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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

This one isn't clear to me...Like to explain why it is E and not A

IF x and y are positive integers, is 2x a multiple of y? a. 2x + 2 is a multiple of y b. y is a multiple of x

From a:

If x = 2 and y = 3, (2x+2) is a multiple of y but not 2x. If x = 2 and y = 2, (2x+2) and 2x are multiple of y.

So not sufficient.

From b: y is a multiple of x means x is equal to or smaller than y.

If y = x = 3, 2x is a multiple of y. If y = 3 and x = 1, 2x is not a multiple of y. not sufficient.

From a and b: (2x + 2) is a multiple of y and y is a multiple of x.

If x = 2 and y = 2, (2x+2) is multiple of y and y is also a multiple of x. So 2x is also a multiple of y. If y = 6 and x = 2, (2x+2) is multiple of y and y is also a multiple of x but 2x is not a multiple of y.

statement 1. just means that y is even, but it does not tell us anything about the direct relationship between x and y. Simplified is really saying 2x + 2 =yk , k being an unknown multiplication of y

as the earlier post did, plug numbers.

2(2) + 2 = yk : when x is 2, y can be 2 multiplied 3 times, and so 2x will be a multiple of y BUT we could also assume y is 3 multiplied 2 times, in which case 2x ie. 4 is not a multiple of 3. this gives a yes/no answer so its insufficient.

2(x) + 2 = y (k times) 2(2) + 2 = 2 (3 times) ...........4 is a multiple of 2 BUT 2(2) + 2 = 3 (2 times)...........4 is not a multiple of 3

"Is \(\frac{2x}{y}\) an integer?" "Is \(2x\) a multiple of (divisible by) \(y\)?" "Is \(y\) a factor of \(2x\)?"

Statement 1) This statements says that \(\frac{2x + 2}{y} = \frac{2(x+1)}{y}\) is an integer. In other words, \(2(x+1)\) is a multiple of \(y\).

In order for both \(2x\) and \(2(x+1)\) to be divisible by \(y\), \(y\) must be either \(1\) (factor of \(2\) and both \(x\) and \((x+1)\)) or \(2\) (factor of \(2\)). Thus if \(y\) equals \(1\) or \(2\), then \(\frac{2x}{y}\) is an integer. If \(y\) has any other value under this constraint, \(\frac{2x}{y}\) is not an integer.

You can also break this statement into two expressions: \(\frac{2x + 2}{y} = \frac{2x}{y} + \frac{2}{y}\). If \(\frac{2x}{y} + \frac{2}{y}=integer\), then in order for \(\frac{2x}{y}\) to be an integer, \(\frac{2}{y}\) must also be an integer. Thus if \(y\) equals \(1\) or \(2\), then \(\frac{2x}{y}\) is an integer. If \(y\) has any other value, \(\frac{2x}{y}\) is not an integer.

Insufficient.

Statement 2) This statement says that \(\frac{y}{x}\) is an integer. So \(y = x*k\), where \(k\) is some integer.

In order for \(\frac{2x}{y} = \frac{2*x}{k*x}\) to be an integer, \(\frac{2}{k}\) must be an integer, ie \(k\) must equal either \(1\) or \(2\). Thus if \(y = 2x\) or \(y = x\), \(2x\) will be a multiple of \(y\). With any other value of \(k\), \(2x\) will not be a multiple of \(y\).

Insufficient.

Combined) From statement 1, \(\frac{2x}{y}\) is an integer when \(y={1,2}\), and not an integer when \(y\) has another value. From statement 2: \(\frac{2x}{y}\) is an integer when \(y=2x\) or \(y=x\), and not an integer when \(y\) is a different multiple of \(x\) than \(2\).

So under the constraints of both statements, \(\frac{2x}{y}\) is an integer when \((x,y)\) = \((1,1)\), \((2,2)\), or \((1,2)\).

It only takes one example that follows the two constraints but is not one of these 3 possibilities to prove the combined statements insufficient. A couple examples are \((x,y) = (1,4)\), or \((2,6)\).

(1) 2x+2 is a multiple of y (2) y is a multiple of x

stmnt1:

If y= 1 x=2 then 2x+2 = 6 and multiple of y. 2x =4 and multiple of y but if y=3 and x=2 then 2x+2=6 and multiple of y but 2x=4 and not a multiple of y. Hence insuff

stmnt 2:

y = 2 and x= 1 then 2x is multiple of y y= 3 and x= 1 then 2x is not multiple of y. Hence insuff

taking together x=1 and y =2 we have y is multiple of x, 2x+2 = 4 multiple of y and 2x= 2 is multiple of y (2) . x=1 and y =4 we have y is multiple of x, 2x+2 = 4 multiple of y but 2x= 2 is not multiple of y (4)

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

(1) 2x+2 is a multiple of y (2) y is a multiple of x

Use some logic and some number plugging:

Question: Is 2x a multiple of y?

(1) 2x+2 is a multiple of y

(2x + 2) is a multiple of y. 2x and (2x+2) are two consecutive even numbers and hence share only 2 factors: 1 and 2 So 2x will also be a multiple of y only if y is 1 or 2. Not sufficient.

(2) y is a multiple of x Here are the multiples: x....y....2x If y is x or 2x, 2x will be a multiple of y, else it will not be. Not sufficient.

Using both together: If y = 2 and x = 2, all conditions are met and 2x IS a multiple of y. If y = 6 and x = 2, all conditions are met but 2x IS NOT a multiple of y. Not sufficient.

Statment 1 tells that y is either 1 or 2. Statment 2 shows that y is 2 as its a multiple of x and 1 cant be a multiple of any number, thats what understand, tell me where am going wrong!

What if x=1 and y=2..it satisfies all the conditions??

sunaimshadmani wrote:

Statment 1 tells that y is either 1 or 2. Statment 2 shows that y is 2 as its a multiple of x and 1 cant be a multiple of any number, thats what understand, tell me where am going wrong!

From (1), from 2x+2 is a multiple of y, we don't have that y is either 1 or 2. It can take many other values.

Is 2x a multiple of y?

(1) 2x+2 is a multiple of y. If x=1 and y=1, then the answer is YES but if x=1 and y=4, then the answer is NO. Not sufficient.

(2) y is a multiple of x. If x=1 and y=1, then then the answer is YES but if x=1 and y=4, then the answer is NO. Not sufficient.

(1)+(2) The same here: if x=1 and y=1, then then the answer is YES but if x=1 and y=4, then the answer is NO. Not sufficient.

Re: If x and y are positive integers, is 2x a multiple of y? [#permalink]

Show Tags

15 Nov 2015, 09:17

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...