GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 18:27

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If xy > 0 and yz < 0, then which of the following must be negative?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58320
If xy > 0 and yz < 0, then which of the following must be negative?  [#permalink]

### Show Tags

23 Jan 2019, 02:55
00:00

Difficulty:

45% (medium)

Question Stats:

53% (01:31) correct 47% (01:33) wrong based on 43 sessions

### HideShow timer Statistics

If $$xy > 0$$ and $$yz < 0$$, then which of the following must be negative?

A $$xyz$$

B $$xy^2z$$

C $$x^2y^2z$$

D $$x^2y^2z^2$$

E $$\frac{xy}{z}$$

_________________
Director
Joined: 09 Mar 2018
Posts: 997
Location: India
Re: If xy > 0 and yz < 0, then which of the following must be negative?  [#permalink]

### Show Tags

23 Jan 2019, 04:59
Bunuel wrote:
If $$xy > 0$$ and $$yz < 0$$, then which of the following must be negative?

A $$xyz$$

B $$xy^2z$$

C $$x^2y^2z$$

D $$x^2y^2z^2$$

E $$\frac{xy}{z}$$

IMO B

If $$xy > 0$$ and $$yz < 0$$

there can be 2 cases

x can be +ive, y can be +ive & y can be +ive, z can be -ive

x can be -ive, y can be -ive & y can be -ive, z can be +ive

Now just go through the options one by one

A $$xyz$$, -ive or +ive, depending on the mentioned cases

B $$xy^2z$$, always -ive
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
VP
Joined: 31 Oct 2013
Posts: 1473
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If xy > 0 and yz < 0, then which of the following must be negative?  [#permalink]

### Show Tags

Updated on: 21 Feb 2019, 16:02
Bunuel wrote:
If $$xy > 0$$ and $$yz < 0$$, then which of the following must be negative?

A $$xyz$$

B $$xy^2z$$

C $$x^2y^2z$$

D $$x^2y^2z^2$$

E $$\frac{xy}{z}$$

xy>0 and yz<0.

multiply these 2 .

$$xy^2z<0.$$

xy*yz <0

xy>0

yz<0

one is positive and another one is negative. ultimate result must be negative.

Originally posted by KSBGC on 23 Jan 2019, 06:07.
Last edited by KSBGC on 21 Feb 2019, 16:02, edited 1 time in total.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4987
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If xy > 0 and yz < 0, then which of the following must be negative?  [#permalink]

### Show Tags

23 Jan 2019, 06:29
Bunuel wrote:
If $$xy > 0$$ and $$yz < 0$$, then which of the following must be negative?

A $$xyz$$

B $$xy^2z$$

C $$x^2y^2z$$

D $$x^2y^2z^2$$

E $$\frac{xy}{z}$$

test the cases
xy >0
when both x & y are either + or -
so in that case yz<0 when either of values are of opposite sign

we can say that
option B stands out

IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)
Re: If xy > 0 and yz < 0, then which of the following must be negative?  [#permalink]

### Show Tags

27 Jan 2019, 19:59
Bunuel wrote:
If $$xy > 0$$ and $$yz < 0$$, then which of the following must be negative?

A $$xyz$$

B $$xy^2z$$

C $$x^2y^2z$$

D $$x^2y^2z^2$$

E $$\frac{xy}{z}$$

Looking at the first inequality we see that either x and y are both positive or they are both negative.

Combine that with the second inequality. If y is positive, z is negative, and when y is negative, z is positive.

Thus, our scenarios are:

x = pos, y = pos, z = neg

Or

x = neg, y = neg, z = pos

We see that x and z always have opposite signs, and thus, (x)(y^2)(z) is always negative.

Alternate solution:

We can use the following fact: If a > 0 and b < 0, then ab < 0. Therefore, we can multiply the two inequalities to obtain:

x(y^2)z < 0

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If xy > 0 and yz < 0, then which of the following must be negative?   [#permalink] 27 Jan 2019, 19:59
Display posts from previous: Sort by