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Number problem - prime number

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Number problem - prime number

by gmatrant » Wed Jan 04, 2012 10:52 am
If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers

A) None
B) I only
C) II only
D) III only
E) I and II
A kudos or thanks would do great if my answer has helped you :)
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by pemdas » Wed Jan 04, 2012 10:58 am
y=!3 and 2x/y is prime
all primes greater than 2 are odd, hence 2(x/y) cannot be even and x/y should be fraction not integer
st(1) is not good, because then x/y isn't fraction
st(2) isn't good, because then x/y=x and this isn't fraction
st(3) this isn't good too, as we don't know if x=y or x=!y, we aren't told x and y are different primes, therefore they may be equal

a
gmatrant wrote:If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers

A) None
B) I only
C) II only
D) III only
E) I and II
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by LalaB » Wed Jan 04, 2012 11:12 am
about st3
pemdas, x and y can not be the same, since 2x/y >2

my choice is D
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by rijul007 » Wed Jan 04, 2012 11:24 am
LalaB wrote:about st3
pemdas, x and y can not be the same, since 2x/y >2

my choice is D
If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers

In statement 3
if you plug numbers
x = 21
y = 14
2x/y = 2*21/14 = 3 [which is a prime number >2]
and neither x nor y is prime.

therefore, statement 3 might be true, but it's not a NECESSARY condition

Hence, Option A is the correct option
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by pemdas » Wed Jan 04, 2012 11:28 am
yes, thanks for correction 2(x/y)>2 and x=!y
answer is D
LalaB wrote:about st3
pemdas, x and y can not be the same, since 2x/y >2

my choice is D
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by pemdas » Wed Jan 04, 2012 11:37 am
rijul007 wrote: In statement 3
if you plug numbers
x = 21
y = 14
2x/y = 2*21/14 = 3 [which is a prime number >2]
and neither x nor y is prime.

therefore, statement 3 might be true, but it's not a NECESSARY condition

Hence, Option A is the correct option
riju, your explanation tends to complicate solution.
We are explicitly told that 2(x/y) is prime and inferred that x=!y, hence all numbers which are non-prime but result in prime with 2(x/y) can be further reduced to primes. Also to bifurcate st(3) you need not to find alternate values (not stated in condition) but to negate the condition itself. That is - find any primes x, y which are not resulting in prime with 2(x/y). To be prime as required by 2(x/y), y must be 2 always (fixed prime) and x can be any prime except for 2 [spoiler](opsss)[/spoiler], because the 2(x/y) is equal to 2.

it's D
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by rijul007 » Wed Jan 04, 2012 11:59 am
pemdas wrote: riju, your explanation tends to complicate solution.
Plugging numbers is by far the most UNcomplicate approach to a solution.

pemdas wrote: We are explicitly told that 2(x/y) is prime and inferred that x=!y
I totally agree and i took care of that while selecting numbers, x = 21 and y = 14

pemdas wrote:hence all numbers which are non-prime but result in prime with 2(x/y) can be further reduced to primes.
I dont understand what you are implying here.
I did reduce 2(x/y) to a prime number
pemdas wrote: Also to bifurcate st(3) you need not to find alternate values (not stated in condition) but to negate the condition itself. That is - find any primes x, y which are not resulting in prime with 2(x/y). To be prime as required by 2(x/y), y must be 2 always (fixed prime) and x can be any prime except for 3, because the 2(x/y) is equal to 2.
As i mentioned in my previous post
If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers
The questions is asking whether there are any NECESSARY CONDITIONS among the three statements.

By Necessary conditions, i mean those conditions which, at any cost, has to be true considering the constraints given in the question.
Last edited by rijul007 on Wed Jan 04, 2012 12:00 pm, edited 1 time in total.
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by maddy4rocking » Wed Jan 04, 2012 11:59 am
A is the answer.

-------------------------------------------------------------------------------
Consider Statement 3
x and y are prime integers

2x
___ > 2 [for any combination of x,y (prime integers) 2x/y !>2 )

y
---------------------------------------------------------------------------------
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by pemdas » Wed Jan 04, 2012 12:29 pm
the way you address this question is of little point (sorry), because if the question states y isn't 3 and y is prime in condition (III), why we should at all consider this condition because 3 is prime and we are told that y is prime?
gmatrant wrote:If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers

A) None
B) I only
C) II only
D) III only
E) I and II
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by rijul007 » Wed Jan 04, 2012 12:43 pm
pemdas wrote:the way you address this question is of little point (sorry), because if the question states y isn't 3 and y is prime in condition (III), why we should at all consider this condition because 3 is prime and we are told that y is prime?
Alright, pemdas
lets say you are right

Can you answer these questions for me?

