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# Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0

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Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]

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10 Jun 2010, 12:52
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Is (x^7)(y^2)(z^3) > 0 ?

(1) yz < 0

(2) xz > 0

[Reveal] Spoiler:
S1 is insufficient because we need the sign of x.

S2 is SUFFICIENT, because x^7*z^3 will always be positive, and y^2 will be positive, so the whole product (x^7)(y^2)(z^3) will be positive. Answer: B.

(m25#34)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 Oct 2013, 11:56, edited 2 times in total.
Edited the question and added the OA

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Re: Data sufficiency +- exponents question [#permalink]

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10 Jun 2010, 13:22
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TheGmatTutor wrote:
My apologies if this has been posted before. Just want to confirm my reasoning (in the spoiler)

Is (x^7)(y^2)(z^3) > 0 ?

(1) yz < 0

(2) xz > 0

[Reveal] Spoiler:
S1 is insufficient because we need the sign of x.

S2 is SUFFICIENT, because x^7*z^3 will always be positive, and y^2 will be positive, so the whole product (x^7)(y^2)(z^3) will be positive. Answer: B.

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative AND $$y$$ must not be zero.

(1) $$yz<0$$ --> $$y\neq{0}$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz>0$$ --> $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Hope it helps.
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Re: Data sufficiency +- exponents question [#permalink]

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10 Jun 2010, 13:59
Bunuel, I agree about S1. But on S2, that quantity y^2 will always be positive, correct? So the whole statement

(x^7)(y^2)(z^3)

must be greater than 0, because the product is either
- + -

or

+++

So I thought S2 was sufficient.
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Re: Data sufficiency +- exponents question [#permalink]

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10 Jun 2010, 14:22
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TheGmatTutor wrote:
Bunuel, I agree about S1. But on S2, that quantity y^2 will always be positive, correct?

No, not correct. $$y^2$$ is not always positive, it's never negative: $$y^2\geq{0}$$.

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (note that both positive or both negative excludes the possibility of either of them to be zero) AND $$y$$ must not be zero. Because if $$y=0$$, then $$x^7*y^2*z^3=0$$.
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Re: Data sufficiency +- exponents question [#permalink]

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10 Jun 2010, 14:30
I think this question would be more interesting if they specified that x,y, and z are non-zero integers.
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Re: Data sufficiency +- exponents question [#permalink]

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13 Jun 2010, 12:12
TheGmatTutor wrote:
I think this question would be more interesting if they specified that x,y, and z are non-zero integers.

Haha it wouldn't be more interesting; it would be easier.

They got me too

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24 Nov 2010, 10:35
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Expert's post
chiragatara wrote:
Is (x^7)(y^2)(z^3) > 0?

1. yz < 0
2. xz > 0

However,
for reaching to the conclusion of YES/NO, we have to be certain that:
(1) x, y, z are not ZERO,
(2) [highlight]x and y are not NEGATIVE[/highlight]

Combined from (1) and (2) we can say that x, y, z are not ZERO. However, I think they are not helpful in deciding the certainty that x and y are not NEGATIVE.

First of all, a trick in the question is 'x, y, z are not ZERO' so good that you figured it.
Next, we don't need to know that x and z are not negative. We need to know [highlight]whether they have the same sign or opposite signs[/highlight] because question asks you whether (x^7)(z^3) is positive. (Ignoring y for now)
For the product to be positive, either both should be positive or both negative. Then, answer will be 'YES'
For the product to be negative only one of them should be negative. Then answer will be 'NO'
In either case, if we get a definite YES/NO, the statements will be sufficient.
If xz> 0, then either x and z both are positive or both are negative. They have the same sign. So (x^7)(z^3) is positive.
y, we know is not 0, so YES, (x^7)(y^2)(z^3) is greater than 0. Sufficient.
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Re: Data sufficiency +- exponents question [#permalink]

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11 Jan 2011, 06:47
Bunuel wrote:
TheGmatTutor wrote:
Bunuel, I agree about S1. But on S2, that quantity y^2 will always be positive, correct?

No, not correct. $$y^2$$ is not always positive, it's never negative: $$y^2\geq{0}$$.

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (note that both positive or both negative excludes the possibility of either of them to be zero) AND $$y$$ must not be zero. Because if $$y=0$$, then $$x^7*y^2*z^3=0$$.

Thanks a ton Bunuel , this example is the perfect for learning that while considering signs we should consider +ve , -ve and zero as well . Superb collection .

