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If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
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01 Apr 2009, 02:27
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If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true? I. x = y II. y = 1 III. x and y are prime integers. (A) None (B) I only (C) II only (D) III only (E) I and III
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Re: PS Number property [#permalink]
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12 Oct 2009, 11:49
If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true? Ⅰ. x = y Ⅱ. y = 1 Ⅲ. x and y are prime integers. (A) None (B) Ⅰ only (C) Ⅱ only (D) Ⅲ only (E) Ⅰ and Ⅲ Answer to this question is A. None of the statements (I,II,III) must be true. This Q. can be solved by number plugging in a minute but it's quite tricky, so let's generalize it so to understand the concept, as there are many similar problems in GMAT: Q. says that: y≠3 and that 3x/y IS a prime integer. Then it asks which of the statements MUST be true? First note that it's not stated that x and y are integers or positive/negative. Generally, the expression 3x/y is always prime in two cases: When x is a multiple of prime and y is same multiple of three: x=pn and y=3n (p prime >2, n ANY number but 1), so we have 3(pn)/3n=p. AND When x=y ≠1 then 3x/y=3=p>2 Note that first formula also gives us the p=3 but only when x and y are the multiples of three (n ANY number but 1, can be 6 or 75 but not 1), thus it exclude all possibilities when x=y and ARE not multiples of three, for instance x=8 and y=8. So from above it's not necessary x=y or y=1 or x,y to be primes. Let's look: I. x = y > not necessarily true: x=25 y=15 3x/y=5 II. y=1 > not necessarily true: x=8 y=8 3x/y=3 III. x and y are prime integers > x=21 y=9 3x/y=7
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Re: Number property........... [#permalink]
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01 Apr 2009, 02:47
good Q Prime Integers are 2,3,5,7,11,13,............ IMO C See, 3x/y is a prime integer greater than 2 say 3 hence That prime integer(3) will have 2 divisors 3 and x/yhence x=y is it from OG 12?20. If y ≠ 3 and 3x/y is a prime integer greater than 2, which of the following must be true? Ⅰ. x = y Ⅱ. y = 1 Ⅲ. x and y are prime integers. (A) None (B) Ⅰ only (C) Ⅱonly (D) Ⅲonly (E) Ⅰand Ⅲ
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Re: Number property........... [#permalink]
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01 Apr 2009, 16:56
I got A.
You can pick numbers that contradict all three statements. What is the OA?



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Re: ps Number property........... [#permalink]
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02 Apr 2009, 15:44
A.
z=3x/y for z to be prime number x=10 y=6 I is not true
Y could be 1 where our question asks must be...
Prime number could be... with x/y 3/3, 15/15



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Re: ps Number property........... [#permalink]
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02 Apr 2009, 23:33
My answer is B.
3x/y = 3*(x/y) < prime number that is greater than 2. if x and y are equal than the eqn becomes 3 * (1) = 3 (prime number greater than 2)
Since we are looking for an integer (all prime numbers are integers) and y != 3 than x must equal y.



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Re: ps Number property........... [#permalink]
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03 Apr 2009, 17:14
matrix777 wrote: My answer is B.
3x/y = 3*(x/y) < prime number that is greater than 2. if x and y are equal than the eqn becomes 3 * (1) = 3 (prime number greater than 2)
Since we are looking for an integer (all prime numbers are integers) and y != 3 than x must equal y. Initially I fell for it but take x=14 and y =6 3x/y = 7 which is still a prime and x ! = y Hence B is not correct.



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Re: ps Number property........... [#permalink]
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06 Apr 2009, 17:42
The answer is A  Other than picking numbers, is there any option here ? I spent more than 2 minutes on this and fell for the wrong answer. pradeep
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Re: ps Number property........... [#permalink]
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08 Apr 2009, 05:36
take x=10 and y=6 and hence the answer is A.



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Re: ps Number property........... [#permalink]
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07 May 2009, 21:22
Ans must be B
3x/y and if x=y then ans is 3 and 3 is prime number, which is greater than 2. so ans must be B. Please post OA.



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Re: PS Number property [#permalink]
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12 Oct 2009, 08:38
(3x/y) is a prime integer greater than 2. which of the following must be true
Suppose P=3x/y
Possible values of P = 3,5,7,11 ......
Statement I: If P = 3 , x=y TRUE If P = 5, x=y FALSE <== Statement I is not always correct
Statement II: If y=1 is TRUE => P = 3x Since P is a prime number, it cannot be a multiple of 3
Statement III: suppose x = 7 and y=5 , P= 21/5 => Not a prime number You can fill some other values of x and y
Answer should be A



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Re: PS Number property [#permalink]
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13 Oct 2009, 11:55
I got A picking x=16 and y=6..we get 3x/y = 7....thus OA A
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Re: Number properties: [#permalink]
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07 Jun 2010, 04:23
I'm assuming that the question reads ... and x is a prime integer greater than 2.
In these questions, always start with III
III. x and y are prime integers. Well x is a prime integer. But y could be any number other than 3. NOT TRUE.
II. y = 1. Need not be true. y could be anything other than 3.
I. x = y. Need not be true. y could be anything other than 3.
Pick A
Rather basic question, doubt you'll see this in the actual test.



