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After a certain test, Amy's preliminary score was one-twelfth of the

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After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 01:46
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After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

A. 24
B. 26
C. 32
D. 35
E. 36


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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 02:12
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1
Quote:
After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

A. 24
B. 26
C. 32
D. 35
E. 36


A = (1/12)*(B+C)

(C+6):(B+6):(A+6): 11:10:3

i.e. if C+6 = 11a i.e. C = 11a-6then
i.e. B+6 = 10a i.e. B = 10a-6
and A+6 = 3a i.e. A = 3a-6

(3a-6) = (1/12)*(10a-6+11a-6)

i.w. 36a - 72 = 21a - 12

i.e. 15a = 60

i.e. a = 4

Amount by which C is greater than A = C-A (required) = (11a-6) - (3a-6) = 8a = 32

Answer: Option C
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 02:13
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Let Amy, Ben and Cameron initial scores are A, B and C
Therefore 12A=B+C
Now initial score of A, B and C
also are
3x-6, 10x-6 and 11x-6 resp
Now
12(3x-6)= 10x-6 +11x-6
x=4
Difference between Cameron and Amy final score =8x =32
Option C is the answer

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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 02:24
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After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

Let the prelim score be A, B and C, and final score be 3x, 10x, and 11x respectively.

So, A=\(\frac{B+C}{12}....B+C=12A\)....
Now A+6 = \(\frac{3}{11+10+3}(A+6+B+6+C+6)=\frac{1}{8}(A+B+C+18)=\frac{1}{8}(A+12A+18)\) ..
\(8A+48=13A+18........5A=30.....A=6\)
Thus final score of \(A=6+6=12=3x....x=4\)

Difference in final score of Cameron and Amy = \(11x-3x=8x=8*4=32\)

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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 03:06
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Let preliminary scores of Amy, Ben and Cameron be a, b, and c, respectively.

Amy's preliminary score is one-twelfth of the sum of the preliminary scores of Ben and Cameron.
---> a = (b+c)/12 …(1)

After each score was increased by 6, final scores of Amy, Ben and Cameron become in the ratio of 3 : 10 : 11. So, we can write:
3k = a+6 …(2)
10k = b+6 …(3)
11k = c+6 …(4)

7*(2)=(3)+(4)
21k = 10k+11k
7a+42=(b+c)+12
30=(b+c)-7a

Substituting a with Eq. (1),
30=(b+c)-7(b+c)/12
30=5(b+c)/12
(b+c)=72
---> So, a =(b+c)/12 =6

Accordingly,
(2)… a+6= 6+6= 12= 3k and thus, k=4.
(4)… 11(4) = c+6 --> c+6=44.

Cameron's final score exceeds Amy's score by
= (c+6)-(a+6)
= 44-12
= 32

FINAL ANSWER IS (C)
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 03:38
Quote:
After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

A. 24
B. 26
C. 32
D. 35
E. 36


a=b+c/12
11x:10x:3x:c+6:b+6:a+6
c+6-a+6=11x-3x=8x
answer must be multiple of 8

if 8x=24, x=3;
c+6=11x, c+6=33, c=33-6=27
b+6=10x, b+6=30, b=24
a=b+c/12, a=27+24/12=not-integer, invalid

if 8x=32, x=4;
c+6=11x, c+6=44, c=44-6=38
b+6=10x, b+6=40, b=34
a=b+c/12, a=34+38/12=integer, valid

Ans (C)
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 03:57
it is given that
b+c=20a
thus
b1+c1-12=20(a1-6)

we have
c1:b1:a1=11x:10x:3x

substituting it
11x+10x-12=60x-120
39x=108
x=3

c1=33
a1=9

Answer 24 (a)
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 08:44
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initial scores be
A, B and C
as given
\(A = \frac{B+C}{12}\)
after review:
\(A+6: B+6:C+6 = 3K:10K:11k\)
OR
A:B:C = 3K-6:10K-6:11K-6
put that back in initial equation
\(\frac{21k-12}{12 }= 3k-6\)
solve for k = 4
new score Amy = 3k = 12
Cameron = 11k = 44
difference
44-12
= 32
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 18:27
1
\(12*A = B+ C \)
\((C+ 6): (B+6): (A+ 6) = 11: 10 : 3\)

—> \(C+ 6= 11y\)
—> \(B+6= 10y \)
———————
Adding them together:
—>\(B+C + 12= 21y\)
\(B+ C =12A\)

—> \(12A = 21y —12\)
\(A= \frac{21y}{12} —\frac{12}{12}= \frac{7y}{4} —1\)

Well, A must be integer
—> In order A to be integer, y should be equal to 4

—> \(A= \frac{7*4}{4} —1 = 6\)
—> \(C= 11*4 —6 = 38\)
—————————————
\((C+6) —(A+6) = 44–12 = 32\)

Answer ( C)

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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 22:50
1
1
After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

A. 24
B. 26
C. 32
D. 35
E. 36
C + 6 - (A + 6) = C - A = ?
\(A = \frac{B + C}{12}\) ----> 12A = B + C --Eqn.. 1
So, C - A = 11B - A = ?

C + 6: B + 6: A + 6 = 11:10:3
\(\frac{C + 6}{B + 6} = \frac{11}{10}\) ----> 10C - 11B = 6 -- Eqn. 2
\(\frac{B + 6}{A + 6} = \frac{10}{3}\) ----> 3B - 10A = 42 -- Eqn. 3

Let's try option C.
C - A = 11B - A = 32
OR 33B - 3A = 96 -- Eqn. 4

Adding Equations 3 and 4
A = 6 Thus C = 38 and B = 34.

Hence C - A = 32
PS: Taking other options also gives us answer but decimal values of A, B and C - a valid result. So, we have to consider odd one out approach to get out answer.
Question should mention that scores are positive integers.


Answer C.
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Re: After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 07 Apr 2020, 22:55
Ans: C

A=(1/12)(B+C)

C+6:B+6:A+6=11:10:3=K

3K-6=(1/12)(10K-6+11K-6)
K=4

C+6=44
A+6=12

So, (44-12)=32
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After a certain test, Amy's preliminary score was one-twelfth of the  [#permalink]

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New post 10 Apr 2020, 02:10
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Bunuel wrote:

Competition Mode Question



After a certain test, Amy's preliminary score was one-twelfth of the sum of the preliminary scores of Ben and Cameron. After a review, the score of each of them increased by 6 points. If the final scores of Cameron, Ben, and Amy were in the ratio 11:10:3, by how many points was Cameron's final score higher than Amy's final score?

A. 24
B. 26
C. 32
D. 35
E. 36


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We can let the final scores of Amy, Ben, and Cameron (i.e., after each receives the 6-point increase) be 3x, 10x, and 11x, respectively, and create the equation:

3x - 6 = 1/12 * (10x - 6 + 11x - 6)

12(3x - 6) = 21x - 12

36x - 72 = 21x - 12

15x = 60

x = 4

Since Cameron's final score is 11x - 3x = 8x higher than Amy's final score, Cameron scores 8(4) = 32 points higher than Amy.

Answer: C

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After a certain test, Amy's preliminary score was one-twelfth of the   [#permalink] 10 Apr 2020, 02:10

After a certain test, Amy's preliminary score was one-twelfth of the

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