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Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]
 10 Jun 2010, 12:52
Question Stats:
35% (01:46) correct
64% (00:43) wrong based on 4 sessions
Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0 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.
Last edited by Bunuel on 16 Feb 2012, 15:05, edited 1 time in total.
Edited the question and added the OA
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Re: Data sufficiency +- exponents question [#permalink]
10 Jun 2010, 13:22
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 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. Answer: C. Hope it helps.
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Re: Data sufficiency +- exponents question [#permalink]
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]
10 Jun 2010, 14:22
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Re: Data sufficiency +- exponents question [#permalink]
10 Jun 2010, 14:24
Got it, I forgot that y can be equal to 0.
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Re: Data sufficiency +- exponents question [#permalink]
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]
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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Is (x^7)(y^2)(z^3) > 0?
1. yz < 0
2. xz > 0
Answer is C.
However,
for reaching to the conclusion of YES/NO, we have to be certain that:
(1) x, y, z are not ZERO,
(2) x and y are not NEGATIVE
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.
Can some one please explain the answer?
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chiragatara wrote: Is (x^7)(y^2)(z^3) > 0?
1. yz < 0
2. xz > 0
Answer is C.
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.
Can some one please explain the answer? 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]
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: Data sufficiency +- exponents question [#permalink]
22 Aug 2011, 12:52
Thanx a lot for the answer. It was most helpful! 
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Re: Data sufficiency +- exponents question [#permalink]
22 Aug 2011, 16:35
You should watch for 0 in these kind of tricky questions. The answer is C.
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Re: Data sufficiency +- exponents question [#permalink]
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. thus, Answer is (C) Regards,
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Re: Data sufficiency +- exponents question [#permalink]
06 Sep 2012, 23:30
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.
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Re: Data sufficiency +- exponents question [#permalink]
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#p736291is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html#p736324And 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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
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Re: Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0 [#permalink]
17 Sep 2012, 06:11
Excellent Take-away there...
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Re: Is (x^7)(y^2)(z^3) > 0 ? (1) yz < 0 (2) xz > 0
[#permalink]
17 Sep 2012, 06:11
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