minimum possible value of the sum of a, b, and c

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 234
Joined: Tue May 31, 2016 1:40 am
Thanked: 3 times
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

OAC

Please explain

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Aug 21, 2016 3:24 am
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
To minimize the sum, the hundreds digits should be AS SMALL AS POSSIBLE:
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Aug 21, 2016 9:12 am
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
Contact Rich at [email protected]
Image

GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pm
Location: East Bay all the way
Thanked: 625 times
Followed by:119 members
GMAT Score:780

by Matt@VeritasPrep » Thu Sep 01, 2016 6:25 pm
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.)