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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X

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Retired Moderator P
Joined: 22 Aug 2013
Posts: 1435
Location: India
X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X  [#permalink]

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1 00:00

Difficulty:   75% (hard)

Question Stats: 36% (01:58) correct 64% (02:11) wrong based on 23 sessions

### HideShow timer Statistics X, Y, Z are integers. Is 3*X > Z?

(1) X + 2*Y > 3*Z

(2) 2*Z > 2*Y - X
examPAL Representative P
Joined: 07 Dec 2017
Posts: 1073
Re: X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X  [#permalink]

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amanvermagmat wrote:
X, Y, Z are integers. Is 3*X > Z?

(1) X + 2*Y > 3*Z

(2) 2*Z > 2*Y - X

As all we're given is equations, we'll work with equation-related tools such as simplification.
This is a Precise approach.

(1) Multiplying our inequality by 3 gives 3x+6y>9z --> 3x > 9z - 6y.
Without knowing if y is positive or negative we definitely cannot know if 3x > 9z, let alone 3x>z.
Insufficient.

(2) We'll once again try to create "3x is larger than" in our expression: Multiplying by 3 gives
6z>6y-3x --> 3x>6y-6z. Similarly to the before, we need some information about y to solve.
Insufficient.

Combined.
We'll notice that one equation has '6y' and another has '-6y'. Adding them together cancels out the y and gives
3x+3x > (3z-6y)+(6y-9z) --> 6x > -6z --> 3x > -3z.
So, to answer the question we need to know if -3z > z. But is it? If z is positive this inequality is always false and if it is negative this inequality is always true.
Insufficient.

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Joined: 26 Mar 2013
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Re: X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X  [#permalink]

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amanvermagmat wrote:
X, Y, Z are integers. Is 3*X > Z?

(1) X + 2*Y > 3*Z

(2) 2*Z > 2*Y - X

(1) X + 2*Y > 3*Z

Let x = 1, Y = 2 & Z = 1.......3 > 1........Answer is Yes (You can notice that you can manipulate Y easily to prove statement 1)

Let x = 1, Y = 100 & Z = 4........... 3 > 4....Answer is NO

Insufficient

(2) 2*Z > 2*Y - X

Let x = 1, Y = 1 & Z = 1.......3 > 1........Answer is Yes

Let x = 1, Y = 1 & Z = 6.......3 > 6........Answer is No

Insufficient

Combining 1 & 2

X + 2*Y > 3*Z

2*Y - X < 2*Z
-----------------------We can subtract

2X > Z

Let x = -1 & z =-3..........-3 > -3...........Answer is NO

Let x = 2 & z = 1.............6 > 1.............Answer is Yes

Insuffecient Re: X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X   [#permalink] 26 Mar 2018, 02:29
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# X, Y, Z are integers. Is 3*X > Z? (1) X + 2*Y > 3*Z (2) 2*Z > 2*Y - X  