TANCET 2014 DS 74: Averages

Directions for TANCET Data Sufficiency Questions

The question is followed by two statements labeled (1) and (2) in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the problem plus your knowledge of mathematics and everyday facts, choose the answer as:

Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
Choice 4 if each statement ALONE is sufficient.
Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

Question

Medium Data Sufficiency

During a five-day period, Monday through Friday, the average (arithmetic mean) high temperature was 86 degrees Fahrenheit. What was the high temperature on Friday?

Statement 1: The average high temperature for Monday through Thursday was 87 degrees Fahrenheit.
Statement 2: The high temperature on Friday reduced the average high temperature for the week by 1 degrees Fahrenheit.

Correct Answer Choice (4). Each statement is INDEPENDENTLY sufficient.

Explanatory Answer - step by step

Question Statement (1) Alone Statement (2) Alone Tabs

What should we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

What kind of an answer will the question fetch?

The question is "What is the high temperature on Friday"

The answer to should be a number followed by a unit of temperature – in this case Fahrenheit. For e.g., 85⁰ F.

When is the data sufficient?

If we are able to come up with a UNIQUE answer for the high temperature on Friday, the data is sufficient.

If we are not able to come up with a UNIQUE temperature, the data is NOT sufficient.

What data do we know from the question stem?

The average (arithmetic mean) high temperature was 86 degrees Fahrenheit for the 5-day period Monday to Friday.
Statement (1) ALONE

The average high temperature for Monday through Thursday was 87 degrees Fahrenheit.

From the question stem, we know that the average high temperature for the 5-day period Monday to Friday was 85⁰ F.

Sum = Average * number of terms.

So, sum of the high temperature for the 4-day period Monday to Thursday = 87 * 4 = 348.

The sum of the high temperature for the 5-day period Monday to Friday = 85 * 5 = 425.

Hence, the high temperature on Friday = Sum for 5 days (Mon to Fri) – Sum for 4 days (Mon to Thu) = 425 – 348 =77⁰ F.

We could get a UNIQUE answer to the question with statement 1.

Statement (1) ALONE is sufficient.

If statement (1) ALONE is sufficient, we can narrow our choices to 1 or 4.
Statement (2) ALONE

The high temperature on Friday reduced the average high temperature for the week by 1 degree Fahrenheit.

So, average high temperature without Friday’s value being counted would have been 1 more than 86 = 87⁰ F

i.e., the average high temperature for Monday through Thursday was 87 degrees Fahrenheit.

This information is the same what statement (1) provided.

So, if statement (1) is sufficient, so will statement (2) be.

Using statement (2) ALONE we could get a UNIQUE answer to the question.

Statement (2) ALONE is ALSO sufficient.

If statement (1) ALONE is sufficient and statement (2) ALONE is ALSO sufficient, each statement is INDEPENDENTLY sufficient.

Hence, choice (4) is the answer.