There are 8 red tegu lizards in the reptile house at a local zoo. If

Official explanation:

The correct response is (D). We know that average = sum of terms / # of terms. Therefore the sum of all the lizards’ lengths is 80 inches. Statement (1) tells us that none are shorter than 10 inches. If this is true, they must all be 10 inches or more. Since we have 8 lizards total, each of the lizards must be 10 inches. Sufficient. Statement (2) is sufficient for a similar reason. If none of the lizards are longer than 10 inches, then they must all be 10 inches. Sufficient.

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

D is correct.

When a question gives you data about the number of values in a data set and the mean of the data set, that’s actually very valuable data. Because, it lets you find the sum of the values in a data set and hence gives you a constraint to work with.

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 the 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.

From statement I alone, 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.

For example, if we consider 4 lizards to be 10 inches long, the remaining 4 have to have heights other than 10. If we consider two lizards to be more than 10 inches long, then there will be two lizards which will be less than 10 inches long, which is not possible according to the data given in statement I.

Therefore, we can conclusively say that all the 8 red lizards should be 10 inches long. This is sufficient to answer the question asked.
Statement I alone is sufficient, so, possible answers are A or D. Answer options B, C and E can be eliminated.

From statement II alone, 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.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.

If you observe carefully, the individual statements are giving you information about the minimum and maximum values of the lengths of the lizards. When you couple this information with a constraint like the one given in the question (i.e. the sum should be 80), it’s easy pickings. The only combination that will fit will be the one with all values equal. This is a commonly tested concept (equalizing values to maximise or minimize) on the GMAT.

Hope that helps!

Bunuel Can you pls solve this doubt for me. for the second statement, I thought that since the total sum should be 80 it would e perfectly fine to have 7 lizards of 8 cm each and 1 of 24 cm. The average remains the same and thus i chose option A. Can you pls tell me why this is wrong?

(2) says "None of the red tegu lizards are longer than 10 inches", so a lizard cannot be 24 inches long.

Thanks Bunuel !!! Totally missed that.

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