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The average of the five numbers is 6.8. If one of the numbers is multi

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Math Expert
Joined: 02 Sep 2009
Posts: 43804
The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 04:16
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The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers is multiplied by 3?

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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Posts: 88
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GMAT 1: 710 Q49 V38
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Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 04:23
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Initial avg is 6.8
So the summation of the nos is 6.8*5 = 34

Now the new avg is 9.2
So summation will be 9.2*5 = 46.
So change in summation is 12.
This comes when a number is multiplied by 3.
In the original sum we already have that number added once. To bring additional 12 increment by multiplying by 3, we get a total increase of 18. Thus, 6 is multiplied by 3.

We can also do trial and error on all nos and see the knw tht gives 12 increase.

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The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 04:54
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Or we can just do some very easy algebra.
$$a_1 + a_2 + a_3 + a_4 + a_5 = 34$$(1)
lets say first number was multiplied by 3
$$3*a_1 + a_2 + a_3 + a_4 + a_5 = 46$$ (2)
subtract (2) from (1), $$2*a_1 = 12, a1 = 6$$
Option E
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The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 08:29
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Bunuel wrote:
The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers is multiplied by 3?

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

Kudos for a correct solution.

$$x_1 + x_2 + x_3 + x_4 + x_5 = 5*(6.8) = 34$$

$$3x_1 +x_2 + x_3 + x_4 + x_5 = 5*(9.2) = 46$$

Subtract the first from the second:

$$2x_1 = 12$$

$$x_1 = 6.$$

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Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 12:03
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Bunuel wrote:
The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers 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

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Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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08 Apr 2015, 13:43
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Equation 1: a+b+c+d+e=6.8*5=34
Equation 2: 3a+b+c+d+e=9.2*5=46
Deducting equation 1 from 2 we get : 2a=46-34=12=>a=6

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Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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09 Apr 2015, 02:28
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a+b+c+d+e = 6.8 * 5
3a+b+c+d+e = 9.2*5

by subtracting the two equations we get
2a = 12 thus a = 6
Math Expert
Joined: 02 Sep 2009
Posts: 43804
Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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13 Apr 2015, 05:13
Bunuel wrote:
The average of the five numbers is 6.8. If one of the numbers is multiplied by 3, the average of the numbers increases to 9.2. Which of the five numbers 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:

You can do this problem in a few different ways, but perhaps the best way is Algebra! No matter how you choose the address the question you will need to determine the magnitude of the increase. Since “sum (total) = average * # of terms” You can take the average of 6.8 times the five terms and get a beginning total of 34. The new total is 9.2 times 5 which equals 46. So the increase is 12.

In order to create an equation you need to ask yourself “what happened to cause that increase of 12?” The question stem tells you that one of the numbers was multiplied by 3. So when one of the numbers (we can call that number “x”) was multiplied by 3 the total increased by 12.

The equation formed from this information is simply “3x = x + 12.” The “3x” is because the number is multiplied by 3 and the “x + 12” is because you had the x to start with (there were five numbers right? and x was one of them) and you added 12 because of the increase to the sum.

So if “3x = x + 12” then x = 6. So the correct answer is E.

This question can be done based on knowledge of number properties and can even be done by working directly with the answer choices. However, neither of these methods is as reliable for most students as the algebra is. I have worked with the question for years and I can tell you that more people choose D than choose the correct answer. Yet very few of the people who get this wrong used algebra. Those who use algebra generally seem to get this question right.

Make sure that you are very comfortable with algebra, after all, bringing your “A Game” is essential to your success on the Quant section!
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Re: The average of the five numbers is 6.8. If one of the numbers is multi [#permalink]

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07 Aug 2017, 23:07
Excellent Question.
Here is what I did on this question =>
Sum (initial) => 5*6.8 => 34
Sum (final) => 5*9.2 => 46

Now difference => 12

Let p be the number multiplied by 3.

p => 3p

Thus we added 2p to the list.

Therefore => 2p = 12

Thus p = 6

Hence D.

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Re: The average of the five numbers is 6.8. If one of the numbers is multi   [#permalink] 07 Aug 2017, 23:07
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