If 3x + 5

Question

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.

Bunuel · Accepted Answer

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.

daviesj · Answer

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.

PrashantPonde · Answer

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

PrashantPonde · Answer

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.

shanmugamgsn · 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 !

Bunuel · Answer

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.

Carcass · Answer

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

karna2129 · 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

karna2129 · Answer

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

Bunuel · Answer

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

BrainLab · Answer

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

hellosanthosh2k2 · Answer

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

fracheva · 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.

amanvermagmat · Answer

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

fracheva · Answer

Oh yeah, you're right indeed. Thanks very much

minustark · Answer

2x < 6 or, x < 3. whether x is an integer or not, we don't know. Nevertheless, for keeping the procedure simple lets consider only the integer options for x.

1) both of x and y have to be either odd or even. As we don't know y is odd or even, so can't answer the question. Insufficient.

2) x and y are both odd. So, x is 1 which is sufficient.

B is the CA.

vps01011989 · Answer

How is the answer C? What if X is -ve?

Rahul5843 · Answer

x. y
1. 3
-1. -3

hence E should be the answer
there is no restriction on x to be non-negative in the question

Bunuel · Answer

The question asks whether x is a prime number. According to the solution, when we consider the statements together, we get a definite NO answer to the question - NO, x is NOT a prime number. In your example x is also not a prime. So, C is correct and E is not.

P.S. Please do not post and report at the same time. A post is enough. Thank you.

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

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