• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

If the average of four numbers is 35, how many of the

This topic has 2 expert replies and 0 member replies

If the average of four numbers is 35, how many of the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Veritas Prep

If the average of four numbers is 35, how many of the numbers are less than 35?

1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.

OA E

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
AAPL wrote:
Veritas Prep

If the average of four numbers is 35, how many of the numbers are less than 35?

1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.
Sum of the 4 numbers = (quantity)(average) = 4*35 = 140.

Statement 1: None of the numbers are exactly 3
To save time, check whether it's possible to get different answers to the question stem while also satisfying Statement 2.

Case 1: 0, 33, 33, 74 --> sum = 0+33+33+74 = 140
In this case, three numbers are less than 35.
Case 2: 33, 33, 36, 38 --> sum = 33+33+36+38 = 140
In this case, two numbers are less than 35.

Since Cases 1 and 2 satisfy both statements but yield different answers to the question stem, the two statements combined are INSUFFICIENT.

The correct answer is E.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post
AAPL wrote:
Veritas Prep

If the average of four numbers is 35, how many of the numbers are less than 35?

1) None of the numbers are exactly 35.
2) Two of the numbers are exactly 33.

OA E
Bunuel wrote:
If the average of four numbers is 35, how many of the numbers are less than 35?

(1) None of the numbers are exactly 35

(2) Two of the numbers are exactly 33
Target question: How many of the numbers are less than 35?

Given: The average of four numbers is 35
All this tells us is that the SUM of the 4 numbers is 140 (since 140/4 = 35)
Given the limited amount of information, it's likely that the correct answer is C or E

Statement 1: None of the numbers are exactly 35
There are many sets of 4 numbers y that satisfy statement 1. Here are two:
Case a: The numbers are {34, 34, 36, 36}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 0, 0, 140}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Two of the numbers are exactly 33
There are many sets of 4 numbers y that satisfy statement 1. Here are two:
Case a: The numbers are {33, 33, 37, 37}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 33, 33, 74}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that the cases I created for statement 2 ALSO satisfy statement 1.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: The numbers are {33, 33, 37, 37}. In this case, the answer to the target question is 2 numbers are less than 35
Case b: The numbers are {0, 33, 33, 74}. In this case, the answer to the target question is 3 numbers are less than 35
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
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!
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • 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
  • 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

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts