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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Please explain
minimum possible value of the sum of a, b, and c
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To minimize the sum, the hundreds digits should be AS SMALL AS POSSIBLE:Needgmat 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
1XX
2XX
3XX
The tens digits should also be as small as possible:
14X
25X
36X
Thus, the units digits must be 7, 8, and 9:
147
258
369
Since 7+8+9 = 24, the sum of the three integers above must have a units digit of 4.
The correct answer is C.
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Hi Needgmat,
Certain Quant questions on Test Day might require that you spend just a little time "playing around", which essentially means "write some stuff down and see if you can spot a pattern." While you might not immediate see the 'best' way to approach this question, the prompt gives you a specific set of instructions that you can use to 'play around' here:
Create three 3-digit numbers using the digits 1-9 one time each. With JUST that information, can you come up with an example (and what would your 3 numbers be)? Once you write them down, you'll either have the correct answer OR a better idea of how to get to the correct answer (What is the MINIMUM possible sum?).
To maximize your performance on Test Day, you're not allowed to think "I don't know what to do here...."; instead, you have to use the information that you're given to your advantage, take some notes, write down some examples, draw a picture, do SOMETHING. You'd be amazed how many of the questions on this Test are 'gettable', once you choose to go get them.
GMAT assassins aren't born, they're made,
Rich
Certain Quant questions on Test Day might require that you spend just a little time "playing around", which essentially means "write some stuff down and see if you can spot a pattern." While you might not immediate see the 'best' way to approach this question, the prompt gives you a specific set of instructions that you can use to 'play around' here:
Create three 3-digit numbers using the digits 1-9 one time each. With JUST that information, can you come up with an example (and what would your 3 numbers be)? Once you write them down, you'll either have the correct answer OR a better idea of how to get to the correct answer (What is the MINIMUM possible sum?).
To maximize your performance on Test Day, you're not allowed to think "I don't know what to do here...."; instead, you have to use the information that you're given to your advantage, take some notes, write down some examples, draw a picture, do SOMETHING. You'd be amazed how many of the questions on this Test are 'gettable', once you choose to go get them.
GMAT assassins aren't born, they're made,
Rich
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Make the hundreds digits the three smallest values, the tens digits the next three smallest, and the units digits the three largest. That gives us
100 + 200 + 300 + 40 + 50 + 60 + 7 + 8 + 9
in whatever order we like. (We could have 147 + 258 + 369, or 159 + 247 + 368, or whatever: the result will always be 774.)
100 + 200 + 300 + 40 + 50 + 60 + 7 + 8 + 9
in whatever order we like. (We could have 147 + 258 + 369, or 159 + 247 + 368, or whatever: the result will always be 774.)