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# The average of a set of 7 integers equal 27. If the smallest number of

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The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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07 Jun 2015, 04:13
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Question Stats:

27% (01:55) correct 73% (01:44) wrong based on 358 sessions

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The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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10 Jun 2015, 03:44
4
8
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

1) In order to receive max number we should minimize all other numbers. So before median we have three equal numbers a1, after median we have two numbers equal to median and at the end we have max number:
a1, a1, a1, 23, 23, 23, a7

We know that the smallest number equal $$\frac{1}{3}$$ of the largest number so we can write equation:
$$a1 = \frac{1}{3}*a7$$

And as we know average we can find the sum of all numbers: average * number of elements = sum
$$27 * 7 = 189$$

So $$a1 + a1 + a1 + 23 + 23 + 23 + a7 = 189$$ and we can rewrite it to
$$3*\frac{1}{3}*a7 + 69 + a7 = 189$$ --> $$2a7 = 120$$ --> $$a7 = 60$$
Sufficient

2) From this statement we know that max element - min element = 40 and that the smallest number equal $$\frac{1}{3}$$ of the largest number, so we can write equation:
$$a1 = \frac{1}{3}*a7$$

By combining this two equations
$$a7 - a1 = 40$$ and $$a1 = \frac{1}{3}*a7$$

$$a7 - \frac{1}{3}*a7=40$$ --> $$\frac{2}{3}*a7=40$$ --> $$a7 = 60$$

Sufficient

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##### General Discussion
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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07 Jun 2015, 04:13
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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07 Jun 2015, 15:58
1
Hi Harley1980,

The 'design' of this DS question is not correct. The question should ask "What IS the largest number in the set?" Given the information that is included in the prompt, we can actually answer the current version of the question as is (without needing either of the two Facts).

GMAT assassins aren't born, they're made,
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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Retired Moderator Joined: 06 Jul 2014 Posts: 1248 Location: Ukraine Concentration: Entrepreneurship, Technology GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink] ### Show Tags 07 Jun 2015, 22:16 EMPOWERgmatRichC wrote: Hi Harley1980, The 'design' of this DS question is not correct. The question should ask "What IS the largest number in the set?" Given the information that is included in the prompt, we can actually answer the current version of the question as is (without needing either of the two Facts). GMAT assassins aren't born, they're made, Rich Hello Rich. Thanks for you reprimand. I put a lot of time to save the "integrity" of DS statements in this task but looks like I miss "initial" state of question. But I have one question: if we use information from statements than we find that max number is 60 and if we don't use information from statements we find that max number is 63. So yes, I completely agree that we can find answer without statements, but this answer contradicts to answer that we get from statements. Can such 'statements-contradicting' answer regards as right? P.S. I definitely agree with you that this is not pure GMAT format of question, but what do you think: technically is a correct or is better to delete this question? _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11984 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink] ### Show Tags 08 Jun 2015, 17:06 1 Hi Harley1980, Other than the wording in the question that is asked, the overall prompt is fine. One of the design elements in DS questions is that you will NOT be able to definitively answer the question with just the given information in the initial prompt. The possible answers to the question will be dependent on the information in the two Facts. In the original version of this prompt, we CAN definitely answer the question (we CAN determine what the largest POSSIBLE value is), so that 'phrase' just needs to be edited to make this DS question line up with the standards that GMAT question writers use. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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09 Jun 2015, 00:31
EMPOWERgmatRichC wrote:
Hi Harley1980,

Other than the wording in the question that is asked, the overall prompt is fine. One of the design elements in DS questions is that you will NOT be able to definitively answer the question with just the given information in the initial prompt. The possible answers to the question will be dependent on the information in the two Facts. In the original version of this prompt, we CAN definitely answer the question (we CAN determine what the largest POSSIBLE value is), so that 'phrase' just needs to be edited to make this DS question line up with the standards that GMAT question writers use.

GMAT assassins aren't born, they're made,
Rich

I've got it. Very subtle difference so I can't catch the sense from the your first reply. But yes, now I see that this difference completely change the question.

