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If 3x + 5 < x + 11, is x prime? [#permalink]
 19 Jan 2013, 21:32
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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.
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Last edited by Bunuel on 20 Jan 2013, 05:30, edited 1 time in total.
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Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 05:46
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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]
19 Jan 2013, 22:58
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, 01:33
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, 02:34
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]
20 Jan 2013, 06:06
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, 06:11
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#p1171395Hope it;s clear.
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Re: If 3x + 5 < x + 11, is x prime? [#permalink]
20 Jan 2013, 07:33
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?
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20 Jan 2013, 07:33
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