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

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GMATinsight · Accepted Answer

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

gurmukh · Answer

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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chetan2u · Answer

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

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

C

freedom128 · Answer

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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exc4libur · Answer

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)

madzaka · Answer

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)

globaldesi · Answer

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
C

lacktutor · Answer

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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unraveled · Answer

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. 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.

debjit1990 · Answer

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

ScottTargetTestPrep · Answer

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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