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QOTD#10 If x, y, and z are consecutive even integers, such

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QOTD#10 If x, y, and z are consecutive even integers, such [#permalink] New post 13 Oct 2016, 14:14
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100% (00:51) correct 0% (00:00) wrong based on 5 sessions
If x, y, and z are consecutive even integers, such that x < y < z and xyz = 960, what is the value of z?

Drill 2
Question: 4
Page: 286



[Reveal] Spoiler: OA
12

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Joined: 07 Jun 2014
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Kudos [?]: 1596 [0], given: 373

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Re: QOTD#10 If x, y, and z are consecutive even integers, such [#permalink] New post 13 Oct 2016, 14:17
Expert's post
Explanation

Ballpark that 960 is about 1,000, which is 10 × 10 × 10. Then test a set of consecutive even integers near 10, such as 10 × 12 × 14 = 1,680. This product is too large. Try 8 × 10 × 12 = 960, giving you z = 12.
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Re: QOTD#10 If x, y, and z are consecutive even integers, such [#permalink] New post 18 Nov 2016, 06:49
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sandy wrote:
If x, y, and z are consecutive even integers, such that x < y < z and xyz = 960, what is the value of z?

Drill 2
Question: 4
Page: 286



[Reveal] Spoiler: OA
12


I like Sandy's solution a lot. It's probably the best/fastest approach.
However, here's one more solution:

Since x, y, and z are EVEN, and since xyz = 960, I assume that one of the values is 10 (since 960 is divisible by 10). Of course, one of the values could also be 20 or 30 or..., but I'll start with 10

If one value is 10, the other two EVEN numbers must have a product of 96 AND the two numbers should be close together since we're dealing with consecutive numbers.
I know that (8)(12) = 96, and these numbers are close together
When we combine 8 and 12 with 10, we see that we do, indeed, have 3 consecutive EVEN integers.
Since x < y < z, we know that x = 8, y = 10 and z = 12

Answer:
[Reveal] Spoiler:
12

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Re: QOTD#10 If x, y, and z are consecutive even integers, such   [#permalink] 18 Nov 2016, 06:49
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