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

Question

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 .

scorpionkapoor77 · Accepted Answer

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

kunal555 · Answer

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

Answer:- E

HBSdetermined · Answer

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

kunal555 · Answer

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

King407 · Answer

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

Answer : E

anudeep133 · Answer

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

harishbiyani8888 · Answer

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

Answer is E

EMPOWERgmatRichC · Answer

Hi HBSdetermined,

Your overall logic is right-on, but you made a minor mistake in your thinking:

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

Bunuel · Answer

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.

LeoN88 · Answer

5 * 6.8 = a+b+c+d+e

3a+b+c+d+e = 5*9.2

2a + (5*6.8) = 5*9.2

a= 6  E

himgkp1989 · Answer

KarishmaB

Is there any logical way to understand how the difference of 12 came after multiplying by 6 to 3 rather than creating equation.

KarishmaB · Answer

The average goes up from 6.8 to 9.2 i.e. by 2.4. So each of the 5 numbers increased by 2.4 which means that the sum increased by 2.4*5 = 12. 
When a number was tripled i.e n became 3n (increased by twice its previous value i.e. increased by 2n), it led to an increase of 12. The increase of 12 was twice of its previous value so 
12 = 2n i.e. n = 6.

Answer (E)

himgkp1989

gkumar08 · Answer

Ans is E
Increase in sum= 2.4*5= 12 
When the no is multiplied by 3 
It is increased by twice its original value.So 2a=12 ,a=6

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messi16 · Answer

In order to calculate this, simply identify that the average increases from 6.8 to 9.2, which is an increase of 2.4. Because we know we have 5 numbers and we are dividing by 5, that increase of 2.4 is actually an increase of 2.4 * 5 = 12. Thus, we need to find the number that when multiplied by 3, yields us an increase of 3, which in this case happens to be the number 6, because 6 * 3 = 18, which is 12 larger than the number we started out with (6).

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

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

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