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Re: A person took a total of 7 tests and received 7 different scores, each [#permalink]
Could someone explain it in another way if possible?? :)
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Re: A person took a total of 7 tests and received 7 different scores, each [#permalink]
Carcass pls provide solution to this question
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Re: A person took a total of 7 tests and received 7 different scores, each [#permalink]
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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.

Therefore A is the answer
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Re: A person took a total of 7 tests and received 7 different scores, each [#permalink]
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a good question but not a proper GRE question in my view
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A person took a total of 7 tests and received 7 different scores, each [#permalink]
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Let the operator for modulo (calculates remainder) be %.
We know,
(a+b) % c = {(a%c)+(b%c)} % c

(E.g. a=12, b=13, c=5. Feel free to test it with other numbers)

Now, the 7th score is 95.
And 95%7 = 4.

Let SumSix = sum of the first 6 scores.
So, (SumSix%7 + 95%7) % 7 = 0
Or, SumSix%7 + 95%7 = 7
Or, SumSix%7 = 7-4 = 3

If the average of the first 6 scores is AvgSix, then it has to be an integer between 93.83 (average of the lowest possible scores i.e. 91, 92, 93, 94, 96 and 97) and 97.33 (average of highest possible scores i.e. 100, 99, 98, 97, 96 and 94).

If AvgSix=94, then:
SumSix=94*6=564, SumSix%7 = 4 ❌
If AvgSix=95, then:
SumSix=95*6=570, SumSix%7 = 3 ✅
If AvgSix=96, then:
SumSix=96*6=576, SumSix%7 = 2 ❌
If AvgSix=97, then:
SumSix=97*6=582, SumSix%7 = 1 ❌

570 is the only sum that satisfies SumSix%7 = 3.

Now, the 6th score can only be 95 (makes SumFive=475) or 100 (makes SumFive=470), as the sum of the first 5 scores must be divisible by 5.

95 can't be repeated.
So the only possible 6th score is 100, which is greater than 96.

So, quantity A is greater.
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A person took a total of 7 tests and received 7 different scores, each [#permalink]
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