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Math Expert V
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The sum of 5 different positive 2-digit integers is 130. What is the  [#permalink]

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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

Kudos for a correct solution.

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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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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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GMAT 1: 710 Q49 V38 Re: The sum of 5 different positive 2-digit integers is 130. What is the  [#permalink]

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

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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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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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Top Contributor
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:

Cheers,
Brent
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The sum of 5 different positive 2-digit integers is 130. What is the  [#permalink]

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Hi All,

This is an example of a "limit" question (a prompt that asks you to solve for the "lowest" or "highest" possible value) and Brent's solution is perfect (it's exactly how I would approach this question). Sometimes Quant questions are more about "playing" with a series of restrictions and saying "what if…?" than doing lots of algebra.

There is an algebra approach to this prompt, but it still involves aspects of what Brent showed in his approach (TESTing VALUES, minimizing values so you can maximize one of them):

Since we're dealing with 5 DIFFERENT positive 2-digit integers, to maximize 1 of them, we have to minimize all of the others.

I'll call the smallest 2-digit integer….X
So the next 3 smallest would be….(X+1), (X+2) and (X+3)

Those 4 values sum to 4X + 6

Since the sum of all 5 terms = 130, the 5th value (the biggest one) is….130 - (4X+6)

If you make X the smallest positive 2-digit number possible, you'd have X=10. Plug THAT value into the calculation and you get…

130 - (40+6) = 84

Final Answer:

While I would NOT recommend approaching the question in this way (since it requires so much more work and time), it does get you to the correct answer.

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

Since we want to maximize the largest integer, we must minimize the four smallest integers. The smallest 2-digit integers are 10, 11, 12, and 13,which have a sum of 46. Thus, the largest integer would be 130 - 46 = 84.

Answer: B
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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: The sum of 5 different positive 2-digit integers is 130. What is the   [#permalink] 10 Jun 2019, 19:29
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