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Intern  Joined: 14 Mar 2010
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If 3x + 5 < x + 11, is x prime?  [#permalink]

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Question Stats: 32% (01:58) correct 68% (01:45) wrong based on 461 sessions

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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.

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Originally posted by monir6000 on 19 Jan 2013, 21:32.
Last edited by Bunuel on 20 Jan 2013, 05:30, edited 1 time in total.
Moved to DS forum.
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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1
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]

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2
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]

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2
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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Finance your Student loan through SoFi and get $100 referral bonus : Click here Senior Manager  Joined: 27 Jun 2012 Posts: 365 Concentration: Strategy, Finance Schools: Haas EWMBA '17 Re: If 3x + 5 < x + 11, is x prime? [#permalink] ### Show Tags 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. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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1
1
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]

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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]

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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]

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

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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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Joined: 02 Sep 2009
Posts: 55236
If 3x + 5 < x + 11, is x prime?  [#permalink]

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1
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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If 3x + 5 < x + 11, is x prime?  [#permalink]

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monir6000 wrote:
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.

It's not an original question, see here https://www.manhattanprep.com/gmat/foru ... t2804.html

Please find below the original question from MGMAT

If x and y are positive integers and 3x + 5 < x + 11, is x a prime number?

(1) The sum of x and y is even.
(2) The product of x and y is odd.

And the answer for the original question is B
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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I have a different variation of this question from my source.

If x and y are positive integers and 3 x + 5 < x + 11, is x a prime number?
(1) The sum of x and y is even.
(2) The product of x and y is odd.

in this case, answer should be B.

If y is not given as integer explicitly in the question, then answer is C
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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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.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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fracheva 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.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.

Hello

Yes, thats the point. If we take your example of x=1, y=3, it satisfies both the question statements as you have just written. And what is x here? x=1, which is NOT prime. So this again proves that x is not a prime number.

No matter which values of x/y we take which satisfy both the given statements, we will always get a value of x which is NOT prime. So this is sufficient to answer the question with a NO. Hence C answer
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Re: If 3x + 5 < x + 11, is x prime?  [#permalink]

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amanvermagmat wrote:
fracheva 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.

I don't really get it. If we assume x = 1 and y = 3 don't we get a different answer? The sum would be even and the product odd.

Hello

Yes, thats the point. If we take your example of x=1, y=3, it satisfies both the question statements as you have just written. And what is x here? x=1, which is NOT prime. So this again proves that x is not a prime number.

No matter which values of x/y we take which satisfy both the given statements, we will always get a value of x which is NOT prime. So this is sufficient to answer the question with a NO. Hence C answer

Oh yeah, you're right indeed. Thanks very much  Re: If 3x + 5 < x + 11, is x prime?   [#permalink] 27 Nov 2018, 01:18
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