A sequence of five integers have the following criteria:

Question

I. The median of the integers is 6
II. The only mode is 2
III. The mean is 5

Which of the following is true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10
C. The median of the three largest integers is 6.
D. The largest integer is 9.
E. The largest integer is 8.

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DhruvBadaya · Answer

Let the five integers be a,b,c,d,e (in ascending order).

I. The median of the integers is 6 
So, c = 6.

II. The only mode is 2 
So, there must at least be two 2s for the mode to be 2.
So, a and b = 2.

III. The mean is 5 
Sum of integers/5 = 5
Sum of integers = 25

Now, let us look at the statements.

A. The sum of the five integers is 30. 
This is false, as sum of integers is 25.

B. The sum of the five integers is 10
  This is false, as sum of integers is 25.

C. The median of the three largest integers is 6. 
This can or cannot be true. If median of c,d,e is 6. This would imply d is 6 and c is also 6. This would contradict the statement that 2 is the mode, since there will be 2 modes now: 2 and 6.

D. The largest integer is 9. 
Sum of integers = 25
a+b+c+d+e = 25
2+2+6+d+e = 25
4 + d + e = 19
d + e = 15

Now, d and e must not be same since the mode is 2 and it would contract with the statement.
The only possibility of d and e is d=7 and e=8.

So, the largest integer is 8.
Hence, this is false.

We have crossed out 4 options and this leaves us with one option only. From our solution above, we know that (E) is the correct solution. Hence, that is the answer.

poojaarora1818 · Answer

A sequence of five integers have the following criteria:

I. The median of the integers is 6
II. The only mode is 2
III. The mean is 5

Which of the following is true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10
C. The median of the three largest integers is 6.
D. The largest integer is 9.
E. The largest integer is 8.

1 The sum of the five integers is 30.  It cannot Be true because sum = Average * No of 5 integers i.e. 5*5 = 25

2  The sum of the five integers is 10  Incorrect

3  The median of the three largest integers is 6.  Incorrect If 2 is mod then no. 2 comes twice before 6 which is the median

4  The largest integer is 9.  Incorrect As we can see that 2 is the only mod so it should come before the median 6. So, the sequence of the five integers should be 2+2+6+ 15=25. The number that must come after 6 should be 7 and the last no should be one no. greater than 7.

5  The largest integer is 8.  Correct As the sequence of the nos should be 2+2+6+7+8=25 And if divide 25/5 then the average must be 5.

IMO Correct answer is E

Shubhradeep · Answer

Option E

Median of an increasing sequence of numbers is the number which appears right in the middle of the sequence.  
 For even number of numbers (2n), the median will be the average of the nth and (n+1)th term
For odd number of numbers (n), median will be the  \frac{(n+1)}{2} th term

Mode of a sequence of numbers is that particular number which has the highest frequency of occuring.

In the question we have been said that the sequence has 5 integers. Median is 6,  Only mode is 2  and average is 5.

That means sum is 25. Eventually option A and B ruled out.

Now, if only mode is 2 we should have the sequence whic looks like -> 2, 2, 6, _x_, _y_

For now, we don't know what will be there in the __s.

But we know we can put neither 2 nor 6.
 Why not 2: Because median is 6. If we write 2,2,2,6,__ median will be 2
Why not 6: Only mode is 2

So, the other 2 integers will have a sum of 25-(2+2+6) = 15
 Only possible way so that x<y and  x,y>6  is x=7 and y=8

Hence, option E is correct

Keshav1404 · Answer

Let's analyze the given information:

I. The median of the integers is 6.
II. The only mode is 2.
III. The mean is 5.

Since the median is 6, the third integer is 6.

The only mode is 2, so at least two of the integers are 2.

The mean is 5, and the sum of the five integers is 5×5=25.

Now, let's consider the options:

A. The sum of the five integers is 30. (Incorrect, as we determined the sum is 25.)
B. The sum of the five integers is 10. (Incorrect, as we determined the sum is 25.)
C. The median of the three largest integers is 6. (Incorrect, as the median is the middle value, and in this case, the median is 6 for all five integer. To be the median of the 3 largest number the forth number should also be 6, but here only 2 is the mode so remaining numbers are unique.)
D. The largest integer is 9. (Incorrect, If the largest number is 9 then the forth number will be 6, which is not possible. Only 7 and 8 will satisfy the conditions for the remaining numbers.)
E. The largest integer is 8. (Correct, As explained in D.)

Answer: E

bumpbot · Answer

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A sequence of five integers have the following criteria:

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