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The average of 9 numbers is 15.

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ShahadatHJ
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The average of 9 numbers is 15. [#permalink] New post   Updated on: 15 Aug 2022, 23:53
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The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7
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E

Originally posted by ShahadatHJ on 09 Aug 2022, 07:21.
Last edited by ShahadatHJ on 15 Aug 2022, 23:53, edited 1 time in total.
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Re: The average of 9 numbers is 15. [#permalink] New post   09 Aug 2022, 10:00
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ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7



Sum of all 9 = 9*15 = 135.
Sum of 5 smallest = 5*9 = 45. So, sum of 4 greatest = 135-45 = 90.
Sum of 5 greatest = 5*20 = 100. So, sum of 4 smallest = 135-100 = 35.
90:35 = 18:7

Answer choice E.
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Re: The average of 9 numbers is 15. [#permalink] New post   09 Aug 2022, 07:30
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The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?
Solution
A1>A2>A3>A4>A5>A6>A7>A8>A9
Total of 9 number =135....1
Total of A9+A8+A7+A6+A5=45
Total of A1+A2+A3+A4+A5=100
Total of both is
A1+A2+A3+A4+2A5+A6+A7+A8+A9=145..,...2
From 1 and 2
We get A5=10
A1+A2+A3+A4=90....3
A9+A8+A7+A6=35....4
Ratio of 3 is to 4
90/35=18/7

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Re: The average of 9 numbers is 15. [#permalink] New post   10 Aug 2022, 07:35
harshittahuja ThatDudeKnows
If the ratio is 18:7; can we say 18*4 : 7*4 = 72:28?
Meaning, the sum of those 8 is 100.
The remaining number is 35, which is the greatest, and we don't include it in the sum of the greatest 4 numbers.

Am I missing sth?
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Re: The average of 9 numbers is 15. [#permalink] New post   10 Aug 2022, 08:51
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ShahadatHJ wrote:
harshittahuja ThatDudeKnows
If the ratio is 18:7; can we say 18*4 : 7*4 = 72:28?
Sure, why not?
Meaning, the sum of those 8 is 100.
:? Nope!
The remaining number is 35, which is the greatest, and we don't include it in the sum of the greatest 4 numbers.

Am I missing sth?


ShahadatHJ

A ratio is just a comparison between the sizes of two things.

Let's take an easy example to see if you can spot where your approach stops working.

Start with two numbers: 2 and 3.
The ratio is 2:3.
We can say 2*20 : 3*20 = 40:60.
Does that mean that our numbers are actually 40 and 60? Or does it still just mean that the second is 1.5x the first?
Is the sum 100? Or is the sum still 5?
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Re: The average of 9 numbers is 15. [#permalink] New post   10 Aug 2022, 09:42
ThatDudeKnows wrote:
ShahadatHJ wrote:
harshittahuja ThatDudeKnows
If the ratio is 18:7; can we say 18*4 : 7*4 = 72:28?
Sure, why not?
Meaning, the sum of those 8 is 100.
:? Nope!
The remaining number is 35, which is the greatest, and we don't include it in the sum of the greatest 4 numbers.

Am I missing sth?


ShahadatHJ

A ratio is just a comparison between the sizes of two things.

Let's take an easy example to see if you can spot where your approach stops working.

Start with two numbers: 2 and 3.
The ratio is 2:3.
We can say 2*20 : 3*20 = 40:60.
Does that mean that our numbers are actually 40 and 60? Or does it still just mean that the second is 1.5x the first?
Is the sum 100? Or is the sum still 5?

The sum could be 100/1000/5 (a multiple of 5, for a 2:3 ratio).
Anyway, I got the math. I considered multiplying a common factor to the ratio to get the totals. I was evaluating answer choices.
Could you explain why 20:9 is a wrong choice?
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The average of 9 numbers is 15. [#permalink] New post   Updated on: 17 Aug 2022, 23:46
ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7

KarishmaB Bunuel Archit3110 chetan2u please solve me this one.

Originally posted by ShahadatHJ on 13 Aug 2022, 07:35.
Last edited by ShahadatHJ on 17 Aug 2022, 23:46, edited 1 time in total.
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Re: The average of 9 numbers is 15. [#permalink] New post   14 Aug 2022, 05:00
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ShahadatHJ wrote:
ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7

KarishmaB Bunuel please solve me this one.



The average of 9 numbers is 15.

Sum of 9 numbers = 9*15 = 135

The average of the 5 smallest numbers in this list is 9

Sum of smallest 5 numbers = 5*9 = 45

and the average of the 5 greatest numbers in the list is 20.

Sum of 5 greatest numbers = 100

So 45 + 100 = 145 is the sum of 10 numbers such that middle number is counted twice.
Since the sum of 9 numbers is 135 and the sum is 145 when the middle number (5th number) is counted twice, the middle number is 10.

