Noshad wrote:
Last year Isabella took 7 math tests and received 7 different scores, each an integer between 91 and 100, inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was 95. What was her score on the sixth test?
(A) 92
(B) 94
(C) 96
(D) 98
(E) 100
A little bit of logical thinking will give you the answer.
The 7th number is 95. The average was an integer before and stays an integer now. Since all the are between 91 - 100, let's assume the average we obtained of the 6 numbers before was 95 too so adding 95 just keeps the average at 95.
Note that the numbers cannot be repeated and that the average is closer to 91 than to 100. So let's start stacking the smaller numbers first.
Let the first number be 91. Next, to get an integer average, add 93.
Add the third number at the average so that it stays an integer i.e. add 92 in.
Now we have 3 numbers with average of 92 so we add 96 to keep the average integer. The new average of 4 numbers has become 93.
Now we need to add 98 to it so that the avg of the 5 numbers in integer. The new average will be 94. (Just focus on the units digits to calculate since 90 will be divisible by 5)
Now we need the average to be 95 after adding the 6th number. We will get 95 average if we add 100 now.
So 6th number should be 100.
Answer (E)
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Karishma
Veritas Prep GMAT Instructor
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