Last visit was: 14 Aug 2024, 06:24 It is currently 14 Aug 2024, 06:24
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 05 Jun 2009
Posts: 51
Own Kudos [?]: 2247 [110]
Given Kudos: 4
Math Expert
Joined: 02 Sep 2009
Posts: 94940
Own Kudos [?]: 649515 [44]
Given Kudos: 86938
Math Expert
Joined: 02 Sep 2009
Posts: 94940
Own Kudos [?]: 649515 [16]
Given Kudos: 86938
General Discussion
Senior Manager
Joined: 01 Apr 2008
Posts: 388
Own Kudos [?]: 4169 [11]
Given Kudos: 18
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
7
Kudos
4
Bookmarks
IMO B.

stmt1: if both x and y are negative such that the product of their absolute values is > 6 then xy>6. eg. x=-8, y=-3

stmt2: x is +ve, -8<y<8.
Let us take max value of x =2/3 and max value of y=8, the product is <6.
Now, let us take max value of x=2/3 and a negative value of y=-8, the product is -ve and hence < 6.
One more try, take x=2/3 and y=5, the product is <6.
Manager
Joined: 14 Feb 2011
Posts: 103
Own Kudos [?]: 405 [1]
Given Kudos: 3
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Bookmarks
Clearly 1) is sufficient. It says x is less than 3 and y is less than 2 so product can not be greater than 6.

Lets examine 2) x lies between 1/2 and 2/3 and y^2 is less than 64, or y lies within (-8,8). On the extreme, xy can be just below 2/3*8 or ~5.33 so it will always be less than 6. Sufficient.

Answer should be D.
Math Expert
Joined: 02 Sep 2009
Posts: 94940
Own Kudos [?]: 649515 [1]
Given Kudos: 86938
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Kudos
beyondgmatscore wrote:
Clearly 1) is sufficient. It says x is less than 3 and y is less than 2 so product can not be greater than 6.

Lets examine 2) x lies between 1/2 and 2/3 and y^2 is less than 64, or y lies within (-8,8). On the extreme, xy can be just below 2/3*8 or ~5.33 so it will always be less than 6. Sufficient.

Answer should be D.

Statement (1) is not sufficient: if x and y are small enough negative numbers, for example -10 and -10 then xy=100>6. So answer is B, not D.
Manager
Joined: 14 Dec 2010
Posts: 92
Own Kudos [?]: 219 [0]
Given Kudos: 5
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 680 Q44 V39
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
How does y^2 <64 become y<8 and y>-8?
Retired Moderator
Joined: 20 Dec 2010
Posts: 1107
Own Kudos [?]: 4768 [1]
Given Kudos: 376
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Kudos
naveenhv wrote:
How does y^2 <64 become y<8 and y>-8?

1/2 < x < 2/3 and y^2<64

It is a general rule;

$$y^2 < 64$$
$$|y| < 8$$ (Watch the less than (<) symbol)
Means;
-8<y<8

$$y^2 > 64$$
$$|y| > 8$$(Watch the greater than (>) symbol)
Means;
y>8 or y<-8

so;
-8<y<8
1/2<x<2/3

Extreme values of xy
-8*1/2 = -4
8*1/2 = 4
-8*2/3 = -16/3 > -6
8*2/3 = 16/3 < 6

Thus;
xy>-6
xy<6

We found that; yes indeed xy<6.
Sufficient.
Manager
Joined: 15 Apr 2011
Posts: 56
Own Kudos [?]: 97 [0]
Given Kudos: 45
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Bunuel, your explanations are so easy to understand. Thanks!
Intern
Joined: 24 Apr 2013
Posts: 35
Own Kudos [?]: 23 [0]
Given Kudos: 76
Schools: Duke '16
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Bunuel wrote:
I didn't understand this one. could someone please explain why C is not the answer? thanks.

Is $$xy<6$$?

(1) $$x<3$$ and $$y<2$$ --> now, if both $$x$$ and $$y$$ are equal to zero then $$xy=0<6$$ and the answer will be YES but if both $$x$$ and $$y$$ are small enough negative numbers, for example -10 and -10 then $$xy=100>6$$ and the answer will be NO. Not sufficient.

(2) $$\frac{1}{2}<x<\frac{2}{3}$$ and $$y^2<64$$, which is equivalent to $$-8<y<8$$ --> even if we take the boundary values of $$x$$ and $$y$$ to maixmize their product we'll get: $$xy=\frac{2}{3}*8\approx{5.3}<6$$, so the answer to the question "is $$xy<6$$?" will always be YES. Sufficient.

i dont understand i put A....i could answer the question with that information. N why are we letting x times y = to 0 why cant we let it be equal to 1 or 2?

if a number times a number is less than 6......cant we just say use 1?
Math Expert
Joined: 02 Sep 2009
Posts: 94940
Own Kudos [?]: 649515 [1]
Given Kudos: 86938
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Kudos
Bunuel wrote:
I didn't understand this one. could someone please explain why C is not the answer? thanks.

