There are 8 Red Tegu Lizards in the Reptile House at a Local Zoo GMAT Data Sufficiency

Question: There are 8 red tegu lizards in the reptile house at a local zoo. If the average length of the red tegu lizards is 10 inch, then how many of the red tegu lizards are exactly 10 inches long?

1. None of the red tegu lizards are shorter than 10 inches
2. None of the red tegu lizards are longer than 10 inches

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Solution and Explanation:
Approach Solution (1):

When the average length is 10, there are 2 possibilities: either all lengths are 10, or some lengths more and some lengths less than 10

(1) Lengths are not shorter than 10, which implies all lengths are 10.
Sufficient

(2) Lengths are not longer than 10, which implies all lengths are 10.
Sufficient

Correct Option: D

Approach Solution (2):

It is given that the average length is 10 inches
Let’s see the choices:

(1) None of the red tegu lizards are shorter than 10 inches
Since none are shorter than 10 inches, none can be greater than 10 inches. Otherwise the average will become > 10
All are 10 inches
Sufficient

(2) None of the red tegu lizards are longer than 10 inches
Same as (1)
Sufficient

Correct Option: D

Approach Solution (3):

In this question, the number of values in the data set(related to the length of the tegu lizards) is 8 and the average length is 10 inches. Therefore, the sum of the lengths of all lizards = 8 * 10 = 80 inches
This means we have 8 values that should add up to 80. Of these 8 values, we are trying to find how many values are equal to 10
S1: None of the lizards are shorter than 10 inches. This is only possible by taking all of the values as 10. No other combination of values will satisfy all constraints specified.

Therefore, we can say that all the 8 lizards should be 10 inches long. This is sufficient to answer the question.
S1 alone is sufficient, so possible answers are A or D. Other options will be automatically eliminated.
S2: None of the lizards are longer than 10 inches. Again, in a similar way, we can say that this is satisfied only when all the lizards are of the same length and that is 10 inches
S2 alone is sufficient. Answer A option can be eliminated

Correct Option: D

“There are 8 red tegu lizards in the reptile house at a local zoo. If the average length of the red tegu lizards is 10 inch, then how many of the red tegu lizards are exactly 10 inches long?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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