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The sum of 5 different positive 2-digit integers is 130. What is the

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The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68

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[Reveal] Spoiler: OA

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Re: The sum of 5 different positive 2-digit integers is 130. What is the [#permalink]

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Bunuel wrote:
The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68

Kudos for a correct solution.


First of all we know that all five nos. are positive and 2digit nos. so the smallest digit will be 10.
since we need to maximize the largest no. we will minimize the other nos. as much as possible.
but these nos. need to be distinct therefore
10+11+12+13+84=130

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Re: The sum of 5 different positive 2-digit integers is 130. What is the [#permalink]

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New post 22 Jan 2015, 11:55
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sum of 5 different 2 digit integers=130

to find out the largest number, we need to make other 4 numbers to the smallest as possible.
smallest 2 digit number is 10
=>10+11+12+13+n=130
=>n=130-46=84

Answer is B

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Re: The sum of 5 different positive 2-digit integers is 130. What is the [#permalink]

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New post 22 Jan 2015, 14:33
We need the other 4 numbers to be different and smallest possible.

10, 11, 12, 13 + x =130
x=84

Answer B.

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New post 28 Jan 2015, 01:03
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Answer = B. 84

Highest number = 130 - (Addition of all 4 smallest numbers)

= 130 - (10+11+12+13)

= 130 - 46 = 84
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Re: The sum of 5 different positive 2-digit integers is 130. What is the [#permalink]

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New post 30 Jul 2017, 00:13
Let the 5 different positive integers be a,b,c,d and e.
a+b+c+d+e = 130

It has been said that these numbers are all different and also 2-digit integers.
The smallest 2 digit integer is 10.
The other smallest integers are 11,12,13. The sum of the smallest 4 integers are 46.

The last integer is 120 - 46 = 84(Option B)
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Re: The sum of 5 different positive 2-digit integers is 130. What is the [#permalink]

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New post 22 Sep 2017, 14:33
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Bunuel wrote:
The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68

Kudos for a correct solution.


Since the 5 numbers are all different, let's let A, B, C, D and E represent the numbers.
Furthermore, let's say A < B < C , D < E, which means E is the biggest value.

We're told that A + B + C + D + E = 130
In order to MAXIMIZE the value of E, we must MINIMIZE the other 4 values.
In other words, we want to MINIMIZE the value of A + B + C + D
Since the numbers must be 2-digit integers, the smallest values for A, B, C and D are 10, 11, 12 and 13 respectively.

So, plugging those values into our equation, we get: 10 + 11 + 12 + 13 + E = 130
Simplify: 46 + E = 130
E = 84

Answer:
[Reveal] Spoiler:
B


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Brent
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Re: The sum of 5 different positive 2-digit integers is 130. What is the   [#permalink] 22 Sep 2017, 14:33
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