The sum of 5 different positive 2-digit integers is 130.

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

The sum of 5 different positive 2-digit integers is 130.

by BTGmoderatorRO » Fri Mar 02, 2018 12:34 pm

The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68
OA is b

what mathematical approach can i use here? Can the generous Experts help me out, please<i class="em em-pray"></i>
Thanks<i class="em em-clap"></i>

Quote

Source: Beat The GMAT — Problem Solving | Fri Mar 02, 2018 12:34 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Mar 02, 2018 1:37 pm

Roland2rule wrote:The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68

Since the 5 numbers are all different, let's let A, B, C, D and E represent the numbers.
Furthermore, let's say A < B < C , D < E, which means E is the biggest value.

We're told that A + B + C + D + E = 130
In order to MAXIMIZE the value of E, we must MINIMIZE the other 4 values.
In other words, we want to MINIMIZE the value of A + B + C + D
Since the numbers must be 2-digit integers, the smallest values for A, B, C and D are 10, 11, 12 and 13 respectively.

So, plugging those values into our equation, we get: 10 + 11 + 12 + 13 + E = 130
Simplify: 46 + E = 130
E = 84

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

[email protected]: 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] » Fri Mar 02, 2018 6:10 pm

Hi Roland2rule,

This is an example of a "limit" question (a prompt that asks you to solve for the "lowest" or "highest" possible value) and Brent's solution is perfect (it's exactly how I would approach this question). Sometimes Quant questions are more about "playing" with a series of restrictions and saying "what if...?" than doing lots of algebra.

There is an algebra approach to this prompt, but it still involves aspects of what Brent showed in his approach (TESTing VALUES, minimizing values so you can maximize one of them):

Since we're dealing with 5 DIFFERENT positive 2-digit integers, to maximize 1 of them, we have to minimize all of the others.

I'll call the smallest 2-digit integer....X
So the next 3 smallest would be....(X+1), (X+2) and (X+3)

Those 4 values sum to 4X + 6

Since the sum of all 5 terms = 130, the 5th value (the biggest one) is....130 - (4X+6)

If you make X the smallest positive 2-digit number possible, you'd have X=10. Plug THAT value into the calculation and you get...

130 - (40+6) = 84

Final Answer: B

While I would NOT recommend approaching the question in this way (since it requires so much more work and time), it does get you to the correct answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jun 10, 2019 6:22 pm

BTGmoderatorRO wrote:The sum of 5 different positive 2-digit integers is 130. What is the highest possible value of the largest of these integers?

A. 88
B. 84
C. 78
D. 74
E. 68
OA is b

Since we want to maximize the largest integer, we must minimize the four smallest integers. The smallest 2-digit integers are 10, 11, 12, and 13,which have a sum of 46. Thus, the largest integer would be 130 - 46 = 84.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]