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DS questions test a variety of skills, including the thoroughness of your thinking. In other words, do you notice when there's more than one possibility? Also, do you realize when enough "restrictions" exist to limit the number of possible answers to just one possibility? Those ideas are at the heart of this DS question.

Right from the beginning, we're given restrictions to work with: X, Y and Z are INTEGERS X, Y and Z are all > 1

We're asked for the value of X + Y + Z.

Fact 1: XYZ = 70

At first glance, many Test Takers would think that this was insufficient information since there are "so many" ways to get a product of 70. HOWEVER, we have to work with those initial restrictions (X, Y and Z are INTEGERS and they're ALL > 1). How many different sets of numbers will get us a product of 70 now?

With a bit of pattern-matching, you should notice that since 70 "ends in 0", one of the numbers MUST be a multiple of 5 and at least one of the numbers MUST be even. Prime-factorization can be used to quickly break the 70 "into pieces":

70 = (2)(5)(7)

A 2, a 5 and a 7 represent the ONLY possible numbers. Since the question asks us for the SUM of the 3 numbers, it doesn't matter which variable is which number. The final answer is 2 + 5 + 7 = 14. Fact 1 is SUFFICIENT

Fact 2: X/YZ = 7/10

With the prior work form Fact 1, the Fact seems to have an obvious solution: X = 7 Y and Z = 2 and 5 So X + Y + Z = 14

The "catch" here is that fractions can be reduced, so while X/YZ = 7/10 gave us this first outcome, X/YZ = 14/20 = 21/30 = 28/40 = etc. are ALSO possibilities that would lead to different answers.

For example: X/YZ = 14/20 X = 14 Y = 2 Z = 10 So X + Y + Z now = 26 and we have a different answer. Fact 2 is INSUFFICIENT

Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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05 Aug 2008, 19:15

arjtryarjtry 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

Given : x,y,z are integers >1 (1)xyz=70 => xyz=5*7*2 => say 5,2,7 are values of x,y,z in any order hence x+y+z is answered =>SUFFI (2)x/yz =7/10 this can be any values for x,y,z say, x=7,y=5,z=2 or x=14,y=5,z=4 hence x+y+z will change INSUFFI

Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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01 Mar 2011, 15:45

Bunuel, if the question states that x, y and z are greater then 1... then is ok to say that one of thoes is 1? as I read it , none of them can be one " GREATER THEN 1"???

Bunuel, if the question states that x, y and z are greater then 1... then is ok to say that one of thoes is 1? as I read it , none of them can be one " GREATER THEN 1"???

Again: "If x, y and z are integers greater than 1 ..." So none of them is one. _________________

Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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20 Oct 2013, 11:48

Bunuel,

The problem doesnt specifically state that the integers are unique or different. Is it possible for A to be insufficient as xyz to be 7*7*5 with a sum of 19 or the answer provided above with 2*5*7 and a sum of 14?

I'm assuming the variables need to be unique integer values, but this threw me off at first.

The problem doesnt specifically state that the integers are unique or different. Is it possible for A to be insufficient as xyz to be 7*7*5 with a sum of 19 or the answer provided above with 2*5*7 and a sum of 14?

I'm assuming the variables need to be unique integer values, but this threw me off at first.

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