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

 It is currently 19 Jan 2019, 04:29

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# The average of 5 numbers is 6.8. If one of the numbers is multiplied

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52294
The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

02 Sep 2015, 21:38
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:40) correct 41% (01:38) wrong based on 132 sessions

### HideShow timer Statistics

The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

Kudos for a correct solution.

_________________
Intern
Joined: 09 May 2012
Posts: 18
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 01:22
1
Average of 5 numbers = 6.8
Total of 5 numbers = 34

New Average = 9.2
New Total Sum = 46

Difference between Old and New Sum = 12
Difference = 3x - x = 2x = 12
Therefore, value of x must be 6.

The number multiplied by 3 is 6. IMO
Manager
Joined: 29 Jul 2015
Posts: 158
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 08:26
1
Bunuel wrote:
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

Kudos for a correct solution.

The average of 5 numbers is 6.8
The sum of 5 numbers will be 6.8 x 5 = 34

The average of 5 number after one of the number is multiplied by 3 is 9.2
The sum of the numbers will now be 9.2 x 5 = 46

So the sum has increased by 46-34 = 12
Let the number multiplied by 3 be n
Then,
3n = n+12
or 2n = 12
or n = 6

Manager
Joined: 04 Feb 2012
Posts: 156
Location: India
Concentration: General Management, Strategy
GRE 1: Q162 V160
GPA: 3.96
WE: Research (Pharmaceuticals and Biotech)
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 08:41
I think the answer should be 4.0 or D... Because when the average to begin with is 6.8 (of the five numbers) that indicates the sum of these five numbers is 6.8*5= 34. When the average is changed to 9.2 then the new sum is edited to 46. The difference between them is 46-34= 12 hence there could be number 4 which could be multiplied from the set to give us a new average of 9.2
Manager
Joined: 29 Jul 2015
Posts: 158
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 09:00
1
HBSdetermined wrote:
I think the answer should be 4.0 or D... Because when the average to begin with is 6.8 (of the five numbers) that indicates the sum of these five numbers is 6.8*5= 34. When the average is changed to 9.2 then the new sum is edited to 46. The difference between them is 46-34= 12 hence there could be number 4 which could be multiplied from the set to give us a new average of 9.2

In that case the sum will be increased by 8 not 12.

Let a,b,c,d and n be the 5 numbers.

1) sum before multiplication of 3 with a number will be
a+b+c+d+n = 34

2) sum after multiplication of 3 with number n will be
a+b+c+d+3n = 46

Now,
subtracting 1 from 2 we get,
(a+b+c+d+3n)-(a+b+c+d+n) = 46-34

or 2n = 12

or n=6
Manager
Joined: 03 Sep 2014
Posts: 74
Concentration: Marketing, Healthcare
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 09:02
1
Bunuel wrote:
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

Kudos for a correct solution.

Let X = {x1,x2,x3,x4,x5}

Sum(X) = 6.8*5 = 34

Let y be the no. that is multiplied by 3

Thus, Sum(X) - y +y*3 = 9.2*5

=> 34 +2y = 46 => 2y = 12 => y = 6

Manager
Joined: 10 Aug 2015
Posts: 103
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

03 Sep 2015, 10:02
1
Solution:

Let the number multiplied be a and sum of other 4 numbers be x.
so, x + a = 6.8(5) = 34 -->(1)
and x+3a = 9.2(5) = 46 --> (2)
(2) - (1) ---> 2a = 12. So, a =6
Option E
Intern
Joined: 12 Nov 2013
Posts: 40
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

05 Sep 2015, 10:45
1
Bunuel wrote:
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

Kudos for a correct solution.

Average of 5 numbers is 6.8, so the sum of the 5 numbers is 34.

Average increased to 9.2, so the new sum is 46.

difference, between the new and the old sum of the 5 numbers = 46 - 34 = 12

Let the number multiplied by a factor of 3 be x,

therefore, the new number becomes 3x.

so, 3x - x = 12

therefore x = 6

_________________

Kindly support by giving Kudos, if my post helped you!

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13346
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

05 Sep 2015, 15:28
1
HBSdetermined wrote:
I think the answer should be 4.0 or D... Because when the average to begin with is 6.8 (of the five numbers) that indicates the sum of these five numbers is 6.8*5= 34. When the average is changed to 9.2 then the new sum is edited to 46. The difference between them is 46-34= 12 hence there could be number 4 which could be multiplied from the set to give us a new average of 9.2

Hi HBSdetermined,

Whatever number is tripled has ALREADY been counted 'once' already, so part of that original sum (in this case, the sum was 34) includes the given number. By tripling the number 4, you would NOT be adding 12 to the sum.... you would be adding 8 to the sum. As such, you actually have to triple the number 6, which would end up adding 12 to the sum.

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

07 Sep 2015, 02:47
Bunuel wrote:
The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3?

(A) 1.5
(B) 3.0
(C) 3.9
(D) 4.0
(E) 6.0

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

As with any problem, you should start with what you know. You know that, if the average of 5 numbers is 6.8, then the sum of those numbers is 5*6.8 or 34. Similarly for the new total, if the average is 9.2, then the sum of those five numbers is 5*9.2 or 46.

So we have:

Old total: 34
New total: 46

When problems involve a change – ratio problems in which a certain number is added or subtracted and the ratio changes; mixture problems in which something is added to or subtracted from the solution and the mixture changes, etc. – the key to solving them is typically the change itself. Almost always, the change is expressed in two ways:

x is added and the new ratio becomes…
one of the numbers is multiplied by 3 and the average becomes…

When you’re given two ways to mathematically express that change, use those two ways to set up an equation – you can then solve for a variable that links the past to the present (or the present to the proposed future, depending on how the question is asked) and that solution will allow you to fill in the entire puzzle.

In this case, we know that “multiplying one number by 3″ also “increases the sum by 12″ (46 – 32). Since the only number that changes is that number that is multiplied by 3, we know that the multiplying by 3 is the same as adding 12 to that number. So, mathematically, we can say that:

3x = x + 12
2x = 12
x = 6

Therefore, the number in question – that which is multiplied by 3 and in doing so is also added to 12 – is 6, and the correct answer is E.

Use change as your “anchor” in problems that emphasize a change in ratios, proportions, or any other elements of a mixture. By expressing the change in two ways, you’ll have an equation that will translate to both the initial and the final mixtures, and therefore will be able to answer any question that the GMAT asks about any part of the relationship. If politicians can use change as their platform to try to get to Washington, you can certainly use change as your springboard to Boston, Palo Alto, Evanston, or the other b-school campus of your choice.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 9444
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied  [#permalink]

### Show Tags

19 Sep 2018, 19:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The average of 5 numbers is 6.8. If one of the numbers is multiplied &nbs [#permalink] 19 Sep 2018, 19:29
Display posts from previous: Sort by