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Math Expert V
Joined: 02 Sep 2009
Posts: 55188
The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Question Stats: 56% (01:35) correct 44% (01:46) wrong based on 218 sessions

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The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

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GMAT 1: 660 Q39 V40 GMAT 2: 700 Q45 V41 Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Not getting this at all.

If the average of 4 integers is 32, then the sum of those 4 integers should be equal to 4*32 = 128

If the greatest of the 4 numbers is 16, then to minimize the smallest integer, I set the 2nd and 3rd integer to the highest that they could be (1 less than 16) = 15.

16+15+15 = 46.

Therefore to get the value of the smallest, i subtracted the sum of what all four should equal to get an avg of 32 (128), from the sum of the greatest 3 integers (46). I get 82 as an answer. This doesn't make any sense at all.

What am i doing wrong here? Help!
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Bunuel wrote:
The average of four integers is 32. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

Hi Bunuel,

If the average is 32, the greatest number cannot be 16.
Can you please check this question?
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Math Expert V
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Posts: 55188
Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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pushpitkc wrote:
Bunuel wrote:
The average of four integers is 32. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

Hi Bunuel,

If the average is 32, the greatest number cannot be 16.
Can you please check this question?

Thank you guys. Edited. The correct version reads: "The average of four integers is 8..."
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Given data:
Average(4 integers) : 8
Max number : 16

Since the average of 4 numbers is 8, the total must be 32.
If the maximum possible value of the integers is 16, the minimum value could be -16 if the other 2 integers are also 16.
Though -13,0 and 1 are also possible, since we are asked to find the minimum value, Option B stands out and is our answer!

Average = $$\frac{16+16+16-16}{4} = \frac{32}{4} = 8$$(Option B)
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GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

sum of all integers will be 8*4 = 32
Greatest of all integers is 16
-32 is not possible as -32+16=-16..we cannot construct 48 with two integers less than 16
-16 is not possible as we cannot construct 32 with two integers less than 16
-13 is possible as -13+16 = 3..we can construct 29 with two integers less than 16 (14 and 15)

C
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The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

Average of four integers is 8. Sum = 32.
Greatest integer is 16, Sum of remaining 3 integers is 32-16 = 16

i.e. sum of ( the least of four integers + remaining 2 integers )= 16
Trial and error based on answer choices above.

A. -32 + x = 16
x = 48 . Sum of remaining two cannot be 48 since it is greater than overall sum. Eliminated
B. -16 + x = 16
x = 32. Eliminated
C. -13 + x = 16
x = 29.
D. 0 +x = 16
x = 16.
E. 1 + x = 16
x = 15.

Answer is C, since that is the lesser value compared D and E.

Originally posted by shruthiarvindh on 31 Aug 2017, 01:02.
Last edited by shruthiarvindh on 31 Aug 2017, 01:05, edited 1 time in total.
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GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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shruthiarvindh wrote:
Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

Average of four integers is 8. Sum = 32.
Greatest integer is 16, Sum of remaining 3 integers is 32-16 = 16

i.e. sum of ( the least of four integers + remaining 2 integers )= 16
Trial and error based on answer choices above.

A. -32 + x = 16
x = 48 . Sum of remaining two cannot be 48 since it is greater than overall sum. Eliminated
B. -16 + x = 16
x = 32. Eliminated
C. -13 + x = 16
x = 39. Eliminated
D. 0 +x = 16
x = 16.
E. 1 + x = 16
x = 15.

Answer is D, since that is the lesser value compared to E.

shruthiarvindh
i think u missed -13 + x = 16 => x= 29 (14,15)
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The average of four integers is 8. If the greatest of the four intege  [#permalink]

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I think answer is B

Avg = sum/no. of integers i.e sum= 4x8 = 32.

-16 + 16 + 16 + 16 = 32.

Correct me if I went wrong somewhere.

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GMAT 1: 730 Q50 V38 The average of four integers is 8. If the greatest of the four intege  [#permalink]

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2
given : a+b+c+d /4 = 8 and let d be greatest and a be smallest number
a+b+c+d =32

given greatest number d=16

greatest number =16 => means other numbers are less or equal to 16.

a+b+c+16 =32 => a+b+c =16

option 1 if a =-32 => b+c =16+32 = 48 . So basically 48/2 =24 will be minimum value of one of the variable. Not possible because d=16 is greatest.

option 2 of a=-16 => b+c=16+16 =32. . So basically 32/2 =16 will be minimum value of one of the variable. so both b and c can be 16. And in this condition also greatest number will remain 16. This satisfy given condition.
Therefore minimum possible value of a =-16

Answer = B
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The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

if the greatest integer=16,
then the first three integers must sum to 16
assume least integer=-16
16-(-16)=32
thus, the two middle integers must sum to 32
32=16+16
thus, the four integers are -16,16,16,16
B

Originally posted by gracie on 31 Aug 2017, 14:36.
Last edited by gracie on 31 Aug 2017, 14:45, edited 2 times in total.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 2742
The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

If the average of four integers is 8, their sum is 32.

