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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
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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
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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]

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15 Dec 2013, 19:58

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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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I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

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]

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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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