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

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Manager
Joined: 13 Sep 2014
Posts: 87
WE: Engineering (Consulting)
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

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11 Jan 2015, 10:29
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
Intern
Joined: 07 Mar 2014
Posts: 16
Location: India
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

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26 Oct 2015, 01:40
1
$$X , Y , Z integers > 1$$

$$x + y + z = ?$$

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.

Intern
Joined: 07 Dec 2016
Posts: 40
Re: If integers x, y and z are greater than 1 what is the value  [#permalink]

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06 May 2017, 13:25
A
1.) Sufficient
xyz = 70 = 7*5*2
so x+y+z = 7+5+2 = 14

2) Insufficient
Can be an multiple of the fraction and thus many different values for x+y+z
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Intern
Joined: 20 Aug 2018
Posts: 27
If integers x, y and z are greater than 1 what is the value  [#permalink]

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24 Nov 2018, 15:11
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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If integers x, y and z are greater than 1 what is the value &nbs [#permalink] 24 Nov 2018, 15:11

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