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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

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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

by M7MBA » Fri Dec 11, 2020 2:29 am

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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.

Answer: C

Source: EMPOWERgmat
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Source: — Data Sufficiency |
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Re: If the 3rd term of sequence \(A\) is \(15\) and all of the terms in the sequence are positive, then what is the 2nd

by deloitte247 » Sun Dec 13, 2020 4:20 am

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Target question => What is the 2nd term?

Statement 1 => A = 5 but the value of 2nd and third term remains unknown so statement 1 is NOT SUFFICIENT

Statement 2 => Each term of A after the 1st term is y times the preceding term
This provides us with the sequence but then the preceding term must be provided so statement 2 is NOT SUFFICIENT

Combining both statements together =>
From statement 1 => first term = 5
From statement 2 => every term after 1st term = y * preceding term
1st term => 5
2nd term => y * 5 = 5y
3rd term => y * 5y = 5y^2 = 15
$$evaluating\ 3rd\ term\ =>\ 5y^2=15$$
$$y^2=\frac{15}{5}=3$$
$$so\ y\ =\ \sqrt{3}$$
$$Hence,\ the\ 2nd\ term\ =\ 5\ \cdot\ \sqrt{3}=5\sqrt{3}$$
$$Combining\ both\ statements\ together\ is\ SUFFICIENT$$
$$Answer\ =\ C$$
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