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

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Math Expert
Joined: 02 Sep 2009
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If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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25 Oct 2018, 02:26
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Difficulty:

35% (medium)

Question Stats:

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

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If the average (arithmetic mean) of four unequal numbers is 40, how many of the numbers are greater than 40?

(1) No number is greater than 70.
(2) Two of the four numbers are 19 and 20.

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Joined: 11 Feb 2016
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GMAT 1: 600 Q47 V25
Re: If the average (arithmetic mean) of four unequal numbers is 40, how ma  [#permalink]

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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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25 Oct 2018, 04:40

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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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

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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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