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The product of integers w, x, y, and z is 210, and w > x > y > z > 0.

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The product of integers w, x, y, and z is 210, and w > x > y > z > 0. [#permalink]

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New post 29 Aug 2017, 23:50
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The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41
[Reveal] Spoiler: OA

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The product of integers w, x, y, and z is 210, and w > x > y > z > 0. [#permalink]

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New post 30 Aug 2017, 00:00
210 when prime factorized is 2*3*5*7

The various options for w,x,y,z are as follows:
Given that w > x > y > z > 0, therefore they are all positive

---------w-----y-----x-----q
---------2-----3-----5------7(sum is 17)
---------1-----2-----3-----35(sum is 41)
---------1-----2-----7-----15(sum is 25)
---------1-----5-----6------7(sum is 19)
---------1-----3-----7-----10(sum is 21)

The only possibility(from the answer options)
that's still missing for the sum of w,x,y, and z is 31(Option D)
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Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0. [#permalink]

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New post 30 Aug 2017, 00:16
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Bunuel wrote:
The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41


210 = 2*3*5*7 =Sum 17
1*6*5*7= Sum 19
1*3*10*7 = Sum 21
1*2*3*35 = Sum 41

But
1*1*14*15 = Sum 31 but w > x > y > z > 0
D
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Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0. [#permalink]

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New post 02 Sep 2017, 07:18
Bunuel wrote:
The product of integers w, x, y, and z is 210, and w > x > y > z > 0. Which of the following could NOT be the sum w + x + y + z?

A. 17
B. 19
C. 21
D. 31
E. 41


Let’s break down 210 as a product of two positive integers:

210 = 1 x 210 = 2 x 105 = 3 x 70 = 5 x 42 = 6 x 35 = 7 x 30 = 10 x 21 = 14 x 15

For each of the expressions except 1 x 210, we can write each factor as the product of two distinct factors. For example:

210 = 2 x 105 = (1 x 2) x (3 x 35) = (1 x 2) x (5 x 21) = (1 x 2) x (7 x 15)

From the above, we see that the sum w + x + y + z could be 41, 29, and 25, respectively. Thus, we can eliminate choice E.

Now let’s use 210 = 3 x 70:

210 = 3 x 70 = (1 x 3) x (2 x 35) = (1 x 3) x (5 x 14) = (1 x 3) x (7 x 10)

From the above, we see that the sum w + x + y + z could be 41, 23, and 21, respectively. Thus, we can eliminate choice C.

Now let’s use 210 = 5 x 42:

210 = 5 x 42 = (1 x 5) x (2 x 21) = (1 x 5) x (3 x 14) = (1 x 5) x (6 x 7)

From the above, we see that the sum w + x + y + z could be 29, 23, and 19, respectively. Thus, we can eliminate choice B.

Now let’s use 210 = 6 x 35:

210 = 6 x 35 = (1 x 6) x (5 x 7) = (2 x 3) x (1 x 35) = (2 x 3) x (5 x 7)

From the above, we see that the sum w + x + y + z could be 19, 41, and 17, respectively. Thus, we can eliminate choice A.

We can stop here since we’ve eliminated choices A, B, C, and E. Thus, D is the correct answer.

Answer: D
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Kudos [?]: 838 [0], given: 5

Re: The product of integers w, x, y, and z is 210, and w > x > y > z > 0.   [#permalink] 02 Sep 2017, 07:18
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