Number Systems

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sukhman: Master | Next Rank: 500 Posts; Posts: 202; Joined: Sun Sep 08, 2013 11:51 amFollowed by: 2 members; Thanked: 3 times

by sukhman » Tue Oct 15, 2013 9:44 am

For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations is in sign for the sequence: 1, -3, 2, 5, -4, -6?

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Source: Beat The GMAT — Problem Solving | Tue Oct 15, 2013 9:44 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Oct 15, 2013 9:47 am

sukhman wrote:For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations is in sign for the sequence: 1, -3, 2, 5, -4, -6?
A. 1
B. 2
C. 3
D. 4
E. 5

We're asked to look at every pair of consecutive terms. If the product of that pair is negative, this counts as one variation.

Let's examine the pairs of consecutive terms:

1 and -3: product is negative
-3 and 2: product is negative
2 and 5: product is positive
5 and -4: product is negative
-4 and -6: product is positive

Since 3 pairs of consecutive terms have negative products, the correct answer is C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Oct 15, 2013 9:50 am

1 x -3 = "-3"
-3 x 2 = "-6"
2 x 5 = 10
5 x -4 = "-20"
-4 x -6 = 24

Answer [spoiler]{3}[/spoiler]

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