BTGmoderatorDC wrote:For a finite sequence of non zero 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 in sign for the sequence 1, -3, 2, 5, -4, -6 ?

A. 1
B. 2
C. 3
D. 4
E. 5

OA C

Source: GMAT Prep

Taking all the possible pairs of consecutive terms out of the sequence 1, -3, 2, 5, -4, -6:

1. {1, - 3}: Product = -3, negative
2. {- 3, 2}: Product = -6, negative
3. {2, 5}: Product = 10, positive
4. {5, - 4}: Product = -20, negative
5. {-4, - 6}: Product = 24, positive

We see that three products are negative, thus, the number of variations in sign = 3.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote:For a finite sequence of non zero 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 in sign for the sequence 1, -3, 2, 5, -4, -6 ?

A. 1
B. 2
C. 3
D. 4
E. 5

We are given the following sequence of numbers: 1, -3, 2, 5, -4, -6.

Every time a pair of consecutive terms produces a negative product, we have a "variation in sign." We must determine the number of variations in sign in the sequence.

1 x (-3) = -3, so this is a variation in sign

(-3) x 2 = -6, so this is a variation in sign

(2) x (5) = 10, so this is NOT a variation in sign

5 x (-4) = -20, so this is a variation in sign

(-4) x (-6) = 24, so this is NOT a variation in sign

Thus, there is a total of 3 variations in sign.

Answer: C