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# If x, y and z are integers greater than 1, what is the value

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If x, y and z are integers greater than 1, what is the value [#permalink]  09 Jun 2008, 06:43
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If x, y and z are integers greater than 1, what is the value of x + y + z?
1) xyz = 70
2) x/yz = 7/10
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Re: DS: GMATPrep xyz [#permalink]  09 Jun 2008, 06:48
1) xyz = 70
decompose 70 into its prime factors: 70 = 2 x 5 x 7
this is the only product of 3 integers greater than 1 that gives 70
=> x+y+z = 2+5+7 = 14
=> 1) is sufficient

2) x/zy = 7/10
doesn't say much about x, y and z. Take any x, y and z that satisfy the equation above, multiply x by a number and z or y by the same number you would still have the equality above but a different sum.
=> 2 is not sufficient

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Re: DS: GMATPrep xyz [#permalink]  09 Jun 2008, 07:03

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Re: DS: GMATPrep xyz [#permalink]  09 Jun 2008, 07:23
The question stem says "integers greater than 1". 1 is not greater than 1. It would be possible if the question asked for positive integers, or integers >= 1, etc. But the way it is written, 1 is not an option.

Why wouldn't D be the answer, "Both statements independently are sufficient to answer the question."

If xyz = 70 is sufficient, and then #2 says $$\frac{x}{yz}=\frac{7}{10}$$

#2 is saying the same thing as #1. It tells you the value of x = 7. and yz = 10. The only possible integers > 1 with product of 10 is 2 & 5. #2 is sufficient as well.

j allen morris
rino wrote:

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Manager Joined: 19 May 2008 Posts: 52 Followers: 0 Kudos [?]: 4 [0], given: 0 Re: DS: GMATPrep xyz [#permalink] 09 Jun 2008, 13:09 Correct. 1 is not "greater than 1". x/yz = 7 / 10 doesn't say anything about the values of x, y and z. Here's an example: x = 7, y = 2, z = 5 sum = 14 x/yz = 7 / (2x5) = 7 / 10 => fine now pick x = 70, y = 2, z = 50 (notice i multiplied x and z by 10... which would be later on simplified) sum = 122 x/yz = 70 / (2x50) = 70/100 = 7 / 10 jallenmorris wrote: The question stem says "integers greater than 1". 1 is not greater than 1. It would be possible if the question asked for positive integers, or integers >= 1, etc. But the way it is written, 1 is not an option. Why wouldn't D be the answer, "Both statements independently are sufficient to answer the question." If xyz = 70 is sufficient, and then #2 says $$\frac{x}{yz}=\frac{7}{10}$$ #2 is saying the same thing as #1. It tells you the value of x = 7. and yz = 10. The only possible integers > 1 with product of 10 is 2 & 5. #2 is sufficient as well. Answer D j allen morris rino wrote: what about 1*14*5 or 10*1*7 the answer is E CEO Joined: 29 Mar 2007 Posts: 2591 Followers: 16 Kudos [?]: 234 [1] , given: 0 Re: DS: GMATPrep xyz [#permalink] 09 Jun 2008, 13:18 1 This post received KUDOS lexis wrote: If x, y and z are integers greater than 1, what is the value of x + y + z? 1) xyz = 70 2) x/yz = 7/10 A. 1: only can be 7,2,5 2: could be 7/(2*5) or 14/(2*10) Current Student Joined: 28 Dec 2004 Posts: 3391 Location: New York City Schools: Wharton'11 HBS'12 Followers: 13 Kudos [?]: 181 [0], given: 2 Re: DS: GMATPrep xyz [#permalink] 09 Jun 2008, 13:29 i too Get A.. 2) is insuff because x/yz=7/10 can easily be x=14, yz=20... or x=7 yz=10 SVP Joined: 30 Apr 2008 Posts: 1892 Location: Oklahoma City Schools: Hard Knocks Followers: 34 Kudos [?]: 468 [0], given: 32 Re: DS: GMATPrep xyz [#permalink] 09 Jun 2008, 13:44 GMATBLACKBELT, Good call on that. I wasn't think of having to reduce x/yz to get 7/10. I was taking what they gave us and not thinking beyond that. That's a mistake on the GMAT (as long as we don't over-think it;)) _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Senior Manager
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Re: DS: GMATPrep xyz [#permalink]  12 Jun 2008, 04:03
Correct. 1 is not "greater than 1".
x/yz = 7 / 10 doesn't say anything about the values of x, y and z.

Here's an example:
x = 7, y = 2, z = 5
sum = 14
x/yz = 7 / (2x5) = 7 / 10 => fine

now pick
x = 70, y = 2, z = 50 (notice i multiplied x and z by 10... which would be later on simplified)
sum = 122
x/yz = 70 / (2x50) = 70/100 = 7 / 10

jallenmorris wrote:
The question stem says "integers greater than 1". 1 is not greater than 1. It would be possible if the question asked for positive integers, or integers >= 1, etc. But the way it is written, 1 is not an option.

Why wouldn't D be the answer, "Both statements independently are sufficient to answer the question."

If xyz = 70 is sufficient, and then #2 says $$\frac{x}{yz}=\frac{7}{10}$$

#2 is saying the same thing as #1. It tells you the value of x = 7. and yz = 10. The only possible integers > 1 with product of 10 is 2 & 5. #2 is sufficient as well.

j allen morris
rino wrote:

OA is A.
Re: DS: GMATPrep xyz   [#permalink] 12 Jun 2008, 04:03
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