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

 It is currently 22 Sep 2018, 15:47

### 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 arithmetic mean of a collection of 5 positive integers, not necess

Author Message
TAGS:

### Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3416
The arithmetic mean of a collection of 5 positive integers, not necess  [#permalink]

### Show Tags

26 Jul 2017, 11:52
Top Contributor
5
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:06) correct 29% (01:09) wrong based on 276 sessions

### HideShow timer Statistics

The arithmetic mean of a collection of 5 positive integers, not necessarily distinct, is 9. One additional positive integer is included in the collection and the arithmetic mean of the 6 integers is computed. Is the arithmetic mean of the 6 integers at least 10 ?

1. The additional integer is at least 14.

2. The additional integer is a multiple of 5.

_________________
Intern
Joined: 09 Jul 2017
Posts: 1
Re: The arithmetic mean of a collection of 5 positive integers, not necess  [#permalink]

### Show Tags

26 Jul 2017, 12:25
Answer should be "C" as with (1) and (2) the smallest of added no is 15 which makes the arith mean 10 (atleast).
Manager
Joined: 01 Feb 2017
Posts: 155
Re: The arithmetic mean of a collection of 5 positive integers, not necess  [#permalink]

### Show Tags

26 Jul 2017, 12:32
Ans C:
From Question Stem, we can determine the required range of value of 6th Integer as >=15, using Formulae for Arithmetic Mean.
To conclude this, we need to use both Statements 1 and 2.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 195
Re: The arithmetic mean of a collection of 5 positive integers, not necess  [#permalink]

### Show Tags

03 Sep 2018, 05:21
carcass wrote:
The arithmetic mean of a collection of 5 positive integers, not necessarily distinct, is 9. One additional positive integer is included in the collection and the arithmetic mean of the 6 integers is computed. Is the arithmetic mean of the 6 integers at least 10 ?

1. The additional integer is at least 14.

2. The additional integer is a multiple of 5.

The solution below explores the homogeneity nature of the average.

$$\left( * \right)\,\,\,5\,\,{\text{ints}} \geqslant 1$$

$$\sum\nolimits_{\,5} {\, = } \,\,5 \cdot 9 = 45$$

$$\sum\nolimits_{\,5} {\, + \,\,x\,\,\left( {6{\text{th}}} \right)\,\,\,\,\mathop \geqslant \limits^? } \,\,\,\,6 \cdot 10\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,x\,\,\,\mathop \geqslant \limits^? \,\,\,15$$

$$\left( 1 \right)\,\,x \geqslant 14\,\,\,\left\{ \begin{gathered} \,x = 14\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,x = 15\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( 2 \right)\, + \,\left( * \right):\,\,\,\,\,x = 5,10,15, \ldots \,\,\,\,\,\,\left\{ \begin{gathered} \,x = 5\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,x = 15\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$$

$$\left( {1 + 2} \right) + \,\left( * \right):\,\,\,\,x = 15,20,25, \ldots \,\,\,\,\, \Rightarrow \,\,x \geqslant 15\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,$$

The above follows the notations and rationale taught in the GMATH method.
_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

Re: The arithmetic mean of a collection of 5 positive integers, not necess &nbs [#permalink] 03 Sep 2018, 05:21
Display posts from previous: Sort by

# The arithmetic mean of a collection of 5 positive integers, not necess

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.