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Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?
  • a)
    32.5 to 37.5
  • b)
    22.5 to 27.5
  • c)
    33.5 to 37.5
  • d)
    23.5 to 27.5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Consider 4 numbers a, b, c and d. Ram figures that the smallest avera...
Solution:

Given, smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40.

Let the four numbers be a, b, c, and d.

Smallest average of some three numbers is 30

This means that the sum of the three smallest numbers divided by 3 is equal to or greater than 30.

a + b + c >= 90

Similarly, the largest average of some three numbers is 40

This means that the sum of the three largest numbers divided by 3 is equal to or less than 40.

b + c + d <=>

Average of all 4 numbers can be found out as:

(a + b + c + d)/4

We need to find the range of values that this expression can take.

Let's assume that b and c are the middle two numbers. Then, we can write:

a + b + c >= 90 (1)

b + c + d <= 120="">

Adding (1) and (2), we get:

a + 2b + 2c + d >= 210

(a + b + c + d) + b + c >= 210

(a + b + c + d) >= 210 - (b + c)

(a + b + c + d) >= 210 - (a + d)

(a + b + c + d)/4 >= (210 - (a + d))/4

(a + b + c + d)/4 >= 52.5 - (a + d)/4

We know that (a + d)/2 <= (a="" +="" b="" +="" c="" +="" d)/4=""><= (a="" +="">

So, we have:

(a + d)/2 <= (a="" +="" b="" +="" c="" +="" d)/4=""><= (a="" +="">

(a + d) <= 2(a="" +="" b="" +="" c="" +="" d)/4=""><= (a="" +="">

(a + d) <= (a="" +="" b="" +="" c="" +="" d)/2=""><= (a="" +="">

2(a + d) <= a="" +="" b="" +="" c="" +="" d=""><= 2(a="" +="">

2a + 2d <= a="" +="" b="" +="" c="" +="" d=""><= 2a="" +="">

a + d <= (a="" +="" b="" +="" c="" +="" d)/4=""><= (a="" +="">

Therefore, the range of values that the average of all 4 numbers can take is from (a + d)/2 to (a + b + c + d)/4, which is from 27.5 to 32.5.

Hence, the correct option is (a) 32.5 to 37.5.
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Community Answer
Consider 4 numbers a, b, c and d. Ram figures that the smallest avera...
We can assume a, b,c d are in ascending order (with the caveat that numbers can be equal to each other)
a + b + c = 90
b + c + d = 120
We need to find the maximum and minimum value of a + b + c + d.
a + b + c + d = 120 + a. So, this will be minimum when a is minimum. Given a + b + c = 90. a is minimum when b + c is maximum. If b + c is maximum, d should be minimum.
Given that b + c + d = 120, the minimum value d can take is 40 as d cannot be less than b or c.
The highest value b + c can take is 80, when b = c = d = 40. When b = c = d = 40, a = 10.
a + b + c + d = 130. Average = 32.5
Similarly, a + b + c + d = 90 + d. So, this will be maximum when d is maximum.
Given b + c + d = 120. d is maximum when b + c is minimum. If b + c is minimum, a should be maximum.
Given that a + b + c = 90, the maximum value a can take is 30 as a cannot be greater than b or c. The lowest value b + c can take is 60, when a = b = c = 30. When a = b = c = 30, d = 60.
a + b + c + d = 150. Average = 37.5
So, the average has to range from 32.5 to 37.5.
Hence, the correct option is (a).
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In each of these questions there are two sets of figures. The figures on the left are Problem Figures(four figures and one question-marked spac e) and those on the right are Answer Figures indicated by number 1, 2, 3, 4 and 5. A series is established if one of the five Answer Figures is placed at the "question-marked space". Problem Figures form a series if they change from left to right according to some rule. The number of the Answer Figure which should be placed in the question-marked space, is the answer. All the five figures, i.e. four Problem Figures and one Answer Figure placed in the question-marked space should be considered as forming the series.Study the following question. If we place the Answer Figure 4 in the question marked space it makes a series which indicates that one vertical line is added in each figure. So the answer is '4', Note that if we go by only one aspect of the number of lines', Answer Figure 3 may also fit in. So you have to consider all different aspects.Now solve the following questions.

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Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?a)32.5 to 37.5b)22.5 to 27.5c)33.5 to 37.5d)23.5 to 27.5Correct answer is option 'A'. Can you explain this answer?
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Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?a)32.5 to 37.5b)22.5 to 27.5c)33.5 to 37.5d)23.5 to 27.5Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?a)32.5 to 37.5b)22.5 to 27.5c)33.5 to 37.5d)23.5 to 27.5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 4 numbers a, b, c and d. Ram figures that the smallest average of some three of these four numbers is 30 and the largest average of some three of these 4 is 40. What is the range of values the average of all 4 numbers can take?a)32.5 to 37.5b)22.5 to 27.5c)33.5 to 37.5d)23.5 to 27.5Correct answer is option 'A'. Can you explain this answer?.
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