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

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

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04 Aug 2008, 11:05
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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
[Reveal] Spoiler: OA
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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04 Aug 2008, 11:10
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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

statement 1 : 70 = 2*5*7
x+y+z = 2+5+7 = 14 suff

statement 2 : x/yz = 7/10 = 14/20 = 21/30 ... not suff

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

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22 Oct 2008, 11:58
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rishi2377 wrote:
If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?

x,y,z >1

(1) xyz = 70 = 2*5*7 so we can find x+y+z

(2) $$\frac{x}{yz} = \frac{7}{10}$$

this just means x is a multiple of 7 and the product yz is a multiple of 10. We have no info to determine values of x,y and z.

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

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04 Aug 2008, 11:11
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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

1) xyz = 70 (suffcient)
= 2 * 5 * 7 ( is only combination which leads to 70)

2) x/yz = 7/10 (not suffcient)

x/yz = 7/10 ( x=7 y = 5 z=2)
x/yz = (7/10)*(k/k) also true for ( x=14 y = 10 z=2)

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

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10 Jan 2015, 12:54
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Hi All,

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

[Reveal] Spoiler:
A

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

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26 Oct 2015, 02:40
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$$X , Y , Z integers > 1$$

$$x + y + z = ?$$

Statement 1

$$xyz = 70$$

Prime factorizing 70 we get 2, 5 and 7 ( we can not take any value to be 1 because all integers are greater than 1)

so $$x + y + z = 14$$

No matter what value we take for x, y, z , sum will always be 14

Hence statement 1 is Sufficient

Statement 2

$$\frac{x}{yz} = \frac{7}{10}$$

here if $$x = 7$$ then y be 2 and z be 5 then $$x + y + z = 14$$

x can also be 14 , then y be 2 and z be 10 then $$x + y + z = 26$$

so clearly statement 2 is not sufficient.

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

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04 Aug 2008, 11:12
1.) xyz = 70
= 7*5*2
therefore, x+y+z = 7+5+2 = 14
sufficient

2.) x/yz = 7/10
x = 70, y = 20 , z = 5
or
x = 7, y = 5, z = 2
Insuff..

Therefore, A
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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
(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

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

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22 Oct 2008, 11:54
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If integers x, y and z are greater than 1 what is the value of x + y + z ?

(1) xyz = 70
(2) x/yz = 7/10

[Reveal] Spoiler:
I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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22 Oct 2008, 12:28
rishi2377 wrote:
If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?

Thats where I stopped as well and figure that (7,2,5) and (14,2,10) satisfy the equation. B insuff

A is (2,5,7). good
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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22 Oct 2008, 14:11
rishi2377 wrote:
If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?

A

1. x+y+z = 14 - Sufficient
2. To many combinations - Not Sufficient
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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23 Oct 2008, 00:25
rishi2377 wrote:
If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

I got this right. but with 2nd statement. I went to only 10x = 7yz
is that the end of 2nd statement or we can drive something with that?

This step may not be required.

x/yz = 7/2*5 = 14/4*5 = 14/2*10 = 28/4*10....and so on and hence there could be many values for x, y and z.
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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23 Oct 2008, 01:17
[quote="rishi2377"]If integers x, y and z are greater than 1 what is the value of x + y + z ?

A. xyz = 70
B. x/yz = 7/10

the second statment provide a proportion as such it give endless combinations.
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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05 Jan 2011, 08:29
xyz = 70
so the values could be 1 7 10
x+y+z = 18
if the values are 2 5 7
x+y+z =14
so a not sufficient
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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05 Jan 2011, 08:40
anilnandyala wrote:
xyz = 70
so the values could be 1 7 10
x+y+z = 18

if the values are 2 5 7
x+y+z =14
so a not sufficient

"If x, y and z are integers greater than 1 ..."

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

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01 Mar 2011, 16:04
marijose wrote:
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.
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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01 Mar 2011, 23:46
I was thinking that statement 1 is not sufficient until i factorized 70 in prime factors. So A it is.
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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.
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Re: If integers x, y and z are greater than 1 what is the value [#permalink]

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20 Oct 2013, 11:51
affalcon12 wrote:
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.

Notice that 7*7*5 = 245 not 70.
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Re: If integers x, y and z are greater than 1 what is the value   [#permalink] 20 Oct 2013, 11:51

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