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EMPOWERgmatRichC
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Expert reply
Updated on: 04 Oct 2019, 15:40
Originally posted by EMPOWERgmatRichC on 01 Oct 2019, 20:06.
Last edited by EMPOWERgmatRichC on 04 Oct 2019, 15:40, edited 1 time in total.
Last edited by EMPOWERgmatRichC on 04 Oct 2019, 15:40, edited 1 time in total.
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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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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.
48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question DS Block 2 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.
To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct
The OA and official explanation will be held until the 48 hour window has lapsed.
minustark
Joined: 14 Jul 2019
Last visit: 01 Apr 2021
Posts: 465
Status:Student
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Products:
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.
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.
EMPOWERgmatRichC
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Last visit: 31 Dec 2023
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Expert reply
Updated on: 07 Oct 2019, 18:31
Originally posted by EMPOWERgmatRichC on 04 Oct 2019, 15:39.
Last edited by EMPOWERgmatRichC on 07 Oct 2019, 18:31, edited 1 time in total.
Last edited by EMPOWERgmatRichC on 07 Oct 2019, 18:31, edited 1 time in total.
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:
GMAT assassins aren't born, they're made,
Rich
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:
GMAT assassins aren't born, they're made,
Rich
minustark
Good logic, but Y^2 should be 3 not 10, y is the square root of 3
EMPOWERgmatRichC
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Joined: 19 Dec 2014
Last visit: 31 Dec 2023
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Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
Hi colinlin1,
Thanks for catching that typo; I've corrected it in my explanation.
GMAT assassins aren't born, they're made,
Rich
Thanks for catching that typo; I've corrected it in my explanation.
GMAT assassins aren't born, they're made,
Rich
EMPOWERgmatRichC
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.?
EMPOWERgmatRichC
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Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
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.
GMAT assassins aren't born, they're made,
Rich
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
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