statement alone is sufficient. (2) x+y−3=|1−y| x = |1−y| - y + 3 If y = 1, x = 0 - 1 + 3 = 2 If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1 So x = y - 1 - y + 3 = 2 So for all cases, x must be 2. This statement alone is sufficient. Answer (D) 0 is neither positive nor negative integer (the only one of this kind). Check for more here: number-properties-tips-and-hints-174996.html _________________ Kudos [?]: 132827 [0], given: 12378 Manager Joined: 30 Apr 2017 Posts: 84 Kudos [?]: 2 [0], given: 67 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 09 Nov 2017, 18:27 VeritasPrepKarishma wrote: bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| "If x and y are positive integers" implies x and y are 1/2/3/4... etc (1) |x−2|<2−y Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer) |x−2| = 0 means x = 2 (prime number) This statement alone is sufficient. (2) x+y−3=|1−y| x = |1−y| - y + 3 If y = 1, x = 0 - 1 + 3 = 2 If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1 So x = y - 1 - y + 3 = 2 So for all cases, x must be 2. This statement alone is sufficient. Answer (D) Hi VeritasPrepKarishma statement 2 cannot be sufficient, question says X AND Y are positive, 0 is not the positive integer! Kudos [?]: 2 [0], given: 67 Math Expert Joined: 02 Sep 2009 Posts: 42269 Kudos [?]: 132827 [1], given: 12378 Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 09 Nov 2017, 21:27 1 This post received KUDOS Expert's post soodia wrote: VeritasPrepKarishma wrote: bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| "If x and y are positive integers" implies x and y are 1/2/3/4... etc (1) |x−2|<2−y Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer) |x−2| = 0 means x = 2 (prime number) This statement alone is sufficient. (2) x+y−3=|1−y| x = |1−y| - y + 3 If y = 1, x = 0 - 1 + 3 = 2 If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1 So x = y - 1 - y + 3 = 2 So for all cases, x must be 2. This statement alone is sufficient. Answer (D) Hi VeritasPrepKarishma statement 2 cannot be sufficient, question says X AND Y are positive, 0 is not the positive integer! Yes, 0 is neither positive nor negative but (2) IS sufficient. Please check the OA under the spoiler and read the whole discussion: https://gmatclub.com/forum/if-x-and-y-a ... l#p1367359 _________________ Kudos [?]: 132827 [1], given: 12378 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7738 Kudos [?]: 17819 [0], given: 235 Location: Pune, India Re: If x and y are positive integers, is x a prime number? [#permalink] ### Show Tags 09 Nov 2017, 22:37 soodia wrote: VeritasPrepKarishma wrote: bekerman wrote: If x and y are positive integers, is x a prime number? [M28-58] (1) |x−2|<2−y. (2) x+y−3=|1−y| "If x and y are positive integers" implies x and y are 1/2/3/4... etc (1) |x−2|<2−y Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer) |x−2| = 0 means x = 2 (prime number) This statement alone is sufficient. (2) x+y−3=|1−y| x = |1−y| - y + 3 If y = 1, x = 0 - 1 + 3 = 2 If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1 So x = y - 1 - y + 3 = 2 So for all cases, x must be 2. This statement alone is sufficient. Answer (D) Hi VeritasPrepKarishma statement 2 cannot be sufficient, question says X AND Y are positive, 0 is not the positive integer! Where did I assume/say that X or Y is 0? _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 17819 [0], given: 235

Manager
Joined: 30 Apr 2017
Posts: 84

Kudos [?]: 2 [0], given: 67

Re: If x and y are positive integers, is x a prime number? [#permalink]

### Show Tags

09 Nov 2017, 23:58
VeritasPrepKarishma wrote:
soodia wrote:
VeritasPrepKarishma wrote:
(1) |x−2|<2−y.

(2) x+y−3=|1−y|

"If x and y are positive integers" implies x and y are 1/2/3/4... etc

(1) |x−2|<2−y
Minimum value of y is 1 which means maximum value of right hand side is 2-1 = 1. An absolute value cannot be negative so left hand side must be 0 only (to be less than 1 but be an integer)

|x−2| = 0 means x = 2 (prime number)
This statement alone is sufficient.

(2) x+y−3=|1−y|
x = |1−y| - y + 3

If y = 1, x = 0 - 1 + 3 = 2
If y is greater than 1, (1-y) will be negative so |1−y| = -(1 - y) = y - 1
So x = y - 1 - y + 3 = 2

So for all cases, x must be 2. This statement alone is sufficient.

Hi VeritasPrepKarishma

statement 2 cannot be sufficient, question says X AND Y are positive, 0 is not the positive integer!

Where did I assume/say that X or Y is 0?[/quote]

WOW!
such a shame!!!
bunuel responded me too! but I did'n' find my mistake
I'm really sorry Karishma
this type of mistake will ruin my exam totally!

Kudos [?]: 2 [0], given: 67

Intern
Joined: 20 Feb 2017
Posts: 18

Kudos [?]: 2 [0], given: 427

Re: If x and y are positive integers, is x a prime number? [#permalink]

### Show Tags

10 Nov 2017, 12:21
From statement 1 : |x−2|<2−y [u][/u]
HERE WE HAVE 2 CASES
CASE 1 :
=> X-2< 2-Y FOR X≥2
=> X+Y< 4 ONLY POSSIBLE WHEN x = 2 (PRIME)
CASE 2 :
OR 2-X < 2-Y FOR X<2
=> X-Y>0 (ONLY POSSIBLE WHEN X IS 1 AND Y IS 0 BUT AS PER THE QUESTION X AND Y MUST BE POSITIVE INTEGERS AND 0 IS NOT A ONE )
THUS FROM STATEMENT 1 WE HAVE X=2 (PRIME) SUFFICIENT
FROM STATEMENT 2
WE HAVE 2 CASES HERE
CASE 1 :
X+Y-3 = 1-Y FOR Y ≤1
=> X+2Y = 4 THIS GIVES ONLY POSSIBLE VALUE FOR X AS 2 (PRIME)
CASE 2 :
X+Y-3= Y-1 FOR Y>1
THIS GIVES AGAIN X=2 (PRIME)
HENCE BOTH THE CASES GIVE X= 2 WHICH IS PRIME .
HENCE STATEMENT 2 IS ALSO SUFFICIENT

Kudos [?]: 2 [0], given: 427

Re: If x and y are positive integers, is x a prime number?   [#permalink] 10 Nov 2017, 12:21
Display posts from previous: Sort by