John has taken four (4) tests that have an average of 82. In order to

Question

John has taken four (4) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?

A. 87
B. 90
C. 92
D. 94
E. 97

Kudos for a correct solution.

A. 87
B. 90
C. 92
D. 94
E. 97

Kudos for a correct  solution .

mejia401 · Answer

Equation:  \frac{{2x + 82*4}}{{6}}=87 , where x is the desired score.
Reduce:  x = 97

Solve to confirm answer:  \frac{97*2 + 82*4}{6}=87

Alternative method:
The following two tests must make up for four tests which hadn't scored as high. The residual is 5 points, and 10 points to be split between the two. Thus, the two test must be 87+residual=97.

Kr,
Mejia

KS15 · Answer

Average in 4 tests=82
Total in 4 tests=82*4=328
Now, for average to increase to 87 in 6 tests, he needs to have a total of 87*6=522
Therefore, score reqd in final 2 tests= 522-328=184
Average of final 2 tests=184/2=97
Answer E

VenoMfTw · Answer

IMO : E

Total score after 4 tests = 82*4 = 328

Total score needed after 6 tests for avg to be 87 = 87* 6 = 522

Thus total score needed in the remaining two tests = 522-328 = 194

Thus avg score required in the remaining two tests = 194/2 = 97

AmoyV · Answer

87-82=5*4=20 points

2*87=174

174+20=194 points to be scored in the 2 tests.

Avg of 2 tests = 194/2=97

Answer: E

Traditional Method:

Total scored till now 82*4=328
Total score to avg 87 in 6 tests = 87*6=522

Total to be scored on 2 tests = 522-328=194

Avg on 2 tests = 194/2 = 97

Answer : E

Mo2men · Answer

Hi AmoyV,
Can you please explain your first method in some detail?
Thanks

Bunuel · Answer

PRINCETON REVIEW OFFICIAL SOLUTION:

There are several ways to attack this problem. I will deal with only one of them today.

What you are looking to find is an average of the final two tests. The question does not ask for them individually. Conceptually you need to see that you need to figure out how much more do I need to add to what I already have to get it up to where I want it to be.

This therefore becomes a question of totals and not just averages.

Currently your average is 82 on 4 tests. You need to bring it to 87 on 6 tests.

Average= Total/Number of items (A=T/N). A good pneumonic device is to say T=A*N.

1) 82=T/4, so the first total is 328.
2) 87=T/6, so new total to get to is 522.

The difference in total points is 194, which needs to be achieved on two tests. Notice that the question did not ask what to get on each individual test, but rather what the average would need to be, so you would need to take that difference and divide by 2 to get  the final answer of 97 .

I do know that some of you did this one algebraically and arrived at the same answer, and others could see that it needed to be one of the higher values because you had to offset the four scores that were 5 below the overall average, so it had to be more than 92.

What technique do you use? Any of them, all of them, a combination. For those of you who read one of my previous articles ‘What is the Question Asking?’, you know that I am a huge fan of discovering what technique is most appropriate to your skill set. There is no best way to do any problem.

This example required you to know what an average is and how to deal with finding an unknown variable. If the question was slightly changed and it asked you what would the final test grade have to be if the 5th test grade was a 99, you would still have to know the basics.

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