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

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Manager
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If 3x + 5 < x + 11, is x prime? [#permalink]  19 Jan 2013, 20:32
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If 3x + 5 < x + 11, is x prime?

(1) The sum of x and y is even
(2) The product of x and y is odd.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 Jan 2013, 04:30, edited 1 time in total.
Moved to DS forum.
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Re: If 3x + 5 < x + 11, is x prime? [#permalink]  19 Jan 2013, 21:58
First of all, the question should be in DS section... and second, question stem seem to be missing Y... is it 3x + 5 < y + 11 or 3y + 5 < x + 11 ?

And if question stem is correct, then here is the solution:
3x + 5 < x + 11
2x <6
x < 3 (so possible values .....0,1,2)

St1. x+y= Even ... this will happen only if both are even or if both are odd.... so not-sufficient

St2. XY=Odd ... both has to be odd....So x can have only one value i.e. 1 as 0 and 2 are Even

So B is sufficient to answer the question.
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Re: If 3x + 5 < x + 11, is x prime? [#permalink]  20 Jan 2013, 00:33
daviesj wrote:
First of all, the question should be in DS section... and second, question stem seem to be missing Y... is it 3x + 5 < y + 11 or 3y + 5 < x + 11 ?

And if question stem is correct, then here is the solution:
3x + 5 < x + 11
2x <6
x < 3 (so possible values .....0,1,2)

St1. x+y= Even ... this will happen only if both are even or if both are odd.... so not-sufficient

St2. XY=Odd ... both has to be odd....So x can have only one value i.e. 1 as 0 and 2 are Even

So B is sufficient to answer the question.

Only B is NOT sufficient. We dont know whether y is integer.
x=2, y=1.5 -> xy=3 odd
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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.

Hence choice(C) is the answer.
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Thanks,
PraPon

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

Hope it;s clear.
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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
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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
Intern
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Kudos [?]: 5 [0], given: 4

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
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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.

Theory on Number Properties: math-number-theory-88376.html
Number Properties - Tips and hints: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59
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