Ques 1
If a and b are two positive integers, and a+b = 10.
Which of the following statements must be true?
(I) a=b
(II) a-b=2

A. I
B. II
C. I and II
D. None


Ques 2
If a and b are two positive integers, and a+b = 10.
Which of the following statements may be true?
(I) a=b
(II) a-b=2

A. I
B. II
C. I and II
D. None
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by pemdas » Wed Jan 04, 2012 1:55 pm
I'm trying to link the relevance of your questions to the doubt I have

you are asking between the difference of MUST and MAY? one is none and the other is two conditions satisfy

Nevertheless, the original question states y cannot be 3 and its condition says x,y are primes. I was asking about the point of giving such information in a question and then supplying prime numbers in the option (III). If the question allows to have primes except for 3, then why don't we have only 2?

I find this question's wording fishy and select option (III) as must.

It's like "To live good I must work". But to say " To live good I must steal" would be also correct, depending on the constraints present. What I mean is that if you cannot bifurcate saying "To live good I must work", then it continues to be MUST. Distinction in how I approach MUST question and you do is that you consider MUST is the only option, but then all GMAT questions with several MUSTs would be violating your logic?

riju, I do agree with you about A, none as I selected earlier, but changed my answer on the grounds of having been provided with info that y isn't 3 and condition (III) y is prime. Such a s****d question (Sorry again), I should have ignored condition (III) right away without any hope of looking after sense here ...
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by rijul007 » Wed Jan 04, 2012 5:49 pm
pemdas wrote:I'm trying to link the relevance of your questions to the doubt I have

you are asking between the difference of MUST and MAY? one is none and the other is two conditions satisfy

Nevertheless, the original question states y cannot be 3 and its condition says x,y are primes. I was asking about the point of giving such information in a question and then supplying prime numbers in the option (III). If the question allows to have primes except for 3, then why don't we have only 2?

I find this question's wording fishy and select option (III) as must.

It's like "To live good I must work". But to say " To live good I must steal" would be also correct, depending on the constraints present. What I mean is that if you cannot bifurcate saying "To live good I must work", then it continues to be MUST. Distinction in how I approach MUST question and you do is that you consider MUST is the only option, but then all GMAT questions with several MUSTs would be violating your logic?

riju, I do agree with you about A, none as I selected earlier, but changed my answer on the grounds of having been provided with info that y isn't 3 and condition (III) y is prime. Such a s****d question (Sorry again), I should have ignored condition (III) right away without any hope of looking after sense here ...
question does mention that y is not equal to 3 but it does not say anything about y being a prime no
and just assuming that would be WRONG

now about the MUST part
The dictionary meaning of must is "To be morally required; to be necessary or essential to a certain quality, character, end, or result; as, he must reconsider the matter; he must have been insane. "

You never have MUST as an "option"
Just like,
You must complete level 1 to reach level 2.
You cannot get to level 2, until or unless you complete level 1. You have no option.


If you still think what I am saying is wrong, I suggest you ask an expert.
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by pemdas » Wed Jan 04, 2012 6:14 pm
riju, let's resume here about this q.

i agree it's D, but I also agree it could be A (as the question is injected with such info which is not corresponding with one of its conditions, namely III).
i think this question is meaningless (really!)
i understand 2(x/y) can be prime if its only factors is the prime number itself or 1 and the number 2 cannot be a factor of (x/y) if (x/y) is not 1 and then 2(x/y) is prime
we are given that 2(x/y) is prime which is greater than 2, so dissect the previous para and consider 2(x/y) can be prime only if (x/y) is not integer (cannot be a whole number factored out)

now these things came to my mind during first minutes of solving this q.

