Last visit was: 20 Jul 2024, 09:01 It is currently 20 Jul 2024, 09:01
Toolkit
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

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

Track

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.

# A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}.

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 11 Sep 2011
Posts: 4
Own Kudos [?]: 68 [65]
Given Kudos: 0
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642513 [33]
Given Kudos: 86706
Intern
Joined: 10 Dec 2011
Posts: 7
Own Kudos [?]: 11 [6]
Given Kudos: 0
General Discussion
Director
Joined: 22 Mar 2011
Posts: 518
Own Kudos [?]: 2160 [0]
Given Kudos: 43
WE:Science (Education)
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
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.

Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642513 [0]
Given Kudos: 86706
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3137 [1]
Given Kudos: 141
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
1
Kudos
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.

C.
Manager
Joined: 28 Feb 2012
Posts: 92
Own Kudos [?]: 190 [1]
Given Kudos: 17
GPA: 3.9
WE:Marketing (Other)
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
1
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.
Intern
Joined: 18 Jun 2013
Posts: 3
Own Kudos [?]: 21 [0]
Given Kudos: 4
Location: United States
Concentration: Technology, Strategy
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
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}
Current Student
Joined: 18 Oct 2014
Posts: 679
Own Kudos [?]: 1787 [0]
Given Kudos: 69
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
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)

We are given 5 non-negative integers and told that 4 are distinct numbers. That means there are two integers that are same.

(1) x ≠ 5. We don't know about y. not sufficient.

(2) 4y + 12 = 6(y + 2)
Solving this equation we get the value of y=5

But we don't know the value of x. Hence not sufficient.

Combining both statements:-
y=5
y+5=10

one value from x, x + 7, 2x is 5 or 10
We know x is not equal to 5
which means 2x is not equal to 10
x+7=10
x= 3

And now we can calculate the average. C is the answer
Senior Manager
Joined: 12 Mar 2013
Posts: 289
Own Kudos [?]: 631 [1]
Given Kudos: 1062
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
1
Kudos
A tough one.. Kudos to bunuel for such nice explanation.
Manager
Joined: 22 Sep 2014
Posts: 126
Own Kudos [?]: 40 [0]
Given Kudos: 51
Location: United States (CA)
A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
(1) x ≠ 5 not sufficient
(2) 4y + 12 = 6(y + 2) => y=0 still not sufficient

1 and 2 together {x, x + 7, 2x, 0, 5}. only four distinct values ,at the same time x ≠ 5 ===> x≠0 ,but we need to have 2 same numbers ,so 2x = x+7 ====> x=7

so {7, 7 + 7, 2*7, 0, 5} ..easy to get the mean

c
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4918
Own Kudos [?]: 7807 [0]
Given Kudos: 221
Location: India
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
Top Contributor
Q.stem says: The set has non negative integers(so 0 included) & two are identical(since 4 of 5 elements are distinct).
To find mean,we need to know the elements in the set.

#St1: x not equal to 5 gives us no information on y.
Insufficient. Eliminate A,D

#St2: 4y + 12 = 6(y+2)
So y=0 and hence two of the elements are 0 and 5(y+5).

Can we have another 0 as x?
In that case x,2x,y would all be 0.3 identical elements. Not possible.

Can we have another 5 as x?
In that case the set {x,x+7,2x,y,y+5} would be {5,12,10,0,5}

Two elements identical. Possible.
Can we have the terms x+7 and 2x identical?

So x+7 = 2x ? ( Two elements identical)
Then the set is {7,14,14,0,5}.Possible.

Thus no definite answer from st2.Eliminate B.
Combine 1 & 2,

You have x as 7 as it cannot be 5(st 1)
So {7,14,14,0,5}

(Sufficient)
(option c)
D.S
GMAT SME
Intern
Joined: 29 Dec 2019
Posts: 47
Own Kudos [?]: 36 [0]
Given Kudos: 38
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
C Q: What is the mean?
--{x,x+7,2x,y,y+5}
--All NON-Negative integers
--Two of those integers are alike and the other 3 all different.

(1) x≠5 Simply Not Sufficient.

(2) 4y+12=6y+12 y=0
{x,x+7,2x,0,5}
Limitations: x+7≠0 (all non-negative. X would be -7)
x≠0, 2x≠0 (Only 2 values are the same)
x≠x+7

Possibilities:
If x=7, we would have 4 values and could calculate a mean.
If x = 1, we would have 4 values and we could calculate a mean
BUT, these means would be DIFFERENT. I CANNOT determine the mean of this set.
Not Sufficient

TOGETHER:
x≠0 or 5 x≠2x (that would mean x=0, see above. Can^' t be true.
SO, x+7=2x and x=7 and we CAN calculate the mean.

Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
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.
Re: A set of nonnegative integers consists of {x, x + 7, 2x, y, y + 5}. [#permalink]
Moderator:
Math Expert
94430 posts