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The average of the five members is 7. If one of the members is multipl

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Bunuel
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The average of the five members is 7. If one of the members is multipl [#permalink] New post   17 Feb 2020, 08:28
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The average of the five members is 7. If one of the members is multiplied by 3, the average of the numbers increases to 9.4. Which of the five numbers is multiplied by 3?

A. 4
B. 5
C. 5.6
D. 6
E. None of these
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Archit3110
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The average of the five members is 7. If one of the members is multipl [#permalink] New post   Updated on: 18 Feb 2020, 02:58
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Bunuel wrote:
The average of the five members is 7. If one of the members is multiplied by 3, the average of the numbers increases to 9.4. Which of the five numbers is multiplied by 3?

A. 4
B. 5
C. 5.6
D. 6
E. None of these


total sum ; 5*7 ; 35
now multiied by 3 ; 9.4 ; sum ; 47
∆ ; 12
if we subtract 2 cases ; 3a+b+c+d+e - (a+b+c+d+e) ; 2a = 12
a= 6
IMO D

Originally posted by Archit3110 on 17 Feb 2020, 11:55.
Last edited by Archit3110 on 18 Feb 2020, 02:58, edited 1 time in total.
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Re: The average of the five members is 7. If one of the members is multipl [#permalink] New post   17 Feb 2020, 12:38
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Let the 5 numbers be a,b,c,d,e

sum(a,b,c,d,e) = 5*7 = 35 = a + b + c + d + e ......(i)

Question states that one of the numbers is multiplied by 3, the average is 9.4
let a be the number multiplied by 3

so we have, sum(3a, b, c, d, e) = 5*9.4 = 47 = 3a + b + c + d + e ....(ii)

(ii) - (i)

2a = 12

a = 6

Thus, D
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Re: The average of the five members is 7. If one of the members is multipl [#permalink] New post   17 Feb 2020, 14:34
Bunuel wrote:
The average of the five members is 7. If one of the members is multiplied by 3, the average of the numbers increases to 9.4. Which of the five numbers is multiplied by 3?

A. 4
B. 5
C. 5.6
D. 6
E. None of these


let x=number multiplied by 3
5*7=35
35+2x=5*9.4→
x=6
D
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Re: The average of the five members is 7. If one of the members is multipl [#permalink] New post   17 Feb 2020, 14:57
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Re: The average of the five members is 7. If one of the members is multipl [#permalink] New post   17 Feb 2020, 23:19
Archit3110 wrote:
Bunuel wrote:
The average of the five members is 7. If one of the members is multiplied by 3, the average of the numbers increases to 9.4. Which of the five numbers is multiplied by 3?

A. 4
B. 5
C. 5.6
D. 6
E. None of these


total sum ; 5*7 ; 35
now multiied by 3 ; 9.4 ; sum ; 47
∆ ; 12
no multiplied by 3 ; 12/3 ; 4
IMO A



Hi Archit 3110,

IMHO, I feel you have made a mistake in your approach.

If we test your answer i.e 4 and assume 'others' as the sum of the other four numbers, we get the following:

4 + others = 35 ---> eqn (1)
others=31

So we know that the sum of 'others' will always remain the same. After the '4' was multiplied by 3, we get the following equationL

12+ others=47
12+31 =47 --> eqn (2) which is NOT CORRECT.

When we multiply by 3, we can say we are adding to the original number a multiple of 2.

So a + others=35
3a + others=47

Hence 2a=12....and a=6.

The answer should be (D): 6

Hope this helps!
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Re: The average of the five members is 7. If one of the members is multipl [#permalink] New post   31 Mar 2024, 05:08
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