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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

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.

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
_________________

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.

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).

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.

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.

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.

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.

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 ) HENCE DISCARD CASE 2 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 HENCE ANSWER IS D