What is the average (arithmetic mean) of the first 90 measurements

Question

What is the average (arithmetic mean) of the first 90 measurements in a certain list of 92 measurements?

(1) The average of 92 measurements is 7.0 centimeters.

(2) The average of the last 2 measurements is 7.2 centimeters.

KarishmaB · Accepted Answer

You need the average of first 90 measurements.

(1) The average of 92 measurements is 7.0 centimeters.

We don't know what the last two measurements are so we cannot find the average of 90 measurements.

(2) The average of the last 2 measurements is 7.2 centimeters.
We don't know what the first 90 measurements are so we cannot find their average

Together we know that the average of all 92 measurements is 7 so sum of all measurements s 7*92.
We know that the average of last 2 is 7.2 so sum of last two is 7.2*2.

So we get the sum of first 90 measurements = 7*92 - 7.2*2
We can calculate this and divide by 90 to get the average. So both statements together are sufficient.

Answer (C)

GMATinsight · Answer

Statement 1: The average of 92 measurements is 7.0 centimeters

To know the average of 90 measurements that the question is talking about we need to know the sum / average of those two measurements which need to be avoided alongwith the given information.

But no information of those measurements two measurements so far

Hence,   NOT SUFFICIENT

Statement 2: The average of the last 2 measurements is 7.2 centimeters.

To know the average of 90 measurements that the question is talking about we need to know the sum / average of those two measurements which need to be avoided. alongwith the information of sum of all the 92 measurements

But no information of those 90 remaining measurements so far

Hence,   NOT SUFFICIENT

Combining the two statements

Sum of 92 measurements = 92*7  
Sum of Last 2 measurements = 7.2*2

Hence, Sum of First 90 Measurements = 92*7 - 7.2*2
Hence,   SUFFICIENT

Answer: Option  C

stonecold · Answer

Nice Official Question.
Here is what i did in this one =>

Let the set be ->
x1
x2
.
.

.
x92

Now Required mean = x1+x2+...x90/90

Statement 1=>
x1+x2+...x90+x91+x92=7*92
No clue of x91 and x92
Hence not sufficient

Statement 2=>
x91+x92=7.2*2
No clue of x1+x2+..x90
Not sufficient

Combing the two statements =>
x1+x2+...x90=7*92-7.2*2

Hence we have the sum => we can get the average

Hence sufficient

Hence C

bumpbot · Answer

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What is the average (arithmetic mean) of the first 90 measurements

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