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Re: GmatClub Math25 qn 34 - is it positive? [#permalink]

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16 Feb 2012, 15:01
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fxsunny wrote:
From the Gmatclub Math 25 practice test:
http://gmatclub.com/tests/m25#q34

Is x^7*y^2*z^3> 0?

(1) yz < 0
(2) xz > 0

Response:
x^7*y^2*z^3 is same as:
(xz)*(x^6)*(y^2)*(z^2)
xz is positive based on assumption #2.
x^6 is (x^2)^3, since x^2 is positive for all real numbers, x^6 is also positive.
z^2 is positive for all real numbers.
y^2 is positive for all real numbers.

So product of 4 positive real numbers is also positive. SUFFICIENT.

Hence, B - Statement 2 Alone is Sufficient.

Per the gmatclub math25 test, the response is C - both statements together are sufficient. What incorrect assumptions am I making?

Thanks!

The red parts are not correct. Square of a number is nonnegative and not positive as you've written. So for (2) if y=0 then x^7*y^2*z^3=0.

Complete solution:
Is x^7*y^2*z^3 > 0 ?

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz<0$$ --> $$y\neq{0}$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz>0$$ --> $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Similar question to practice: m21-q30-96613.html?hilit=conditions#p744188

Hope it helps.
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Re: Is x^7*y^2*z^3 > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]

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23 Mar 2012, 05:59
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x^7*y^2*z^3>0
y is positive, we need to know regarding x and z
insufficient

2) xz>0

either of them is negative hence

the answer to our question is no

sufficient

hence B
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Re: Is x^7*y^2*z^3 > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]

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23 Mar 2012, 06:03
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x^7*y^2*z^3>0
y is positive, we need to know regarding x and z
insufficient

2) xz>0

either of them is negative hence

the answer to our question is no

sufficient

hence B

OA for this question is C, not B.

(2) $$xz>0$$ means that$$x$$ and $$z$$ are either both positive or both negative. So, $$x^7*z^3 > 0$$ but y can still be zero and in this case $$x^7*y^2*z^3=0$$, hence this statement is not sufficient.

Refer to the complete solution above.

Hope it helps.
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Re: Data sufficiency +- exponents question [#permalink]

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13 Jun 2012, 12:24
Hi,

Simplifying the expression,
$$x^7y^2z^3$$,
it can be written as, $$(xz)^3x^4y^2$$ or $$(yz)^2x^6(xz)$$

Clearly, in both the expressions $$x^4y^2$$ as well as $$(yz)^2x^6$$ are positive.
Thus the sign of expression depends on sign of xz,
but since value of y can be 0,
Using (1), we can say y is not equal to 0.

Regards,

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Re: Data sufficiency +- exponents question [#permalink]

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07 Sep 2012, 02:02
sreenunna wrote:
Statement B Alone is sufficient.

irrespective of sign, any number power to even number is positive.
hence (x^7) = (x^6)x ---> so remove (x^6) and we are left with x.

since (y^2) is always positive, leave it

(z^3), apply above rule.. we are left with z.

hence the given question can be re-write as Is xz > 0?

Statement is clearly stating same , hence Statement B Alone is sufficient.

Please note that correct answer is C, not B. You can check OA under the spoiler in the first post.

Next, check these posts:
is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html#p736291
is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html#p736324

And finally, square of a number is not always positive it's non-negative: $$y^2\geq{0}$$. So, for (2) if y=0 then x^7*y^2*z^3=0 not >0.

Hope it's clear.
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Re: GmatClub Math25 qn 34 - is it positive? [#permalink]

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22 Aug 2013, 17:16
Bunuel wrote:
fxsunny wrote:
From the Gmatclub Math 25 practice test:
http://gmatclub.com/tests/m25#q34

Is x^7*y^2*z^3> 0?

(1) yz < 0
(2) xz > 0

Response:
x^7*y^2*z^3 is same as:
(xz)*(x^6)*(y^2)*(z^2)
xz is positive based on assumption #2.
x^6 is (x^2)^3, since x^2 is positive for all real numbers, x^6 is also positive.
z^2 is positive for all real numbers.
y^2 is positive for all real numbers.

So product of 4 positive real numbers is also positive. SUFFICIENT.

Hence, B - Statement 2 Alone is Sufficient.

Per the gmatclub math25 test, the response is C - both statements together are sufficient. What incorrect assumptions am I making?

Thanks!

The red parts are not correct. Square of a number is nonnegative and not positive as you've written. So for (2) if y=0 then x^7*y^2*z^3=0.

