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# Product of Integers

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Intern
Joined: 12 Oct 2007
Posts: 24
Product of Integers  [#permalink]

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21 Aug 2008, 17:54
I just can't seem to understand this question and I really don't like the explanation. Hopefully someone can explain it better.
Question comes from PowerPrep Test 1

If the product of the integers w, x, y, and z is 770, and if 1 < w < x < y < z, what is the value of w + z?
10
13
16
18
21

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Director
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Re: Product of Integers  [#permalink]

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21 Aug 2008, 18:06
770 = 2*5*7*11

w + z = 13

Intern
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Re: Product of Integers  [#permalink]

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21 Aug 2008, 18:16
how exactly did you come up with the 2,5,7,11? Is it some kind of prime factor rule?
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Joined: 30 Apr 2008
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Re: Product of Integers  [#permalink]

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21 Aug 2008, 20:17
1
If you know the product of w, x, y & z is 770 and you cannot use 1 because every variable is larger than 1, as indicated by the stem.

You see that 77 * 10 - that gives you 2 numbers

77 breaks down to 7 * 11 and 10 breaks down to 2 * 5. These are all prime numbers. There isn't a way to break 770 in to 4 numbers where one of the numbers is NOT prime.

Because it is impossible to use 4 numbers to define 770 without using all prime numbers, we know that 2, 5, 7, 11 are the numbers which must be used and because the stem gives us the order, we can identify which numbers are w and z, therefore the sum will be 13.

freestyla86 wrote:
how exactly did you come up with the 2,5,7,11? Is it some kind of prime factor rule?

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Re: Product of Integers  [#permalink]

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19 Dec 2018, 05:17
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Re: Product of Integers &nbs [#permalink] 19 Dec 2018, 05:17
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# Product of Integers

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