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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 _________________
Re: PS Number property [#permalink]
12 Oct 2009, 10:49
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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
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 _________________
Re: PS section 1 q20 [#permalink]
08 Jun 2010, 11:28
1
This post received KUDOS
Expert's post
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 \(y=15\) --> \(\frac{3x}{y}=5=prime\).
Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
15 Dec 2013, 18:58
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Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
03 Jan 2014, 06:11
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
Re: Number properties: [#permalink]
14 Jan 2014, 19:42
Expert's post
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
Re: If y ≠ 3 and 3x/y is a prime integer greater than 2, which [#permalink]
19 Apr 2014, 20:28
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]
19 Apr 2014, 20:28
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