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.

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:

A set of nonnegative integers consists of [#permalink]
09 Oct 2012, 07:33

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

29% (03:07) correct
71% (01:56) wrong based on 379 sessions

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

Re: A set of nonnegative integers consists of [#permalink]
09 Oct 2012, 08:33

madimo wrote:

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

(1) x ≠ 5 (2) 4y + 12 = 6(y + 2)

can anybody help? I think the answer should be E, however I saw the answer in some references as C!

Hi, It goes like this:

Statement 1: X not equal to 5, Which is INSUFFICIENT as we need to know the value of Y. Statement 2 says: 4y+12=6y+12 Solving STATEMENT 2, We get Y=0, Hence the series become, X, X+7, 2X, 0, 5 Now, we know that 2 numbers are identical, Which arises following possibilities:

1: x=2x Which means X=0, (But this is not possible as Three numbers in the series will be equal, which refuted the given condition) 2: X+7=2x, which means, X=7 3: X=5 4: X+7=5, (This is also not possible as it gives negative values of X)

A set of nonnegative integers consists of [#permalink]
09 Oct 2012, 08:51

8

This post received KUDOS

Expert's post

madimo wrote:

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

(1) x ≠ 5 (2) 4y + 12 = 6(y + 2)

can anybody help? I think the answer should be E, however I saw the answer in some references as C!

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

Notice couple of things: 1. We are told that all numbers in the set are integers; 2. We are told that all those integers are non-negative; 3. We are told that the set contains four distinct values out of five (so two integers out of 5 are alike and other three are distinct).

(1) x ≠ 5. Clearly insufficient.

(2) 4y + 12 = 6(y + 2) --> 4y+12=6y+12 --> 2y=0 --> y=0. So, we have that our set is {x, x + 7, 2x, 0, 5}. Since we know that two integers out of 5 are alike then:

1. x, x+7 or 2x is 0. If x=0, then 2x=0 too, so in this case we'll have three alike integers x, 2x, and y. Thus this case is out. If x+7=0, then x=-7 and we know that all integers must be non-negative so this case is out too.

2. x, x+7 or 2x is 5 If x=5, then x+7=12 and 2x=10. This scenario is OK. The set in this case would be: {5, 12, 10, 0, 5} If x+7=5, then x=-2 and we know that the integers in the set must be non-negative. Thus this case is out. If 2x=5, then x=5/2 and we know that the numbers in the set must be integers. Thus this case is out.

3. Two out of x, x+7 and 2x are alike. x=2x is not possible, since in this case x=2x=0 and in this case we'll have three alike integers x, 2x, and y. x=x+7 has no solution. 2x=x+7 --> x=7. This scenario is OK. The set in this case would be: {7, 14, 14, 0, 5}.

Two cases are possible. Not sufficient.

(1)+(2) Since from (1) x ≠ 5, then from (2) x=7. So, the set is {7, 14, 14, 0, 5}. Sufficient.

Re: A set of nonnegative integers consists of [#permalink]
09 Oct 2012, 08:52

siddharthismu87 wrote:

madimo wrote:

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

(1) x ≠ 5 (2) 4y + 12 = 6(y + 2)

can anybody help? I think the answer should be E, however I saw the answer in some references as C!

Hi, It goes like this:

Statement 1: X not equal to 5, Which is INSUFFICIENT as we need to know the value of Y. Statement 2 says: 4y+12=6y+12 Solving STATEMENT 2, We get Y=0, Hence the series become, X, X+7, 2X, 0, 5 Now, we know that 2 numbers are identical, Which arises following possibilities:

1: x=2x Which means X=0, (But this is not possible as Three numbers in the series will be equal, which refuted the given condition) 2: X+7=2x, which means, X=7 3: X=5 4: X+7=5, (This is also not possible as it gives negative values of X)

So Statement 2 says either X=7 or X=5,

So Statement 2 is also Insufficient,

Combining bo S 1 and 2, X=7, Hence C..

[size=150][b]thank you for your response, I understand the logic now, cheers

Re: A set of nonnegative integers consists of [#permalink]
09 Oct 2012, 09:08

madimo wrote:

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

(1) x ≠ 5 (2) 4y + 12 = 6(y + 2)

can anybody help? I think the answer should be E, however I saw the answer in some references as C!

