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EMPOWERgmatRichC
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From Statement 1, we get the 1st term of the sequence, 5. But, from this we cannot infer about the 2nd term. It can be of any value. NOT SUFFICIENT.
Statement 2 tells us each term of the sequence is y times the preceding term. But it doesn't specify the value of y, without which we cannot get the value of any other term. NOT SUFFICIENT.

Together, 1st term, A= 5
2nd term, A*y=5y
3rd term, A* y^2 = 5y^2 =15 , or y^2= 10,

So y will be the positive root of 10 as 3rd term is greater than 1st term. From this we will get the 2nd term. SUFFICIENT.

Answer is C.

Good logic, but Y^2 should be 3 not 10, y is the square root of 3
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Hi colinlin1,

Thanks for catching that typo; I've corrected it in my explanation.

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EMPOWERgmatRichC
OFFICIAL EXPLANATION

Hi All,

We're told that all of the terms in a sequence are positive and the 3rd term of sequence A is 15. We're asked for the 2nd term of the sequence.

1) The 1st term of A is 5.

Knowing 2 terms of the sequence is not enough to define how the sequence 'works' - or any of the other terms in the sequence. It's certainly possible that the sequence is Arithmetic and 'increases by 5' from term to term... meaning that the first three terms would be 5, 10 and 15.... and the answer to the question would be 10.

However, it's also possible that the sequence is Geometric and each term increases by some constant product (such as √3)... meaning that the first three terms would be 5, 5√3 and 15... and the answer to the question would be 5√3.
Fact 1 is INSUFFICIENT



2) Each term of A after the 1st term is y times the preceding term.

Fact 2 tells us how the sequence works, but without the first term in the sequence, we cannot determine the second term in the sequence.
Fact 2 is INSUFFICIENT

Combined, we know...
-The 1st term of A is 5.
-Each term of A after the 1st term is y times the preceding term.

With the information in both Facts, we know that the first term is 5, the third term is 15 and each term increases by some constant product. The only way for that sequence to exist is if y = √3... meaning that the first three terms are 5, 5√3 and 15... and the answer to the question is 5√3.

Combined, SUFFICIENT

Final Answer:
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Rich


Hi, from both, Y^2 =3==> Y= +/- √3, shouldn't the answer still be E?? or should I ignore the -ve sign because its an AP.?
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Hi ankitprad,

You pose an important question - and under certain situations, you would have to consider negative values. However, the prompt tells us that all of the terms in the sequence are POSITIVE... and if you multiplied the first, positive term by a negative number, then the second term would be NEGATIVE. That does not fit the 'restrictions' given by the prompt, so it's not a possibility.

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