If the average (arithmetic mean) of 4 numbers is 30, how

Question

If the average (arithmetic mean) of 4 numbers is 30, how many of the numbers are greater than 30 ?

(1) Two of the numbers are equal to 20.
(2) None of the numbers are equal to 30.

Bunuel · Accepted Answer

If the average (arithmetic mean) of 4 numbers is 30, how many of the numbers are greater than 30 ?

It's almost always better to express the average in terms of the sum : the average of 4 numbers is 30 --> the sum of 4 numbers is 4*30=120

(1) Two of the numbers are equal to 20 --> the sum of the other two numbers is 120-2*20=80. Now, if both of them are 40 then there are two numbers greater than 30 but if one number is 25 and another is 55 then there is only one number greater than 30. Not sufficient.

(2) None of the numbers are equal to 30. Clearly insufficient.

(1)+(2) Example from (1) is still valid, so we still have two answers. Not sufficient.

Answer: E.

Hope it's clear.

Bunuel · Answer

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shivanigs · Answer

Stmt 1 : Average = Sum/Total number of items

Hence, the sum of the 4 numbers is 120

Since 2 of the numbers are equal to 20,there could be multiple scenarios

20+20+0+80 = 120 (in this case only 1 number is greater than 30)

Or 20+20+32+48 = 120 (in this case 2 numbers are greater than 30)

Since there is no definite answer,this statement is insufficient

Stmt 2 : None of the numbers are equal to 30,there could be multiple scenarios

0+0+70+50 = 120 (in this case 2 numbers are greater than 30)

Or 120+0+0+0 = 120 (in this case only 1 number is greater than 30)

Since there is no definite answer,this statement is also insufficient

Both : 20+20+32+48 = 120 (in this case 2 numbers are greater than 30)
 
20+20+0+80 = 120 (in this case only 1 number is greater than 30)

Since there is no definite answer,both statements are insufficient

Answer : E

mau5 · Answer

When it is given that the average of 4 nos is 30, we can ASSUME that each no is equal to 30.

Thus, we can represent the nos as 30,30,30,30.Note that if we reduce any one of the quantity, say 30 by 10, we will have to redistribute that same quantity amongst the other 3 nos to keep the same average.

From F.S 1, two of the nos are equal to 20. Thus, this could either lead to 20,20,30,50 OR 20,20,40,40. In both the scenarios, we get different answers for # greater than 30. Insufficient.

From F.S 2, the given set can be represented as 29,29,31,31 OR 28,28,28,36. Again, Insufficient.

Taking both together also, we can have either 20,20,31,49 OR 20,20,25,55. Insufficient.

E.

bumpbot · Answer

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If the average (arithmetic mean) of 4 numbers is 30, how

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