Complete solution:
Is x^7*y^2*z^3 > 0 ?

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz<0$$ --> $$y\neq{0}$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz>0$$ --> $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Similar question to practice: m21-q30-96613.html?hilit=conditions#p744188

Hope it helps.

So in short you want to say that by using both we can infer X,Y,Z are not equal to 0?
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Re: GmatClub Math25 qn 34 - is it positive? [#permalink]

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22 Aug 2013, 17:24
honchos wrote:
Bunuel wrote:
fxsunny wrote:
From the Gmatclub Math 25 practice test:
http://gmatclub.com/tests/m25#q34

Is x^7*y^2*z^3> 0?

(1) yz < 0
(2) xz > 0

Response:
x^7*y^2*z^3 is same as:
(xz)*(x^6)*(y^2)*(z^2)
xz is positive based on assumption #2.
x^6 is (x^2)^3, since x^2 is positive for all real numbers, x^6 is also positive.
z^2 is positive for all real numbers.
y^2 is positive for all real numbers.

So product of 4 positive real numbers is also positive. SUFFICIENT.

Hence, B - Statement 2 Alone is Sufficient.

Per the gmatclub math25 test, the response is C - both statements together are sufficient. What incorrect assumptions am I making?

Thanks!

The red parts are not correct. Square of a number is nonnegative and not positive as you've written. So for (2) if y=0 then x^7*y^2*z^3=0.

Complete solution:
Is x^7*y^2*z^3 > 0 ?

Inequality $$x^7*y^2*z^3>0$$ to be true $$x$$ and $$z$$ must be either both positive or both negative (in order $$x^7*z^3$$ to be positive) AND $$y$$ must not be zero (in order $$x^7*y^2*z^3$$ not to equal to zero).

(1) $$yz<0$$ --> $$y\neq{0}$$. Don't know about $$x$$ and $$z$$. Not sufficient.

(2) $$xz>0$$ --> $$x$$ and $$z$$ are either both positive or both negative. Don't know about $$y$$. Not sufficient.

(1)+(2) Sufficient.

Similar question to practice: m21-q30-96613.html?hilit=conditions#p744188

Hope it helps.

So in short you want to say that by using both we can infer X,Y,Z are not equal to 0?

yz < 0 implies that neither y nor z is 0.
xz > 0 implies that neither x nor z is 0.
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Re: Is x^7*y^2*z^3 > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]

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24 Aug 2013, 05:44
You do have to pay attention in DS . The key thing here is that y can be zero, so b is not the answer; it is c.
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12 Sep 2013, 03:15
shameekv wrote:
Is (x^7)(y^2)(z^3)>0 ?
(1) yz<0

(2) xz>0

Hi, When I solved this i get an answer as B. i.e. only 2nd statement is sufficient. But GMAT Club test says its C. Can anyone please help.

According to me, if xz > 0 then the inequality can be written as [(xz)^3 (x^4) (y^2)] Now since x^4 and y^2 are going to be positive always then the statement in itself gives us the answer.

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12 Sep 2013, 03:16
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shameekv wrote:
shameekv wrote:
Is (x^7)(y^2)(z^3)>0 ?
(1) yz<0

(2) xz>0

Hi, When I solved this i get an answer as B. i.e. only 2nd statement is sufficient. But GMAT Club test says its C. Can anyone please help.

According to me, if xz > 0 then the inequality can be written as [(xz)^3 (x^4) (y^2)] Now since x^4 and y^2 are going to be positive always then the statement in itself gives us the answer.

Check here: is-x-7-y-2-z-3-0-1-yz-0-2-xz-127692.html#p1063962

Hope it helps.
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12 Sep 2013, 03:18
shameekv wrote:
shameekv wrote:
Is (x^7)(y^2)(z^3)>0 ?
(1) yz<0

(2) xz>0

Hi, When I solved this i get an answer as B. i.e. only 2nd statement is sufficient. But GMAT Club test says its C. Can anyone please help.

According to me, if xz > 0 then the inequality can be written as [(xz)^3 (x^4) (y^2)] Now since x^4 and y^2 are going to be positive always then the statement in itself gives us the answer.

Got it. Forgot to consider y = 0. As always. Thanks anyways.

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Re: Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]

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29 Dec 2013, 06:48
I forgot to consider 0 while doing this question in GMAT Club Test... so marked B.
Now, I got why it is C.
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Re: Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0   [#permalink] 29 Dec 2013, 06:48

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