The greatest integer of the four is 16.

Nothing in the problem says the integers cannot be the same.

The least of the four integers will be the smallest when the two "middle" values are equal to the greatest possible integer, which is given as 16 -- if we "weight" the average heavily on the high end, then we allow one value with less weight to be very small.

So if three of the four = 16, the least possible value of the fourth integer is

16 + 16 + 16 + x = 32
48 + x = 32
x = -16

(And $$\frac{-16 +16 +16 +16}{4}$$ = $$\frac{32}{4}$$ = 8 average)

Answer B
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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1
Bunuel wrote:
The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

A. -32
B. -16
C. -13
D. 0
E. 1

Using the formula average = sum/quantity, we see that the sum of the integers is 8 x 4 = 32. If the greatest integer is 16, the next two “smaller” integers can also be 16. So, the sum of the three largest integers is 16 x 3 = 48 and the smallest-value integer would be 32 - 48 = -16.

Answer: B
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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I think the main issue with this problem is how we translate the expression "If the greatest of the four integers is 16"

I've interpreted as there is no other number in the set bigger or even equal to 16, given me the lowest possible value -14, but it's not an answer option.

Could someone clarify the intent on this kind of language in GMAT exercises?

Much appreciated
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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The average of four integers is 8. If the greatest of the four integers is 16, what is the minimum possible value of the least of the four integers

The average of four integers is 8 -> (w+x+y+z)/4=8
Greatest of the four is 16 -> (16+x+y+z)/4=8

32= 16+x+y+z (multiple both sides by four)
16= x+y+z (subtract 16 from both sides)

If we are trying to find the minimum value of the smallest, then we can maximize the other two: 15 +14. Please remember 16 was the highest of all the numbers (given). Therefore the next two highest could be 29 (15+14). 29 + X =16. Therefore answer c (-13) is my response.

Please let me know your thoughts. First time posting, looking forward to this GMAT journey with all of you!
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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When you're working with a Min/Max problem - such as this one that asks you to minimize the least value in a set of numbers - you will want to organize your work by asking yourself:

Quote:
1) Do the values have to be integers? (Here you're told that they do)

Quote:
2) Are zero and/or negative numbers possible? (Here they are not ruled out, so they are indeed possible.) Note that in most word problems negative numbers won't fit the situation (you cannot have -5 children, flowers, or sales), but when a Min/Max problem lacks the "story problem" aspect you will want to make sure you consider negatives.

Quote:
3) Can the numbers repeat? (Here, again, you're not told that they cannot, so the values can repeat)

Then if you're asked to minimize a value, you will want to maximize the others, and if you're asked to maximize a value, you should try to minimize the others (all while adhering to the constraints you've identified above).

You want to minimize the least value, so you will want to maximize the highest value. You're told that that value must be 16, and since there is no prohibition on repeating numbers you can maximize the other two values (you're working with "least," "greatest," and "two others") at 16. That means that your values are 16, 16, 16, and x.

Since the four values average to 8, that means that their sum is 32. Therefore 16 + 16 + 16 + x = 32. This then means that x = -16, making answer choice B correct.
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The average of fhour integers is 8. If the greatest of the four intege  [#permalink]

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Please, could someone help me to understand?

if someone gives you 3 numbers a, b and c.
a = 1
b = 1
c = 1

and ask you to pick the greatest.

If the 3 numbers are equal, how are you supposed to choose?

Can a number be the greatest and still be the same as others? Does anyone have a formal definition for "greatest"?

The average of four integers is 8. If the greatest value the integers can be is 16, what is the minimum possible value of the least of the four integers?
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Re: The average of four integers is 8. If the greatest of the four intege  [#permalink]

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Hi. I solved this quite quickly and accurately but feel that I am missing something as I thought this was quite easy. Do people agree that this is a 700 question ? Or what is the trick here? I simply found that numbers x, y, z should add to 16 or -16 and the numbers can also be 0 so the smallest possible number is -16. Re: The average of four integers is 8. If the greatest of the four intege   [#permalink] 02 Mar 2019, 15:22
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