Five integers between 10 and 99, inclusive,

BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:26 pm

Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?

A. 98
B. 91
C. 59
D. 50
E. 37

Answer: C
Source: Official Guide

See here: five-integers-between-10-and-99-inclusi ... 10880.html

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:26 pm

Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?

A. 98
B. 91
C. 59
D. 50
E. 37

Answer: C
Source: Official Guide

To minimize the sum of the five integers, we will make the tens digits as smallest possible.
This means we'll use 1, 2, 3, 4, and 5 as the TENS digits.

So, for the moment, the five integers look like this: 1_, 2_, 3_, 4_, and 5_

At this point we need to use the other five possible digits (0, 6, 7, 8, and 9) for the UNITS digits

IMPORTANT: It doesn't matter where we place these units digits.
For example, if we make our five integers 10, 26, 37, 48, and 59, their sum is 180
Alternatively, if we make our five integers 19, 20, 38, 46, and 57, their sum is still 180
And, if we make our five integers 17, 28, 39, 46, and 50, their sum is still 180
etc..

The question asks "What is the greatest possible integer that could be among these five numbers?"
So, the greatest possible integer value is 59

Answer: C

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Feb 26, 2020 4:26 pm

Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?

A. 98
B. 91
C. 59
D. 50
E. 37

Answer: C
Source: Official Guide

SInce we want the sum of the 5 two-digit numbers to be as small as possible, we want the tens digits of each number to be as small as possible. Since the tens digit can’t be 0, the five smallest non-zero digits are 1, 2, 3, 4, 5. Therefore, the largest possible integer is in the 50s. How we pair 0, 6, 7, 8 and 9 (as the units digits) with 1, 2, 3, 4, 5 (as the tens digits) doesn’t matter. For example, the sum of 10, 26, 37, 48 and 59 is equal to the sum of 19, 28, 37, 46 and 50 (notice that either sum is 180). Therefore, the greatest possible integer is 59.

Answer: C