• Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

The sum of two numbers is 13. . .

This topic has 4 expert replies and 1 member reply

The sum of two numbers is 13. . .

Post Sun Sep 24, 2017 7:06 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The sum of two numbers is 13, and their product is 30. What is the sum of the squares of the two numbers?

    (A) -229

    (B) -109

    (C) 139

    (D) 109

    (E) 229

    The OA is D.

    Clearly options A and B are not correct. Can I solve this PS question without finding the values of the two numbers?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Sep 24, 2017 7:15 am
    Vincen wrote:
    The sum of two numbers is 13, and their product is 30. What is the sum of the squares of the two numbers?

    (A) -229
    (B) -109
    (C) 139
    (D) 109
    (E) 229
    I suggest that you start looking for a number pair that ADD to 13 and have a PRODUCT of 30
    It doesn't take long to discover that 3 and 10 work

    What is the sum of the squares of the two numbers?
    3² + 10² = 9 + 100 = 109

    Answer: D

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Mon Sep 25, 2017 3:46 pm
    Hi Vincen,

    Certain Quant questions on Test Day can be solved rather easily with a bit of 'brute force' math - simply list out the possibilities until you find the one that 'fits' the given information.

    Here, we're told that the SUM of two numbers is 13 and the PRODUCT of those two numbers is 30. By definition, BOTH of those numbers must be positive. Since the sum, product and all 5 answer choices are all INTEGERS, it's highly likely that the two numbers will be integers as well.

    2 Positive integers that sum to 13:
    1 and 12; product = 12
    2 and 11; product = 22
    3 and 10; product = 30

    The question asks us for the sum of the squares of the two values....
    3^2 + 10^2 = 109

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    GMAT/MBA Expert

    Post Tue Sep 26, 2017 5:19 pm
    a + b = 13
    ab = 30

    a² + b² = (a + b)² - 2ab

    a² + b² = 13² - 2*30

    a² + b² = 109

    Thanked by: Vincen
    Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
    Post Tue Oct 10, 2017 2:24 pm
    Vincen wrote:
    The sum of two numbers is 13, and their product is 30. What is the sum of the squares of the two numbers?

    (A) -229

    (B) -109

    (C) 139

    (D) 109

    (E) 229

    The OA is D.

    Clearly options A and B are not correct. Can I solve this PS question without finding the values of the two numbers?
    Hi Vincen,
    Lets have a look at your question.
    It can easily be solved using a polynomial identity.

    The question states,
    "The sum of two numbers is 13, and their product is 30. "
    Let the two numbers be 'x' and 'y', then
    x + y = 13 --- (i)
    xy = 30 ---(ii)

    What is the sum of the squares of the two numbers?
    x^2 + y^2 = ?

    We will use the the identity
    (x + y)^2 = x^2 + y^2 + 2xy
    Plugin the values of (x + y) and xy from (i) and (ii) in the above identity.

    (13)^2 = x^2 + y^2 + 2(30)
    169 = x^2 + y^2 + 60
    x^2 + y^2 = 169 - 60
    x^2 + y^2 = 109
    Sum of squares of the two numbers is 109.

    Therefore, Option D is correct.

    Hope this helps.
    I am available if you'd like any follow up.

    _________________
    GMAT Prep From The Economist
    We offer 70+ point score improvement money back guarantee.
    Our average student improves 98 points.

    Thanked by: Vincen
    Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
    Post Wed Oct 11, 2017 7:04 pm
    Hello EconomistGMATTutor, Matt, Rich and Brent. I really appreciate your answer. Thank you all of you.

    Best Conversation Starters

    1 Vincen 152 topics
    2 lheiannie07 61 topics
    3 Roland2rule 49 topics
    4 ardz24 40 topics
    5 LUANDATO 32 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    141 posts
    2 image description EconomistGMATTutor

    The Economist GMAT Tutor

    107 posts
    3 image description GMATGuruNY

    The Princeton Review Teacher

    106 posts
    4 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    104 posts
    5 image description Matt@VeritasPrep

    Veritas Prep

    76 posts
    See More Top Beat The GMAT Experts