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Z is the set of all fractions of the form n/(n-1) ; where n

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by Brent@GMATPrepNow » Wed May 10, 2017 6:13 am
ziyuenlau wrote:Z is the set of all fractions of the form n/(n-1) ; where n is a positive integer and 1 < n < 20.

What is the product of all the fractions in the set Z?

A)21
B)20
C)19
D)11
E)1
Set Z = {2/1, 3/2, 4/3, 5/4, . . . 18/17, 19/18}

What is the product of all the fractions in the set Z?
Product = 2/1 x 3/2 x 4/3 x 5/4 x . . . x 18/17 x 19/18
= (2 x 3 x 4 x . . .x 17 x 18 x 19)/(1 x 2 x 3 x 4 x . . .x 17 x 18)
= 19/1
= 19
= C

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by DavidG@VeritasPrep » Wed May 10, 2017 6:21 am
And if you're interested in a similar official question, see here: https://www.beatthegmat.com/sequence-sum-t290859.html
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by [email protected] » Wed May 10, 2017 10:19 am
Hi ziyuenlau,

When a Quant questions appears to involve a really big series of calculations, there is almost certainly going to be a pattern involved (since the GMAT would never actually require that you perform that type of gigantic calculation. Thus, given the details of this question, let's perform some simpler versions of what is asked for and look for a pattern.

IF... we just multiplied the first 2 terms, we'd have... (2/1)(3/2) = 3
IF... we just multiplied the first 3 terms, we'd have... (2/1)(3/2)(4/3) = 4
IF... we just multiplied the first 4 terms, we'd have... (2/1)(3/2)(4/3)(5/4) = 5

Notice how - in each calculation - the terms in the denominator end up 'cancelled out' by the terms in the numerator... and all that's left is the last numerator. Also notice how the product is simply increasing by 1 for every additional term that we include...

This question asks us to calculate the product of 18 terms. Using the pattern defined above, the product would have to be 19.

Final Answer: C

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