What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

Sum of 4 smallest numbers = 45 - 10 = 35
Sum of 4 greatest numbers = 100 - 10 = 90

Ratio of sum of 4 greatest : sum of 4 smallest = 90 : 35 = 18 : 7

Answer (E)
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The average of 9 numbers is 15. [#permalink] New post   15 Aug 2022, 23:52
KarishmaB wrote:
ShahadatHJ wrote:
ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7

KarishmaB Bunuel please solve me this one.



The average of 9 numbers is 15.

Sum of 9 numbers = 9*15 = 135

The average of the 5 smallest numbers in this list is 9

Sum of smallest 5 numbers = 5*9 = 45

and the average of the 5 greatest numbers in the list is 20.

Sum of 5 greatest numbers = 100

So 45 + 100 = 145 is the sum of 10 numbers such that middle number is counted twice.
Since the sum of 9 numbers is 135 and the sum is 145 when the middle number (5th number) is counted twice, the middle number is 10.

What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

Sum of 4 smallest numbers = 45 - 10 = 35
Sum of 4 greatest numbers = 100 - 10 = 90

Ratio of sum of 4 greatest : sum of 4 smallest = 90 : 35 = 18 : 7

Answer (E)

Thank you, KarishmaB ma'am.
And, could you please explain why B cannot be the choice?
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Re: The average of 9 numbers is 15. [#permalink] New post   18 Aug 2022, 00:41
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total numbers in list is 9 whose sum is 135
Let A1 be smallest number and A9 be the largest number
The average of the 5 smallest numbers in this list is 9
Sum from A1 to A5 = 9*5 ; 45
the average of the 5 greatest numbers in the list is 20
Sum from A5 to A9 ; 5*20 ; 100
we see that there is overlap of A5 in both
total sum is 135
135-(100+45) ; 10 which is nothing but A5 which has been considered twice


sum of greatest 4 number will be
Sum from A5 to A9 ; 5*20 ; 100-10 ; 90

Sum from A1 to A5 = 9*5 ; 45 - 10 ; 35

ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers
90/35; 18/7


ShahadatHJ


ShahadatHJ wrote:
ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7

.
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Re: The average of 9 numbers is 15. [#permalink] New post   18 Aug 2022, 01:16
Archit3110 wrote:
total numbers in list is 9 whose sum is 135
Let A1 be smallest number and A9 be the largest number
The average of the 5 smallest numbers in this list is 9
Sum from A1 to A5 = 9*5 ; 45
the average of the 5 greatest numbers in the list is 20
Sum from A5 to A9 ; 5*20 ; 100
we see that there is overlap of A5 in both
total sum is 135
135-(100+45) ; 10 which is nothing but A5 which has been considered twice


sum of greatest 4 number will be
Sum from A5 to A9 ; 5*20 ; 100-10 ; 90

Sum from A1 to A5 = 9*5 ; 45 - 10 ; 35

ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers
90/35; 18/7


ShahadatHJ


ShahadatHJ wrote:
ShahadatHJ wrote:
The average of 9 numbers is 15. The average of the 5 smallest numbers in this list is 9 and the average of the 5 greatest numbers in the list is 20. What is the ratio of the sum of the 4 greatest numbers to the sum of the 4 smallest numbers?

A. 20:7
B. 20:9
C. None
D. 9:20
E. 18:7

.

Archit3110 Why B is not the correct option?
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Re: The average of 9 numbers is 15. [#permalink] New post   18 Aug 2022, 01:38
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ShahadatHJ wrote:
Thank you, KarishmaB ma'am.
And, could you please explain why B cannot be the choice?


Because 18:7 is not the same as 20:9. Adding/subtracting the same number to/from the numerator and the denominator does not keep the fraction same.

18:7 is 18/7 = 2.57/1
20:9 is 20/9 = 2.22/1
They are not the same.

3:4 is the same as 6:8 (we multiply both terms by 2). 3/4 = 6/8
20:30 is the same as 2:3 (we divide both terms by 10). 20/30 = 2/3. But 21/31 is not the same as 20/30.

Suggest you to check out the ratios theory.
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Re: The average of 9 numbers is 15. [#permalink] New post   18 Aug 2022, 06:21
I dont understand why since the middle number is counted twice and equals 10 (i.e., 145 - 135 = 10) that the middle number is thus not 5?
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Re: The average of 9 numbers is 15. [#permalink] New post   18 Aug 2022, 06:38
GmatMike1234 wrote:
I dont understand why since the middle number is counted twice and equals 10 (i.e., 145 - 135 = 10) that the middle number is thus not 5?

The middle number is counted twice does not mean 2X = 10; rather 10 (the middle) is counted with the large and smaller numbers.
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Re: The average of 9 numbers is 15. [#permalink] New post   30 Sep 2023, 08:58
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Re: The average of 9 numbers is 15. [#permalink]
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