Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number

Question

Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the numbers greater than 35 are greater than 40. Which of the following could be the median number?

I. 34 
II. 35 
III. 36

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

I get till this part...200*0.165=x*0.333 =>x=99

Can someone help me with next steps??

Aj85 · Answer

yes I think you have deducted correctly till now. If 99 numbers are > 35 , it means rest 101 numbers are equal to or less than 35.

median in the list of a set of 200 members will be the average of 100th and 101st member of the set when we arrange the members of the set in  ascending order . From deduction we know that 102nd member to 200th member of the set are greater than 35 , and 1st member to 101st member are less than or equal to 35. 100th and 101st member could be 34 or 35 . so 34 and 35 could be the median.

bodleyev · Answer

The median occurs at term \frac{(n + 1)}{2}=\frac{201}{2}=100.5 , and for a set with an even count (200 in this case), it will be the average of terms  100  and  101 .

With  200*16.5% = \frac{1}{3}x , you have established that the  x = 200*16.5%*3=99  highest observations are each greater than 35 and that the  200*16.5%=33  highest observations are each greater than 40. All other terms must be less than or equal to 35.

The average of the 101st and 100th terms is the median. The 99th term in descending order is the  200-99+1=102 nd term in ascending order. The average of the 101st term and the 100th term, which are each less than or equal to 35, can only be 34 or 35.

aserghe1 · Answer

In my opinion, the fact that there are 200 numbers is irrelevant. We can deduce the median just by working with the percentages.

We're given that:
- 16.5% of the 200 numbers are greater than 40
- 33.3% of the numbers greater than 35 are greater than 40

Combining the 2 statements:
- 33.3% of the numbers greater than 35 are 16.5% of the 200 numbers

So, 100% of the numbers greater than 35 are 49.5% of the 200 numbers

Since the median is at the 50% mark when the numbers are arranged in order, and since 49.5% are greater than 35, then the median must be less than or equal to 35.

Answer: D

ScottTargetTestPrep · Answer

Solution:

We see that 0.165 x 200 = 33 numbers are greater than 40. We are given that 33.3% or 1/3 of the numbers greater than 35 are also greater than 40. If we let n = the number of numbers of greater than 35, we can create the equation:

1/3 * n = 33

n = 99

Therefore, there are 99 numbers greater than 35. That is, the 102nd to the 200th number (after the numbers are sorted in ascending order). Since the median of 200 numbers is the average of the 100th and 101st numbers, the median must be less than or equal to 35.

Answer: D

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Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number

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Of the 200 numbers, 16.5% are greater than 40, and 33.3% of the number

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