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

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Question Stats: 53% (01:28) correct 47% (01:37) wrong based on 746 sessions

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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
Senior Manager  Joined: 27 May 2008
Posts: 387
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

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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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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)

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

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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

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

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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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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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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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 ..."

Correct answer is 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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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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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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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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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]

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Bunuel,
Yes, good correction. Obviously. For some reason I was thinking 7+7 = 14 and 14*5 = 70. Dumb mistake by me. Thank you!
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

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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

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

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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

We know x,y,z > 1

Read St.A --> xyz = 70 = 2*5*7
as x,y and z are greater than 1 we cant have (10,7,1), (70,1,1) or other combinations
Hence x+y+z = 2+5+7 = 14
A is sufficient

St. B --> x/yz = 7/10
now x is 7k, y is 2m and z is 5n
Hence x+y+z will be variable
Hence B is useless.

Only A is 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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$$X , Y , Z integers > 1$$

$$x + y + z = ?$$

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.

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

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A video explanation can be found here:

Practically every GMAT will ask you a question that requires you to think about prime factorization, so always have than in the back of your mind.

70 = 2*5*7, so the sum of primes is 14. Statement (1) is sufficient

In statement (2) x, y and z COULD be 7, 2 and 5, but could also be a multiple of x and a multiple of y or z, such that the expression simplifies to 7/10 (for e.g. x = 14, y = 4, and z = 5), so (2) not sufficient
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Re: If x, y and z are integers greater than 1, what is the value  [#permalink]

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_________________ Re: If x, y and z are integers greater than 1, what is the value   [#permalink] 17 Jul 2019, 21:58
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