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Manager  Joined: 02 Sep 2008
Posts: 99
If y ≠ 3 and 3x/y is a prime integer greater than 2, which  [#permalink]

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23 00:00

Difficulty:   75% (hard)

Question Stats: 48% (01:44) correct 52% (01:42) wrong based on 536 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 55732

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5
6
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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Director  Joined: 04 Jan 2008
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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/y
hence 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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Manager  Joined: 19 Aug 2006
Posts: 200

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I got A.

You can pick numbers that contradict all three statements.
What is the OA?
Current Student Joined: 13 Jan 2009
Posts: 310
Location: India

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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
Intern  Joined: 21 Jul 2006
Posts: 16

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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.
VP  Joined: 05 Jul 2008
Posts: 1182

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matrix777 wrote:

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.
Senior Manager  Joined: 01 Mar 2009
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1
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.

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Intern  Joined: 09 Nov 2008
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take x=10 and y=6 and hence the answer is A.
Senior Manager  Joined: 12 Oct 2008
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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.
Intern  Joined: 21 Jul 2009
Posts: 11

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1
(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

Manager  Joined: 18 Jul 2009
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1
I got A picking x=16 and y=6..we get 3x/y = 7....thus OA A
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I'm assuming that the question reads ... and x is a prime integer greater than 2.

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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Joined: 02 Sep 2009
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Re: PS section 1 q20  [#permalink]

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1
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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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

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

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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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AbhayPrasanna wrote:
I'm assuming that the question reads ... and x is a prime integer greater than 2.

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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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

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

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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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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   [#permalink] 21 Mar 2016, 18:16

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