Five integers between 10 and 99, inclusive, are to be formed

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Five integers between 10 and 99, inclusive, are to be formed

by BTGmoderatorDC » Sat Dec 28, 2019 6:02 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

OA C

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Sat Dec 28, 2019 6:02 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Dec 30, 2019 10:01 pm

BTGmoderatorDC wrote: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

OA C

Source: Official Guide

Since we want the sum of the five integers to be as small as possible, we must start with the smallest of them such that units digit is 9 so that the greater digits are consumed in units digits and the smaller digits are consumed in tens digits. With such an arrangement, the five integers are 19, 28, 37, 48, and 50. The 5th integer cannot be 59 since 9 is already used in the 1st integer.

However, 50 is not the greatest possible integer such that the sum of the five integers is as small as possible. We can exchange the units digits of 19 and 50, keeping the sum the same. Thus, the 1st integer is 10 and the 5th, the greatest integer = 59.

The correct answer: C

Hope this helps!

-Jay
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by Scott@TargetTestPrep » Sat Jan 04, 2020 7:25 pm

BTGmoderatorDC wrote: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

OA 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

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