Next, i decided condition (I) is out as x=y means (x/y) is whole number, i.e. 1 (I almost forgot here that the prime number must be > 2). In condition (II) I saw y=1 and decided x should be integer by mistake , although x could be any real value like x=3/2. Since it doesn't say explicitly about x, its value may be anything and condition (II) isn't MUST - ignore.
Condition (III) says x,y are primes and ideally prime divided by another prime considering each prime's value is different (corrected by Lala as 2x/y >2) is non-integer. It could be the case, x=11 and y=7, then 2(11/7) would return non-prime and we are explicitly stated in the question that 2x/y is prime . Hence, I decided to fix the value of y as y=2 (otherwise the meaning of question is devoid) and put any prime for x. But later, you came up with exclamation that non-primes put for x and y would replace primes and bifurcate condition (III).

What I was asking you were

- can GMAT problem have two and/or more conditions which are must for one expression? Or you think there's only one condition which can be must for the question?
- if you answer Yes to the question above, why you believe that plugging in non-prime values for x and y bifurcate that x,y are prime MUST be true. Because it can be that x,y are primes MUST be true and then any other value reduced to primes MUST be true. Look your values which are non-prime, all your values, should be reduced to primes in the num/denom, otherwise your non-prime values are not suitable here. Do you see that???

I reiterate this question is devoid of meaning for GMAT
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by rijul007 » Wed Jan 04, 2012 6:44 pm
pemdas wrote: i understand 2(x/y) can be prime if its only factors is the prime number itself or 1 and the number 2 cannot be a factor of (x/y) if (x/y) is not 1 and then 2(x/y) is prime
we are given that 2(x/y) is prime which is greater than 2, so dissect the previous para and consider 2(x/y) can be prime only if (x/y) is not integer (cannot be a whole number factored out)

now these things came to my mind during first minutes of solving this q.

I totally agree with this.. and this would lead to the ans choice A


pemdas wrote: Condition (III) says x,y are primes and ideally prime divided by another prime considering each prime's value is different (corrected by Lala as 2x/y >2) is non-integer. It could be the case, x=11 and y=7, then 2(11/7) would return non-prime and we are explicitly stated in the question that 2x/y is prime . Hence, I decided to fix the value of y as y=2 (otherwise the meaning of question is devoid) and put any prime for x. But later, you came up with exclamation that non-primes put for x and y would replace primes and bifurcate condition (III).
FIX the value as 2??? why do you want to do that???

This question whether or not is up to the standards of GMAT, I dont know.
But even for the real GMAT, fixing a single number to a variable isnt a right thing to do.

pemdas wrote: - can GMAT problem have two and/or more conditions which are must for one expression? Or you think there's only one condition which can be must for the question?
Yes, there can be more than one conditions that can be must for a single expression.

pemdas wrote: - if you answer Yes to the question above, why you believe that plugging in non-prime values for x and y bifurcate that x,y are prime MUST be true. Because it can be that x,y are primes MUST be true and then any other value reduced to primes MUST be true. Look your values which are non-prime, all your values, should be reduced to primes in the num/denom, otherwise your non-prime values are not suitable here. Do you see that???

I reiterate this question is devoid of meaning for GMAT
Heres what you are saying
x=21
y=14
(x/y) = 21/14 = 3/2

They've reduced to prime numbers.
But does this simplification change the individual values of x and y?
No.
Their values are still the same


Yes, this question isnt as elegant as those in the real GMAT.
But the question is not wrong.

GMAT might too ask a ques, which might include an extra or irrelevant information that is not required in the solution.
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by pemdas » Wed Jan 04, 2012 6:54 pm
rijul007 wrote:FIX the value as 2??? why do you want to do that???

This question whether or not is up to the standards of GMAT, I dont know.
But even for the real GMAT, fixing a single number to a variable isnt a right thing to do.
if you don't have y=2 or any non-prime fraction consequently reduced in the denom. to 2, then you don't comply with
gmatrant wrote:If y not equals 3, and 2x/y is a prime integer greater than 2, which of the following must be true?
1. x=y
2. y=1
3. x and y are prime integers
and if you don't comply with the highlighted question text, then with what you should comply to solve this question?

say x=5/3 and y=2/3, consequently you have 5/3 : 2/3 = 5/2. Both 5/3 and 2/3 are non-primes (they are also non-integers) but MUST be reduced to 2 for 2x/y to be prime.

It MUST be true for x,y to be primes, given y is 2 (prime) and the values of x and y are primes. Other non-prime values of x and y MUST be true, given their ratio returns 2x/y as prime.
Last edited by pemdas on Wed Jan 04, 2012 7:07 pm, edited 1 time in total.
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