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

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by BTGmoderatorDC » Fri Sep 22, 2017 1:12 pm
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

What should be my first step in solving this problem? Can experts help me on this?

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by Brent@GMATPrepNow » Fri Sep 22, 2017 1:33 pm
lheiannie07 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
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: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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