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EMPOWERgmat Instructor V
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If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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Question Stats: 55% (01:17) correct 45% (01:17) wrong based on 67 sessions

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EMPOWERgmat DS Series:
Pack 2, Question 1

If the 3rd term of sequence A is 15 and all of the terms in the sequence are positive, then what is the 2nd term?

1) The 1st term of A is 5.
2) Each term of A after the 1st term is y times the preceding term.

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Originally posted by EMPOWERgmatRichC on 01 Oct 2019, 21:06.
Last edited by EMPOWERgmatRichC on 04 Oct 2019, 16:40, edited 1 time in total.
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Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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2
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.

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If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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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

GMAT assassins aren't born, they're made,
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Originally posted by EMPOWERgmatRichC on 04 Oct 2019, 16:39.
Last edited by EMPOWERgmatRichC on 07 Oct 2019, 19:31, edited 1 time in total.
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Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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1
minustark wrote:
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.

Good logic, but Y^2 should be 3 not 10, y is the square root of 3
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Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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Hi colinlin1,

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

GMAT assassins aren't born, they're made,
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Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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1
EMPOWERgmatRichC wrote:
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

GMAT assassins aren't born, they're made,
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.?
EMPOWERgmat Instructor V
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Re: If the 3rd term of sequence A is 15, what is the 2nd term?  [#permalink]

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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.

GMAT assassins aren't born, they're made,
Rich
_________________ Re: If the 3rd term of sequence A is 15, what is the 2nd term?   [#permalink] 14 Oct 2019, 16:37
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# If the 3rd term of sequence A is 15, what is the 2nd term?  