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Each of the positive integers a, b, and c is a three-digit integer. If

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Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 17 Sep 2014, 10:51
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Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?

A. 45
B. 666
C. 774
D. 801
E. 1368

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Re: Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 17 Sep 2014, 11:55
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clipea12 wrote:
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?

A. 45
B. 666
C. 774
D. 801
E. 1368


According to the stem we should use the digits 1 through 9 to construct 3 three-digit integers, so that their sum is as small as possible.

To minimize the sum, minimize the hundreds digits of a, b, and c, so make them 1, 2, and 3.
Next, minimize tens digits. Make them 4, 5, and 6.
Use the remaining digits (7, 8, and 9) for units digits.

So, a would be 147, b would be 258 and c would be 369.

147 + 258 + 369 = 774.

Answer: C.
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Re: Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 17 Sep 2014, 12:04
crystal clear :) thanks :)
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Re: Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 17 Sep 2014, 22:39
1
clipea12 wrote:
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?

A. 45
B. 666
C. 774
D. 801
E. 1368


Let me add a line to Bunuel's perfect solution here:

The highest digits should be accorded the lowest place value so that they add lowest value to the sum.

Given a 3 digit number such as xyz, to get the lowest number, you should given the lowest digit to the highest place value i.e. to hundreds and the highest digit to the lowest place value i.e. units digit.
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Re: Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 08 Dec 2015, 23:58
clipea12 wrote:
Each of the positive integers a, b, and c is a three-digit integer. If each of the digits 1 through 9 appears in one of these three integers, what is the minimum possible value of the sum of a, b, and c?

A. 45
B. 666
C. 774
D. 801
E. 1368


We are given three 3-digit integers and told that each digit from 1-9 comes in the integers.
This means that there is no repetition of digits as there are 9 places to fill and we have 9 items with us.

Now coming to the next portion. We need to find the minimum sum of the three 3-digit integers.
To make a 3-digit number smallest, we need to give the largest digit to the units place.

Hence the numbers would look like this at this stage: _ _ 9, _ _ 8, _ _ 7
Placing the left out largest integers on the tens places: _ 69, _58, _47
Left ones in the hundreds places: 369, 258, 147
Sum = 774

Option C
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Re: Each of the positive integers a, b, and c is a three-digit integer. If  [#permalink]

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New post 18 Apr 2018, 21:54
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Re: Each of the positive integers a, b, and c is a three-digit integer. If &nbs [#permalink] 18 Apr 2018, 21:54
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