This GMAT Problem Solving practice question combines core concepts of statistics including mean and median. It is a typical example of a question which requires you to iterate to get to the correct answer.
Question 13: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c?
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 11) + (a + 11) = 60 (b and c are equal and b, the median, is a + 11)
Or 3a = 38 or a = 12.66
So, b = c = 12.66 + 11 = 23.66
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b.
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 11) + (a + 12) = 60
Or 3a = 37. The value of the numbers is not an integer in this scenario as well.
Let us increment c again by 1. i.e., c = b + 2
Now, a + (a + 11) + (a + 13) = 60
Or 3a = 36 or a = 12.
If a = 12, b = 23 and c = 25.
The least value for c that satisfies all these conditions is 25.
Register in 2 easy steps and
Start learning in 5 minutes!
Next Integrated (Online + Offline) GMAT Batch
Feb 2, 2021
11. GMAT 700 Level Sample Question in Statistics
12. GMAT Hard Math Algebra - Absolute Values | GMAT Problem Solving
13. GMAT Challenging Question | Statistics Problem Solving
14. GMAT Hard Math | Arithmetic | Permutation Combination Sample Question
15. GMAT Challenging Math Question | Arithmetic | Number Properties DS Practice
16. 700 800 Level GMAT Word Problem | Number Properties & Equations Problem Solving Question
17. GMAT DS Sample Question | Geometry | Triangles
18. GMAT 700 800 Level Question | Coordinate Geometry & Permutation Combination
19. GMAT Hard Math Question | Algebra | Difficult Equations Question
20. GMAT Hard Math Questions | Arithmetic | Number Properties DS
Copyrights © 2016 - 21 All Rights Reserved by Wizako.com - An Ascent Education Initiative.
Privacy Policy | Terms & Conditions
GMAT® is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.
GRE® is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.
SAT® is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.
Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
48/1 Ramagiri Nagar
Velachery Taramani Link Road.,
Velachery, Chennai 600 042. India
Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message