Thank you very much for your time, attention and propositions )
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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28 Sep 2015, 03:03
1
1
Harley1980 wrote:
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

1) In order to receive max number we should minimize all other numbers. So before median we have three equal numbers a1, after median we have two numbers equal to median and at the end we have max number:
a1, a1, a1, 23, 23, 23, a7

We know that the smallest number equal $$\frac{1}{3}$$ of the largest number so we can write equation:
$$a1 = \frac{1}{3}*a7$$

And as we know average we can find the sum of all numbers: average * number of elements = sum
$$27 * 7 = 189$$

So $$a1 + a1 + a1 + 23 + 23 + 23 + a7 = 189$$ and we can rewrite it to
$$3*\frac{1}{3}*a7 + 69 + a7 = 189$$ --> $$2a7 = 120$$ --> $$a7 = 60$$
Sufficient

2) From this statement we know that max element - min element = 40 and that the smallest number equal $$\frac{1}{3}$$ of the largest number, so we can write equation:
$$a1 = \frac{1}{3}*a7$$

By combining this two equations
$$a7 - a1 = 40$$ and $$a1 = \frac{1}{3}*a7$$

$$a7 - \frac{1}{3}*a7=40$$ --> $$\frac{2}{3}*a7=40$$ --> $$a7 = 60$$

Sufficient

Hi Harley1980,

In my opinion, this question cannot be solved sufficiently by (1).
While solving for (1), consider this:

1 18 (smallest)
2 23
3 23
4 23 (median)
5 23
6 25
7 54 (largest)

Sum of above is = 189
By what you had solved: smallest was 20 and largest was 60.
From what i have solved: smallest is 18 and largest is 54.

So IMO, the answer is B and not D.
Am i missing something here?
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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28 Sep 2015, 12:55
awesomearjun100 wrote:
Harley1980 wrote:
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

1) In order to receive max number we should minimize all other numbers. So before median we have three equal numbers a1, after median we have two numbers equal to median and at the end we have max number:
a1, a1, a1, 23, 23, 23, a7

We know that the smallest number equal $$\frac{1}{3}$$ of the largest number so we can write equation:
$$a1 = \frac{1}{3}*a7$$

And as we know average we can find the sum of all numbers: average * number of elements = sum
$$27 * 7 = 189$$

So $$a1 + a1 + a1 + 23 + 23 + 23 + a7 = 189$$ and we can rewrite it to
$$3*\frac{1}{3}*a7 + 69 + a7 = 189$$ --> $$2a7 = 120$$ --> $$a7 = 60$$
Sufficient

2) From this statement we know that max element - min element = 40 and that the smallest number equal $$\frac{1}{3}$$ of the largest number, so we can write equation:
$$a1 = \frac{1}{3}*a7$$

By combining this two equations
$$a7 - a1 = 40$$ and $$a1 = \frac{1}{3}*a7$$

$$a7 - \frac{1}{3}*a7=40$$ --> $$\frac{2}{3}*a7=40$$ --> $$a7 = 60$$

Sufficient

Hi Harley1980,

In my opinion, this question cannot be solved sufficiently by (1).
While solving for (1), consider this:

1 18 (smallest)
2 23
3 23
4 23 (median)
5 23
6 25
7 54 (largest)

Sum of above is = 189
By what you had solved: smallest was 20 and largest was 60.
From what i have solved: smallest is 18 and largest is 54.

So IMO, the answer is B and not D.
Am i missing something here?

Hello awesomearjun100

54 is one of the possible variants but
firstly: this is not the largest of this set
secondly: 54 contradicts to second statement and this is not possible in DS questions.

P.S. this is actually "bad" question because it is not GMAT style, but it is good to know how to solve such questions algebraically and not by picking numbers.
Here is algebraic way of solution:
the-average-of-a-set-of-7-integers-equal-27-if-the-smallest-number-of-199439.html#p1536356
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The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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28 Sep 2015, 19:30
1
Harley1980 wrote:
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

1) In order to receive max number we should minimize all other numbers. So before median we have three equal numbers a1, after median we have two numbers equal to median and at the end we have max number:
a1, a1, a1, 23, 23, 23, a7

We know that the smallest number equal $$\frac{1}{3}$$ of the largest number so we can write equation:
$$a1 = \frac{1}{3}*a7$$

And as we know average we can find the sum of all numbers: average * number of elements = sum
$$27 * 7 = 189$$

So $$a1 + a1 + a1 + 23 + 23 + 23 + a7 = 189$$ and we can rewrite it to
$$3*\frac{1}{3}*a7 + 69 + a7 = 189$$ --> $$2a7 = 120$$ --> $$a7 = 60$$
Sufficient

2) From this statement we know that max element - min element = 40 and that the smallest number equal $$\frac{1}{3}$$ of the largest number, so we can write equation:
$$a1 = \frac{1}{3}*a7$$