(1) If x = 0, the numbers are 0, 7, 0, y, y + 5. If we take y different from 0, 7 and 2, for sure we get four distinct values. Therefore, we cannot know the average of the numbers. For example y = 1: 0, 7, 0, 1, 6, for y = 10 - 0, 7, 0, 10, 15. Not sufficient.

(2) From the given equality, y = 0. We have the numbers x, x + 7, 2x, 0, 5. x cannot be 0 - 0, 7, 0, 0, 5 - only 3 distinct values x can be 5 - 5, 12, 10, 0, 5 - exactly 4 distinct values x can be 7 - 7, 14, 14, 0, 5 - exactly 4 distinct values Not sufficient.

(1) and (2) together: If x is not 5, and x cannot be 0, then x, 2x, 0, and 5 are distinct numbers. It means that x + 7 must be one of them. Since x + 7 > x, x + 7 > 0, x + 7 > 5 (x is positive), the only possibility left is x + 7 = 2x, from which x = 7. The numbers are 7, 14, 14, 0, 5. Sufficient.

Answer C. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A set of nonnegative integers consists of [#permalink]
04 Jun 2013, 23:29

1

This post received KUDOS

Expert's post

madimo wrote:

A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. The numbers of this set have four distinct values. What is its average (arithmetic mean)?

(1) x ≠ 5 (2) 4y + 12 = 6(y + 2)

From F.S 1, all we know is that x ≠ 5. Now as there are 4 distinct values, any 2 of the elements have to be exactly same. Thus, we can have :

x = 2x --> x= 0 OR x+7 = 2x--> x = 7. In both cases we could assume the value of y = 1 and have the set as (0,7,0,1,6)--> Average = 14/5 = 2.8 OR the set would be (7,14,14,1,6) --> Average = 42/5 = 8.4.

Thus,even after adhering to the condition given in the F.S; as we are getting two different values for average-->Insufficient.

From F.S 2, we know that y=0. Thus, the set reads as (x,x+7,2x,0,5).

To make the elements assume 4 distinct values, we can set x = 5, and have the set as (5,12,10,0,5) We could also assume x = 7 just as above and get the set as (7,14,14,0,5). Again, Insufficient.

Taking both the fact statements together, we now know that x = 7. Sufficient.

Re: A set of nonnegative integers consists of [#permalink]
05 Jun 2013, 03:03

1

This post received KUDOS

An interesting question.

1statement) It tells us tha x does not equal to 5, lets take x=1 and y=1 (I am taking these numbers because in the question stem i see that there are four distinct numbers but we have five numbers, this means that two out of five numbers should be identical, so it is easier to take x and y as the same numbers. But to make this question even clearer i would add the word EXACTLY or ONLY four distinct numbers) then we have 1; 8; 2; 1; 6. If we take x=2 and y=2 then we have 2; 9; 4; 2; 7. Two sets which satisfies the question conditions of having four distinct numbers. Not sufficient.

2 statement) if we solve the equation it tells us that y=0. In this case we have last two numbers: 0 and 5. Lets see what are possible other numbers. We have x; x+7 and 2x. According to the question conditions there should be four distinct numbers, in order that to happen x should be equal to 5 or to 7, because in other cases we would have more than 4 distinct numbers or less than 4 distinct numbers. Two possible options - not sufficient.

Combining both statements we see that x does not equall to 5 then it means it is equall to 7. Both statements together are sufficient - choice C. _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: A set of nonnegative integers consists of [#permalink]
19 Aug 2013, 07:38

I miss-read the second stmt, but I think this can be an alternate question where stmt 2 is alone sufficient (1) x ≠ 5 (2) 4x + 12 = 6(y + 2) Came up with answer B – please let me know if my approach is right here.

Set: {x, x + 7, 2x, y, y + 5} Stmt 2 gives: 4x=6y i.e. 2x=3y hence x ≠ y or y ≠ 2x Given that all are integers and are non-negative, hence x ≠ 2x, so from above set only 2 possible scenarios 1. y=x+7 (when combined with 2x=3y) leads to x = -21 -negative -not possible 2. x=y+5 (when combined with 2x=3y) leads to y = 10 so the set becomes {15, 22, 30, 10, 15} hence answer is B

Re: A set of nonnegative integers consists of [#permalink]
15 Sep 2014, 23:55

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. _________________