Question

Directions: The problem below consists of a problem followed by two statements.
Decide whether the data in the statements are sufficient to answer the question. Select your answer depe
whether the data provided in:
(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
(B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
(C) both statements taken together are sufficient to answer the question, but neither statement alone is
answer the question
(D) each statement alone is sufficient to sufficient to answer the question
(E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
Problem: Find the value of third number?
Statement 1: The average of five consecutive even numbers is 26.
Statement 2: When five numbers are written in ascending order, the average of first three numbers is 13 and last three numbers is 17.​

Answer 1

Data interpretation and inference

Given:

5 consecutive even numbers are given.

In 1st statement the average of 5 numbers are 26.

In 2nd statement the average of first 3 numbers is 13 and that of last 3 numbers is 17, when arranged in ascending order.

To find:

Sufficiency of statement for finding the value of 3rd number.

Explanation:

Let the 5 even consecutive numbers be $x-4, x-2, x, x+2, x+4$

According to 1st statement,

$\frac{(x-4)+(x-2)+ (x)+( x+2)+ (x+4)}{5}=26\\\\x=26$

We can see that 3rd number is x i.e. 26, so 1st statement is sufficient to find 3rd number.

According to 2nd statement,

$\frac{(x-4)+(x-2)+(x)}{3}=13\\\\\&\\\\\frac{(x)+(x+2)+(x+4)}{3}=17$

On solving any of these equation we will get the value of x , which is 3rd number , which means 2nd statement is also sufficient for finding 3rd number.

Hence option (D) is correct, each statement alone is sufficient to sufficient to answer the question.

Answer 2

Answer: option (D)

(D) each statement alone is sufficient to sufficient to answer the question

Step-by-step explanation:

Data analysis and inference

Given: There are 5 consecutive even integers.

The average of the first statement's five digits is 26.

When put in ascending order in the second sentence, the average of the first three numbers is 13 and the average of the final three digits is 17.

To determine: Whether a statement is sufficient to determine the third number's value.

Justify your answer by using five consecutive even integers.

As stated in the first sentence,

Since the third number is clearly x, or 26, the first statement is sufficient to determine the third number.

The second statement reads,

The third number will be determined by solving either of these equations, hence the second assertion is likewise sufficient to determine the third number.

hence, option (D)

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