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Averages Practice Test - 2 - CAT MCQ


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15 Questions MCQ Test - Averages Practice Test - 2

Averages Practice Test - 2 for CAT 2024 is part of CAT preparation. The Averages Practice Test - 2 questions and answers have been prepared according to the CAT exam syllabus.The Averages Practice Test - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Averages Practice Test - 2 below.
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Averages Practice Test - 2 - Question 1
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. What will happen to R’s average?

Detailed Solution for Averages Practice Test - 2 - Question 1
Will always decrease since the net value transferred from R to E will be higher than the net value transferred from E to R.

Averages Practice Test - 2 - Question 2
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. What can be said about E’s average?

Detailed Solution for Averages Practice Test - 2 - Question 2
Since the lowest score in Class R is 23 which is more than the highest score of any student in Class E. Hence, E’s average will always increase.

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Averages Practice Test - 2 - Question 3
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. At the end of the 2 steps mentioned above (in the direction) what could be the maximum value of the average of class R?

Detailed Solution for Averages Practice Test - 2 - Question 3
The maximum possible value for R will happen when the E to R transfer has the maximum possible value and the reverse transfer has the minimum possible value.

Averages Practice Test - 2 - Question 4
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. For question 3, what could be the minimum value of the average of class R?
Detailed Solution for Averages Practice Test - 2 - Question 4
For the minimum possible value of R we will need the E to R transfer to be the lowest possible value while the R to E transfer must have the highest possible value. Thus, E to R transfer -> 18* 5 while R to E transfer will be 31*5. Hence the answer is 22.4.

Averages Practice Test - 2 - Question 5
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. What could be the maximum possible average achieved by class E at the end of the operation?

(a) 25.2

(b) 23.25

(c) 26

(d) 23.75

Detailed Solution for Averages Practice Test - 2 - Question 5
The maximum value for E will happen in the case of Q4. Then the increment for group E is

31* 5 – 18 * 5 = 5 * (31 – 18) = 65.

Thus the maximum possible value is 465 / 20 = 23.25.

Averages Practice Test - 2 - Question 6
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Read the following and answer the question that follow.

If 5 people are transferred from E to R and another independent set of 5 people are transferred back from R to E, then after this operation (Assume that the set transferred from R to E contains none from the set of students that came to R from E)

Q. What could be the minimum possible average of class E at the end of the operation?
Detailed Solution for Averages Practice Test - 2 - Question 6
The minimum possible average will happen for the transfer we saw in Q. 3. Thus the answer will be 405 / 20 = 20.25.

Averages Practice Test - 2 - Question 7
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The average of 7 consecutive numbers is E. If the next three numbers are also added, the average increases by (IIFT 2013)
Detailed Solution for Averages Practice Test - 2 - Question 7
If the numbers are 1,2,3,4,5,6,7 and we add 8, 9,10.

Initial average = (1 + 2 + 3 + 4 + 5 + 6 + 7) / 7 = 4 Final average = (1 + 2 + 3 + 4 + -----10) / 10 = 5.5

Therefore, the average increases by 1.5.

Averages Practice Test - 2 - Question 8
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In 2001 there were 6 members in Barney’s family and their average age was 28 years. He got married between 2001 and 2004 and in 2004 there was an addition of a child in his family. In 2006, the average age of his family was 32 years. What is the present age (in 2006) of Barney’s wife (in years) is:
Detailed Solution for Averages Practice Test - 2 - Question 8
If the present age of Barney’s wife is x years. Then according to the question

(33 X 6 + x + 2) / 8 = 32

x + 2 + 198 = 256 x + 2 = 58

x = 56

x = 56 years

Averages Practice Test - 2 - Question 9
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The weight of a metal piece as calculated by the average of 7 different experiments is 53.735 gm. The average of the first three experiments is 54.005 gm, of the fourth is 0.004 gm greater than the fifth, while the average of the sixth and seventh experiment was 0.010 gm less than the average of the first three. Find the weight of the body obtained by the fourth experiment.
Detailed Solution for Averages Practice Test - 2 - Question 9
You can take 53 as the base to reduce your calculations. Otherwise, the question will become highly calculation-intensive. Let the fifth experiment’s measurement be ‘x’ above 53.

Then you get:

0.735 X 7 = 1.005 X 3 + (x + 0.004) + x + 0.995 X 2

-> 5.145 = 3.015 + 2x + 0.004 + 1.99.

On solving this you get x = 0.068. Hence, the weight of the fifth body is 53.068 and the weight of the fourth body is 53.072. Hence, the option (d) is correct.

Averages Practice Test - 2 - Question 10
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One collective farm got an average harvest of 21 tons of wheat per hectare and another collective farm that had 12 acres of land less given to wheat, got 25 tons from a hectare. As a result, the second farm harvested 300 tons of wheat more than the first. How many tons of wheat did each farm harvest?
Detailed Solution for Averages Practice Test - 2 - Question 10
Check through options to solve. Option (a) is correct since if the first farm harvested 3150 tons of wheat, with an average harvest of 21 tons per hectare – the number of hectares would be 3150 / 21 = 150. The second farm would then harvest 12 hectares less (as given in the question) - thus would harvest 138 hectares with an average output of 25 tons per hectare. The total harvest would be in this case 138 X 3450 – and is 300 tons more than the first farm as required. Hence, this answer is correct.

Averages Practice Test - 2 - Question 11
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If the dates of birth, of four of them are prime numbers, then find the maximum average of the sum of their dates of birth.
Detailed Solution for Averages Practice Test - 2 - Question 11
The prime dates must be 29th, 23rd, 19th and 5th. This represents a reduction in the totals from 30+25+20+5 to 29+23+19+5 – a drop of 4.

Hence, the maximum possible average will reduce by 4/5 = 0.8.

Hence, the answer will be 27.2.

Averages Practice Test - 2 - Question 12
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The average age of a group of persons going for a movie is 20 years. 10 new persons with an average age of 10 years join the group on the spot due to which the average of the group becomes 18 years. Find the number of persons initially going for the movie.
Detailed Solution for Averages Practice Test - 2 - Question 12

Averages Practice Test - 2 - Question 13
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Read the following and answer the questions that follow.

If 5 people are transferred from C to B, further, 5 more people are transferred from B to A, then 5 are transferred from A to B and finally, 5 more are transferred from B to C.

Q. What is the maximum possible average achieved by class C?
Detailed Solution for Averages Practice Test - 2 - Question 13
The maximum possible value for C will be achieved when the transfer from C is of five 26’s and the transfer back from B is of five 31’s.

Hence, difference is totals will be +25.

Hence, max. average = (900 + 25)/30 = 30.833.

[Note here that 900 has come by 30*30]

Averages Practice Test - 2 - Question 14
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What is the maximum possible average of class B?
Detailed Solution for Averages Practice Test - 2 - Question 14
For the maximum possible value of Class B the following set of operations will have to hold: Five 33’s are transferred from C to B, whatever goes from B to A comes back from A to B, then five 23’s are transferred from B to C.

This leaves us with: Increase of 50 marks -> average increases by 2 to 27

Averages Practice Test - 2 - Question 15
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What is the maximum possible average value attained by class A?

(a) 22.75

(b) 23.5

(c) 23.75

(d) 24

Detailed Solution for Averages Practice Test - 2 - Question 15
A will attain maximum value if five 33’s come to A from C through B and five 18’s leave A. In such a case the net result is going to be a change of +75. Thus the average will go up by 75/20 = 3.75 to 23.75.
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