GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 05 Dec 2019, 14:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The average (arithmetic mean) of 17 consecutive integers is an odd num

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59561
The average (arithmetic mean) of 17 consecutive integers is an odd num  [#permalink]

### Show Tags

15 Nov 2019, 01:47
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:22) correct 45% (02:06) wrong based on 47 sessions

### HideShow timer Statistics

The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Are You Up For the Challenge: 700 Level Questions
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
Re: The average (arithmetic mean) of 17 consecutive integers is an odd num  [#permalink]

### Show Tags

15 Nov 2019, 04:10

Solution

Given
• Average (arithmetic mean) of 17 consecutive integers is an odd number

To find
• Correct statements

Approach and Working out

Let the consecutive integers are a, a+1, a+2, a+3, ……., a+16.
• Sum of all the integers = 17a + (1+2+3+ .. +16) = 17a + 16*17/2 = 17a + 8*17= 17(a+8)
o Average = 17(a + 8)/17 = a + 8 =odd
 So, a = Odd
 Thus, first term is odd.

Statement 1:
• a + 16 = odd + even = odd
• Not true
.

Statement 2:
• Sum = 17(a+8) = odd × odd = odd
• True

Statement 3:
• Largest integer – Smallest integer = a+ 16 – a = 16= Even
• True

Thus, option E is the correct answer.
_________________
Director
Joined: 24 Nov 2016
Posts: 917
Location: United States
Re: The average (arithmetic mean) of 17 consecutive integers is an odd num  [#permalink]

### Show Tags

19 Nov 2019, 04:49
Bunuel wrote:
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

{1,2,3,4,5}: mean = 3 (odd); rng=5-1=4 (even); sum=3*5=15 (odd)
{2,3,4,5,6}: mean = 4 (even); rng=6-2=4 (even); sum=4*5=20 (even)

Ans (E)
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4835
Location: India
GPA: 3.5
Re: The average (arithmetic mean) of 17 consecutive integers is an odd num  [#permalink]

### Show Tags

19 Nov 2019, 11:32
Bunuel wrote:
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Are You Up For the Challenge: 700 Level Questions

Sum of first n numbers is $$1+ 2+ ... + n = \frac{n(n+1) }{ 2}$$

Now, sum of first 17 numbers will be $$\frac{17*18}{2} = 153$$ and its average will be $$\frac{153}{17} = 9$$ (Odd)

1. Largest number is Odd (17)
2. Sum of all integers is Odd (153)
3. Difference between largest and smallest integer is even. ( 17 - 1 = 16)

Hence, only (E) holds true, Answer must be (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Manager
Joined: 10 Dec 2017
Posts: 150
Location: India
Re: The average (arithmetic mean) of 17 consecutive integers is an odd num  [#permalink]

### Show Tags

22 Nov 2019, 07:20
Bunuel wrote:
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only

Are You Up For the Challenge: 700 Level Questions

a9 is odd
For this a1 is odd and a17 is odd
so largest integer is odd
For consecutive integers
Sum of the terms= AM*no. of terms
and AM= (First +Last)/2=odd (given)
Sum of the terms= odd* odd=odd
a1 is odd and a17 is odd
Difference=a17-a1= Even
E:)
Re: The average (arithmetic mean) of 17 consecutive integers is an odd num   [#permalink] 22 Nov 2019, 07:20
Display posts from previous: Sort by