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Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 01:34

Question: If 3x + 5 < x + 11, is x prime? Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even INSUFFICIENT: We dont know y

(2) The product of x and y is odd. INSUFFICIENT: We dont know whether y is integer e.g. x=2, y=1.5 then xy=3 (ODD) e.g. x=1, y=3 then xy=3 (ODD) x can be 1 or 2, hence its not sufficient.

Combining (1) & (2) SUFFICIENT: If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN. If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD Thus if x=2, both statements cannot be true simultaneously. This information is SUFFICIENT to prove x cannot be 2.

Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 04:46

1

This post received KUDOS

Expert's post

If 3x + 5 < x + 11, is x prime?

3x + 5 < x + 11 --> x<3. So, we have that x is less than 3. There is only one prime number less than 3, namely 2. So, the question basically asks whether x=2. Notice here that we are not told that x and y are integers.

(1) The sum of x and y is even. It's certainly possible that x is a prime number, for example if x=y=2, but it's also possible that x is NOT a prime number, for example if x=y=1. Not sufficient.

(2) The product of x and y is odd. The same here: it's possible that x is a prime number, for example if x=2 and y=0.5, but it's also possible that x is NOT a prime number, for example if x=y=1. Not sufficient.

(1)+(2) Suppose x=2=prime, then from (1) it follows that y=even, but in this case xy=even, not odd as stated in (2). Thus our assumption that x=2=prime was wrong. Therefore, x cannot be a prime number. Sufficient.

Answer: C.

Hope it's clear.

P.S. Please post PS questions in PS forum and DS questions in DS forum. Thank you.
_________________

Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 05:06

PraPon wrote:

Question: If 3x + 5 < x + 11, is x prime? Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even INSUFFICIENT: We dont know y

(2) The product of x and y is odd. INSUFFICIENT: We dont know whether y is integer e.g. x=2, y=1.5 then xy=3 (ODD) e.g. x=1, y=3 then xy=3 (ODD) x can be 1 or 2, hence its not sufficient.

Combining (1) & (2) SUFFICIENT: If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN. If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD Thus if x=2, both statements cannot be true simultaneously. This information is SUFFICIENT to prove x cannot be 2.

Hence choice(C) is the answer.

Hi PraPon,

Here u are assuming x=2 and moving forward!

But wat if x is negative? if x= -3 or x= -10

coz question doesnt state x is positive !
_________________

GMAT - Practice, Patience, Persistence Kudos if u like

Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 05:11

Expert's post

shanmugamgsn wrote:

PraPon wrote:

Question: If 3x + 5 < x + 11, is x prime? Simplify equation to x<3. Hence question becomes is x=2?

(1) the sum of x and y is even INSUFFICIENT: We dont know y

(2) The product of x and y is odd. INSUFFICIENT: We dont know whether y is integer e.g. x=2, y=1.5 then xy=3 (ODD) e.g. x=1, y=3 then xy=3 (ODD) x can be 1 or 2, hence its not sufficient.

Combining (1) & (2) SUFFICIENT: If x = 2, y must be 1.5 or -1.5 to make xy (ODD), however x + y cannot be EVEN. If x = 2, y must be 0 or even to make x + y (EVEN), however xy cannot be ODD Thus if x=2, both statements cannot be true simultaneously. This information is SUFFICIENT to prove x cannot be 2.

Hence choice(C) is the answer.

Hi PraPon,

Here u are assuming x=2 and moving forward!

But wat if x is negative? if x= -3 or x= -10

coz question doesnt state x is positive !

The point is if we assume that x=2=prime, then both statements cannot be true at the same time, which means that x cannot be 2. Check here: if-3x-5-x-11-is-x-prime-146067.html#p1171395

Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 06:33

Expert's post

Moreover if we rephrasing the question we have to find if x=2 yes or not....but if x=2 (prime or not prime) then we deal only with positive number. Prime are only positive integers
_________________

KUDOS is the good manner to help the entire community.

gmatclubot

Re: If 3x + 5 < x + 11, is x prime?
[#permalink]
20 Jan 2013, 06:33