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Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 04:46
3
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, 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, 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 _________________
Re: If 3x + 5 < x + 11, is x prime? [#permalink]
10 Jul 2014, 03:40
PrashantPonde 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.
According to my knowledge 1 is Neither Prime nor Composite. Please correct me if GMAT thinks the other way. I am really concerned about this
Re: If 3x + 5 < x + 11, is x prime? [#permalink]
10 Jul 2014, 03:42
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 !
Are prime No. Negative as well.
I thought Primes are from 2,3,5...And 1 being neither prime nor Composite. Please help me on this
If 3x + 5 < x + 11, is x prime? [#permalink]
10 Jul 2014, 03:46
Expert's post
karna2129 wrote:
PrashantPonde 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.
According to my knowledge 1 is Neither Prime nor Composite. Please correct me if GMAT thinks the other way. I am really concerned about this
GMAT doe not have some kind of their own math.
Facts about primes: 1. 1 is not a prime, since it only has one divisor, namely 1. 2. Only positive numbers can be primes. 3. There are infinitely many prime numbers. 4. the only even prime number is 2. Also 2 is the smallest prime. 5. All prime numbers except 2 and 5 end in 1, 3, 7 or 9.
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