GMAT Boost Challenge Question #2

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Thu Aug 11, 2011 9:15 am

[EDIT: Sorry, this is a DS question, is there anyway to move it to the other forum?]
[EDIT2: I'll just leave it in PS, I'll be more careful in the future]

Here is a GMAT Boost Challenge Question. If you have any questions, let me know.

The solution to last week's question is available here: https://www.beatthegmat.com/post395822.html#395822
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In a certain sequence, each term after the first is equal to the product of the previous term and -2. What is the seventh term in the sequence?

1. The sum of the first three terms is 27 more than the sum of the 4th, 5th and 6th terms
2. The sum of the 4th, 5th and 6th terms is -24

Last edited by gmatboost on Thu Aug 11, 2011 10:38 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Thu Aug 11, 2011 9:15 am

Touseef: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Jul 30, 2011 10:39 pm; Location: India; Thanked: 3 times

by Touseef » Thu Aug 11, 2011 9:35 am

The Sequence is{n,-2n,4n,-8n,16n,-32n,64n)

Hence,the 7th number in the series is 64n.

Statement 1:n-2n+4n=-8n+16n-32n+27
n can be calculated.
SUFFICIENT

Statement 2:-8n+16n-32n=24
n=1 i.e 7th term=64
SUFFICIENT

Either statement alone is sufficient.

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rppala90: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Mon Nov 15, 2010 12:12 pm; Thanked: 2 times

by rppala90 » Thu Aug 11, 2011 9:43 am

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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

by saketk » Fri Aug 12, 2011 12:11 pm

Let the first term = a,

as per the condition given:--

the series will look like

a, -2a, 4a, -8a, 16a, -32a , 64a.

1. The sum of the first three terms is 27 more than the sum of the 4th, 5th and 6th terms

3a = 27- 24a
a = 1. SUFFICIENT

2. The sum of the 4th, 5th and 6th terms is -24

-24a = -24
a =1. SUFFICIENT.

IN both cases, we get the answer as 64.

Either statement alone is sufficient

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Fri Aug 12, 2011 1:14 pm

Let the first term = x,
Hence the series is a GP

x, -2x, 4x, -8x, 16x, -32x , 64x

statement 1:

3x = 27- 24x
x = 1.
sufficient

statement 2:

-24x = -24
x =1.
sufficient

Answer D

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Fri Aug 26, 2011 11:28 am

The answer to this question was D.
Check out the next challenge question, it will be posted in a couple of minutes.

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sat Aug 27, 2011 7:00 am

Hey Greg if you could post a simple solution to the question too, that would be great.

It will be helpful to match the math!

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Tue Aug 30, 2011 7:07 am

1st term x, 2nd = -2x
3rd = 4x
4th = -8x
5th = 16x
6th = -32x
7th = 64x

now consider the option 1 and option 2 both would yield the ans. You will be able to find x = 1

D

This time no looking back!!!
Navami

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AN24: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Wed Aug 17, 2011 7:34 amFollowed by: 1 member; Thanked: 3 times

by AN24 » Tue Aug 30, 2011 10:24 am

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Sep 14, 2011 9:59 am

Nth term = (-2)^n * a (where a is first term)
B) a*[(-2)^3 + (-2)^4 + (-2) ^5 ] = -24.
We can find a, and thus 7th term
Sufficient
A) again we will get one equation in a, which can be solved. Sufficient

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Sep 14, 2011 10:41 am

a1
a2=a1*(-2)
a3=a1*4
a4=a1*(-8)
a5=a1*16
a6=a1*(-32)
a7=a1*64 ?
Statement 1
a1+a2+a3=27+a4+a5+a6. This is solvable for a1. Sufficient

Statement 2
a4+a5+a6=24. Solvable for a1. Sufficient

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