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

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If 3x + 5 < x + 11, is x prime? [#permalink] New post 19 Jan 2013, 20:32
00:00
A
B
C
D
E

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Question Stats:

24% (01:55) correct 75% (00:47) wrong based on 53 sessions
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] New post 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] New post 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] New post 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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Re: If 3x + 5 < x + 11, is x prime? [#permalink] New post 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.

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Re: If 3x + 5 < x + 11, is x prime? [#permalink] New post 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] New post 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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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