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If the average (arithmetic mean) of four unequal numbers is 40, how ma

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If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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New post 25 Oct 2018, 02:26
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A
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C
D
E

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Question Stats:

70% (01:50) correct 30% (01:41) wrong based on 55 sessions

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Re: If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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New post 25 Oct 2018, 03:30
The Ans is (C). Considering only 1st statement: we might get 1, 2 or 3 as an answer. Hence not sufficient
Considering only 2nd statement, we might get 1 or 2 as an answer. Not sufficient.
Combining 1st and 2nd, if the two nos. are 19 and 20, the remaining 121 has to be contributed by another 2 nos. Both of these have to be more than 40 as one number alone being restricted by 70 would not be sufficient and hence, 2 nos. will be more than 40.


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If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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New post 25 Oct 2018, 04:40
The answer is C.

1) the answer could be 0 (they are all 40!), 1 (39, 40, 40, 41), 2 (39,39,41,41) or 3 (37, 41,41,41). Insufficient!
2) If the sum of the 1st 2 number is 39 (19+20), the sum of the next 2 must be 121 (160-39). This can be accomplished by 2 answers larger than 40 (60,61), or one (30, 81). Insufficient!

Combined: 2 numbers cannot be sum to 121, with a number smaller than 41 and a number smaller than 71 (40+70=110, the max) - BOTH number have to be larger than 40 (60+61, 70+51, etc). Sufficient! Answer C.
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Re: If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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New post 25 Oct 2018, 06:27

Solution


Given:
    • The average of four unequal numbers = 40

To find:
    • The number of numbers, which are greater than 40

Approach and Working:
    • Sum of the four numbers = 40 * 4 =160

Analysing Statement 1
    • Given that no number is greater than 70

We cannot conclude anything from this information

Therefore, Statement 1 alone is not sufficient to answer this question

Analysing Statement 2
    • Two numbers are 19 and 20
    • Thus, the sum of remaining two numbers = 160 – 19 - 20 = 121

We cannot conclude anything from this, since both the numbers can be greater than 40 or only one can be greater than 40

Therefore, Statement 2 alone is not sufficient to answer this question

Combining Both Statements
    • Combining both statements, we get,
      o Two numbers are 19 and 20,
      o The sum of remaining two numbers = 121 and
      o No number is greater than 70

    • So, the maximum value of an unknown number = 70
      o Implies, the other number = 121 – 70 = 51.

    • So, both the numbers cannot be less than 51
    • Thus, two numbers are greater than 40

Therefore, both statements together are sufficient to answer this question

Hence, the correct answer is Option C

Answer: C

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Re: If the average (arithmetic mean) of four unequal numbers is 40, how ma   [#permalink] 25 Oct 2018, 06:27
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