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Math Expert V
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Is the average of ten integers greater than 10?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 77% (01:14) correct 23% (01:16) wrong based on 66 sessions

### HideShow timer Statistics Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.

(2) Half of the integers are less than 10.

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Re: Is the average of ten integers greater than 10?  [#permalink]

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1
Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.
Having information about only 5 of the 10 integers is not going to be
enough to calculate the average of the 10 integers (Insufficient)

(2) Half of the integers are less than 10.
Having information about only 5 of the 10 integers is not going to be
enough to calculate the average of the 10 integers (Insufficient)

When we combine the information in both the statements,

Case 1: If first 5 integers have an average of 11 and the other 5 integers
have an average of 8, The total average will be less than 10
Case 2: If first 5 integers have an average of 12 and the other 5 integers
have an average of 9, The total average will be more than 10 (Insufficient - Option E)
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Re: Is the average of ten integers greater than 10?  [#permalink]

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Bunuel wrote:
Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.

(2) Half of the integers are less than 10.

solu I think answer must be E as following:-
statement 1 5 integers are greater than 10 so lets say all 11 we don't know about other 5 if they are also above then then answer straight forward grater than 10 but if less than 10 then maybe.\
statement 2 rejected for same reason as above.
statement c is incorrect as 5 less than 10 so can be 0 and other 5 can be 11 so answer is less than 10 and if other 5 is 9 all of them and rest are 11,12,13,14,15 then answer is greater than 10 so we can't say anything so answer is option E
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Re: Is the average of ten integers greater than 10?  [#permalink]

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Bunuel wrote:
Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.

(2) Half of the integers are less than 10.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 10 variables $$(x_1, x_2, \cdots, x_{10})$$ and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
$$x_1 = x_2 = \cdots = x_5 = 9$$, $$x_6 = x_7 = \cdots = x_{10} = 12$$ : $$(x_1 + x_2 + \cdots + x_{10}) / 10 = 105 / 10 = 10.5$$ : Yes
$$x_1 = x_2 = \cdots = x_5 = 8$$, $$x_6 = x_7 = \cdots = x_{10} = 11$$ : $$(x_1 + x_2 + \cdots + x_{10}) / 10 = 95 / 10 = 9.5$$ : No

Thus, both conditions together are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: Is the average of ten integers greater than 10?  [#permalink]

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Bunuel wrote:
Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.

(2) Half of the integers are less than 10.

Question : Is the average of ten integers greater than 10?

In order to answer such question we need to know if the sum those 10 integers is greater than 10*10 = 100 or not

Statement 1) We have no information how much Greater are half of the values from 10 and how much smaller are other half hence

NOT SUFFICIENT

Statement 2) We have no information how much smaller are half of the values from 10 and how much greater are other half hence

NOT SUFFICIENT

Combining the two statements

Since no exact prediction about the sum of those 10 integers is available as how much smaller are half the values from 10 and how much greater are other half of the values hence

NOT SUFFICIENT

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Re: Is the average of ten integers greater than 10?  [#permalink]

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Bunuel wrote:
Is the average of ten integers greater than 10?

(1) Half of the integers are greater than 10.

(2) Half of the integers are less than 10.

Statement One Alone:

Half of the integers are greater than 10.

Although we know that 5 of the 10 integers are greater than 10, we do not know anything regarding the 5 other integers. Therefore we cannot determine whether the average is greater or less than 10. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Although we know that 5 of the 10 integers are less than 10, we do not know anything regarding the 5 other integers. Therefore, we cannot determine whether the average is greater or less than 10. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Logically using the information from both statements, we see that we still cannot determine whether the average is greater or less than 10. We do not know how far above 10 the 5 integers are or how far below 10 the other 5 integers are. Thus, it’s possible to get an average that is greater than 10, equal to 10, or less than 10.

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