|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (01:43) correct
62%
(01:39)
wrong
based on 2170
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
Guys, I am sure this might have come earlier, but I am kind of confused about these MUST be true questions.
Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!
Here, if 3x/y is a prime number greater than 2 then x and y should always be equal so that they can cancel out. We cant have any other factor of 3x/y!!
12 Oct 2009, 11:49
Kudos
Bookmarks
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
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
jlgdr
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,302
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
11 Sep 2013, 12:51
Kudos
Bookmarks
Tricky question. Took 1.50min to solve it.
But this is what I did.
1st Statement: From first looking at the expression, 'x=y' is the easiest way to have a Prime Integer greater > 2 (3 in this case) from the original question stem. Now we must ask ourselves, is there anyway that this number is a prime number greater than 2 and different from 3? Say for example 5. First look at the denominator, to have 5 as the answer we need to get rid of the 3 so 'y=3', could be an option. Then if 'x = 5, we have that the expression is in fact 5.
So x/y = 5/3 could be an option.
2nd Statement: Does 'y=1" ? We just found out that 'y=3' is an option so this one is out.
3rd Statement: This is a bit more difficult. We need to ask ourselves again, do they both have to be prime integers? Let's start with the denominator, we used 'y=3' in the last example but 'y' could be in fact any multiple of 3, lets say we picked 6. Now, to have '5' (Prime>2) as an answer we could use 10 in the numerator. Since both 'x' and 'y' are 10 and 6 they don't both have to be prime numbers.
So answer is (a) None
But this is what I did.
1st Statement: From first looking at the expression, 'x=y' is the easiest way to have a Prime Integer greater > 2 (3 in this case) from the original question stem. Now we must ask ourselves, is there anyway that this number is a prime number greater than 2 and different from 3? Say for example 5. First look at the denominator, to have 5 as the answer we need to get rid of the 3 so 'y=3', could be an option. Then if 'x = 5, we have that the expression is in fact 5.
So x/y = 5/3 could be an option.
2nd Statement: Does 'y=1" ? We just found out that 'y=3' is an option so this one is out.
3rd Statement: This is a bit more difficult. We need to ask ourselves again, do they both have to be prime integers? Let's start with the denominator, we used 'y=3' in the last example but 'y' could be in fact any multiple of 3, lets say we picked 6. Now, to have '5' (Prime>2) as an answer we could use 10 in the numerator. Since both 'x' and 'y' are 10 and 6 they don't both have to be prime numbers.
So answer is (a) None
