Three numbers are in geometric progression such that the product of them is 27 and the sum of the products taken in pairs is 91. What is the third number in the progression?

Answer Choices

Correct answer marked below

1/3

1/3 or 27

Correct

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Explanation

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Official Explanation

Official

You don't need to know what a "geometric progression" is on the GMAT, but it's a sequence where we multiply by some constant to find the next term.

If

a

is the first term, and we multiply by

r

to find each subsequent term, we could write the three terms this way:

a, ar, ar^2

.

But if that's a geometric sequence, so is this:

ar^2, ar, a

because here we're multiplying by

1/r

to find the next term. These sequences have exactly the same terms, so will have the same product, and the same "sum of products taken in pairs".

So there will need to be two different solutions here unless every term of the sequence is identical, and since we can quickly confirm that's not the case (the terms would need to all be 3 since their product is 27, but then we don't get the right "sum of terms taken in pairs"). So the answer must be E.…

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What this question tests

What it tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Common trap

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.