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Re: PS section 1 q20 [#permalink]
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08 Jun 2010, 12:28
sunland wrote: 20. If y ≠ 3 and is a prime integer greater than 2, which of the following must be true? Ⅰ. x = y Ⅱ. y = 1 Ⅲ. x and y are prime integers. (A) None (B) Ⅰ only (C) Ⅱonly (D) Ⅲonly (E) Ⅰand Ⅲ
the solution booklet says answer is A but shouldnt x=y making B the answer if the number is prime and greater than 2, then the number has to be 3. which is possible only if x=y. First of all the question misses important part (\(\frac{3x}{y}=prime\)). Second this question is MUST be true question not COULD be true. Refer to the solutions above to see that it's not necessary x=y to be true for 3x/y to be a prime integer greater than 2. For example \(x=25\) and \(y=15\) > \(\frac{3x}{y}=5=prime\). Hope it's clear.
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Re: PS Number property [#permalink]
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01 Aug 2011, 00:38
Except for A, the rest I just need to determine the other two which one is prime number SMAbbas wrote: (3x/y) is a prime integer greater than 2. which of the following must be true
Suppose P=3x/y
Possible values of P = 3,5,7,11 ......
Statement I: If P = 3 , x=y TRUE If P = 5, x=y FALSE <== Statement I is not always correct
Statement II: If y=1 is TRUE => P = 3x Since P is a prime number, it cannot be a multiple of 3
Statement III: suppose x = 7 and y=5 , P= 21/5 => Not a prime number You can fill some other values of x and y
Answer should be A



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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
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03 Jan 2014, 07:11
Done by Plugging in y#3 and 3x/y = prime number > 2 ,so 3,5,7,11... 1. x = y , x,y = 2 answer is 3 ; x,y = 3 or 4 or 5... answer is 3 which is a prime number then why this option is wrong 2. y = 1 its straight away wrong 3. x,y both prime any prime numbers so wrong why 1 option is wrong?? but after seeing with other numbers and bunnel post i realized that even if x= 35 , y = 15 the prime number is 7 even though which is >2
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Re: Number properties: [#permalink]
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13 Jan 2014, 20:22
AbhayPrasanna wrote: I'm assuming that the question reads ... and x is a prime integer greater than 2.
In these questions, always start with III
III. x and y are prime integers. Well x is a prime integer. But y could be any number other than 3. NOT TRUE.
II. y = 1. Need not be true. y could be anything other than 3.
I. x = y. Need not be true. y could be anything other than 3.
Pick A
Rather basic question, doubt you'll see this in the actual test. Can you explain your reasoning to (I)?



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Re: Number properties: [#permalink]
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14 Jan 2014, 20:42
TooLong150 wrote: Can you explain your reasoning to (I)? If a prime number is written as a product of two numbers, one of them must be prime and the other must be 1. 3x/y would be prime if 'x/y is 1' (in which case 3x/y = 3) or '3 gets canceled off from a 3 in y and the leftover is a prime number' So some solutions are: x = y = 1 x = y = Anything other than 0 y is a multiple of 3, say 3n and x/n is a prime number. We are given that y is not 3 but we are not given that it is not a multiple of 3. Say, y = 6 = 3n. In that case x/n can be a prime number. e.g. x = 10 or 14 or 26 etc 3x/y = 3*10/6 = 5 3x/y = 3*14/6 = 7 etc So x = 14, y = 6 is a solution. So it not NECESSARY (but it is possible) that x=y, y = 1, x and y are prime Answer (A)
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
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19 Apr 2014, 21:28
y !=3 x * (3/y) I. x = y x * 3/x > 2 3> 2 Hence Must be true for the inequality to hold II. y = 1 x * 3/1 > 2 Could be true if x=1 III. x and y are prime integers. Then the expression itself wont be an integer except when x=y Could be true Hence only (1) is must be true
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
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21 Mar 2016, 18:16
I got A! 3x3x5/3x3 = 5  prime number x=15, y=9  so x=y  no. B and E out. y=1  above mentioned example  C out. x=15, y=9  D is out.




Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which
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