By combining this two equations
$$a7 - a1 = 40$$ and $$a1 = \frac{1}{3}*a7$$

$$a7 - \frac{1}{3}*a7=40$$ --> $$\frac{2}{3}*a7=40$$ --> $$a7 = 60$$

Sufficient

This solution is perfectly fine if we are asked about lagest POSSIBLE number.and hence i am still not getting why are assuming a1, a1, a1, 23, 23, 23, a7 as elements in SET,
The question just asks what is the largest number, so there is already a set preset and we are supposed to find the largest number.
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The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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29 Sep 2015, 03:59
dav90 wrote:

This solution is perfectly fine if we are asked about lagest POSSIBLE number.and hence i am still not getting why are assuming a1, a1, a1, 23, 23, 23, a7 as elements in SET,
The question just asks what is the largest number, so there is already a set preset and we are supposed to find the largest number.

Hello dav90

the largest value can be only in one exemplar because we can't have two variants of largest number in one set.
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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14 Jul 2016, 00:36
1
Consider the following set S = {19,20,20,23,23,27,57}.
If we take the sum, 19+20+20+23+23+27+57=189 => avg(S) = 27
19 = 57/3
The largest number in the set is 57
The median is clearly 23

Now consider set S = {20,20,20,23,23,23,60}.
If we take the sum, 20+20+20+23+23+23+60=189 => avg(S) = 27
20 = 60/3
The largest number in the set is 60
The median is clearly 23

As shown above, the largest number can be 57 or 60 if the median is 23. Not Sufficient.

The answer, as the question is currently written, should be B.
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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30 Nov 2017, 01:10
dav90 wrote:
Harley1980 wrote:
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

1) In order to receive max number we should minimize all other numbers. So before median we have three equal numbers a1, after median we have two numbers equal to median and at the end we have max number:
a1, a1, a1, 23, 23, 23, a7

We know that the smallest number equal $$\frac{1}{3}$$ of the largest number so we can write equation:
$$a1 = \frac{1}{3}*a7$$

And as we know average we can find the sum of all numbers: average * number of elements = sum
$$27 * 7 = 189$$

So $$a1 + a1 + a1 + 23 + 23 + 23 + a7 = 189$$ and we can rewrite it to
$$3*\frac{1}{3}*a7 + 69 + a7 = 189$$ --> $$2a7 = 120$$ --> $$a7 = 60$$
Sufficient

2) From this statement we know that max element - min element = 40 and that the smallest number equal $$\frac{1}{3}$$ of the largest number, so we can write equation:
$$a1 = \frac{1}{3}*a7$$

By combining this two equations
$$a7 - a1 = 40$$ and $$a1 = \frac{1}{3}*a7$$

$$a7 - \frac{1}{3}*a7=40$$ --> $$\frac{2}{3}*a7=40$$ --> $$a7 = 60$$

Sufficient

This solution is perfectly fine if we are asked about lagest POSSIBLE number.and hence i am still not getting why are assuming a1, a1, a1, 23, 23, 23, a7 as elements in SET,
The question just asks what is the largest number, so there is already a set preset and we are supposed to find the largest number.

I agree. The question stem is incorrectly worded.

"Find the Largest Number" in the set means find the largest of the seven numbers in the particular set
{14,23,23,23,37,37,42} and {15,23,23,23,30,30,45} are both valid sets giving value of largest number a7 = 42, 45 (or increasing multiples of 3 upto 54).

"Find the Largest POSSIBLE number" means find the largest value that any one of the seven number in the set can take. (which is what OP has provided the solution for).

imo edit the question stem to say "What is the largest possible number in the set?" or remove this question.
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Re: The average of a set of 7 integers equal 27. If the smallest number of [#permalink]

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01 Mar 2018, 00:38
Harley1980 wrote:
The average of a set of 7 integers equal 27. If the smallest number of set equal $$\frac{1}{3}$$ of the largest number of set, what is the largest number in the set?

(1) The median of the set equal 23
(2) The range of the set equal 40

Say the largest number in the set is L. Then the smallest number is L/3. Note that "the largest number of set" does not mean "the largest possible value of the largest number of the set". If we can create two sets with different largest numbers, the data is not sufficient.

Stmnt 1:

L/3, ?, ?, 23, ?, ?, L
Not sufficient

Stmnt 2:
L - L/3 = 40
2L/3 = 40
L = 60
Sufficient

In the form presented, the question and the solution do not match. Kindly update.
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Re: The average of a set of 7 integers equal 27. If the smallest number of   [#permalink] 01 Mar 2018, 00:38
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