Is $$xy<6$$?

(1) $$x<3$$ and $$y<2$$ --> now, if both $$x$$ and $$y$$ are equal to zero then $$xy=0<6$$ and the answer will be YES but if both $$x$$ and $$y$$ are small enough negative numbers, for example -10 and -10 then $$xy=100>6$$ and the answer will be NO. Not sufficient.

(2) $$\frac{1}{2}<x<\frac{2}{3}$$ and $$y^2<64$$, which is equivalent to $$-8<y<8$$ --> even if we take the boundary values of $$x$$ and $$y$$ to maixmize their product we'll get: $$xy=\frac{2}{3}*8\approx{5.3}<6$$, so the answer to the question "is $$xy<6$$?" will always be YES. Sufficient.

i dont understand i put A....i could answer the question with that information. N why are we letting x times y = to 0 why cant we let it be equal to 1 or 2?

if a number times a number is less than 6......cant we just say use 1?

On DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

Now, for x=y=0 we got an YES answer and for x=y=-10 we got a NO answer, thus the statement is NOT sufficient.

Of course we could use some other numbers to get an YES and a NO answers to prove that the statement is not sufficient: x=y=0 and x=y=-10 are just examples of many possible sets.

Hope it's clear.
Manager
Joined: 23 Jun 2008
Posts: 69
Own Kudos [?]: 67 [4]
Given Kudos: 24
Location: Australia
Schools: AGSM '21
GMAT Date: 04-01-2014
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
4
Kudos

Statement (1)

We are given x < 3 and y < 2 ; no lower bound specified for either of the variables.
x and y could be x=-3 and y=-2 we get xy=6 or they could be very small negative numbers then xy would be much greater than 6.
On the other hand x=1 y=1 which results in xy=1 which is smaller than 6 so Statement (1) is not sufficient

Statement (2)

y^2 < 64 can be rewritten as -8< y <8 ,
Since x is positive, we can test the extremes without worrying about changing the direction of the inequality sign
-8*(2/3) < xy < 8*(2/3)

-5.3333 < xy < 5.333
So we can answer the question "Is xy<6" with the Statement (2) ALONE.

Originally posted by code19 on 31 Jan 2014, 00:46.
Last edited by code19 on 01 Feb 2014, 14:04, edited 1 time in total.
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6693 [3]
Given Kudos: 1646
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
2
Kudos
1
Bookmarks
Geronimo wrote:
Is xy < 6

(1) x < 3 and y < 2

(2) 1/2 < x < 2/3 and y^2 < 64

We need to determine whether the product of x and y is less than 6.

Statement One Alone

x < 3 and y < 2

Using the information in statement one we do not have enough information to determine whether the product of x and y is less than 6. For example, if x = -4 and y = -2, the product of x and y is 8, which is greater than 6. However, if x = 0 and y = 0, the product of x and y is 0, which is less than 6. We can eliminate answer choices A and D.

Statement Two Alone

1/2 < x < 2/3 and y^2 < 64

Using the information in statement two, we see that x is less than 2/3 and that y is less than 8. Thus, the maximum product of x and y is less than (2/3)(8) = 16/3, which is less 5.33 and thus less than 6. Since the maximum product of x and y is less than 6, statement two is sufficient to answer the question. Note that we did not even consider the case when -8 < y < 0 because in that case, xy will be negative and thus will be less than 6.

VP
Joined: 14 Feb 2017
Posts: 1085
Own Kudos [?]: 2189 [0]
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Test values

Statement 1
x<3 and y<2
x=-6 y=-1 xy <6? No
x=2 y=1 xy <6? yes

Statement 2
Convert to decimal for ease
0.5 <x < 0.66 and -8<y<8

We don't need to bother with negative values for y since xy with a negative y will always be less than 6 since x is known to be >0

Maximise the value of y as a positive
y=8 (not allowed but maximise to see)
x=0.6
xy=4.8
Even when maximised xy<6

Sufficient
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31010 [0]
Given Kudos: 799
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Top Contributor
sacmanitin wrote:
Is $$xy < 6$$ ?

(1) $$x < 3$$ and $$y < 2$$

(2) $$\frac{1}{2} < x < \frac{2}{3}$$ and $$y^2 < 64$$

Target question: Is xy < 6?

Statement 1: x < 3 and y < 2
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 0. In this case, xy = (0)(0) = 0. So, the answer to the target question is YES, xy IS less than 6
Case b: x = -5 and y = -5. In this case, xy = (-5)(-5) = 25. So, the answer to the target question is NO, xy is NOT less than 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1/2 < x < 2/3 and y² < 64
Let's see if we can find the greatest possible value of xy.
Since we can see that x is POSITIVE, the maximum value of xy will be achieved when y is also POSITIVE
From the inequality y² < 64, we can conclude that y < 8
He also know that x < 2/3
(8)(2/3) = 16/3 = 5 1/3 (which is less than 6)

Since x < 2/3 and y < 8, we can be certain that xy is less than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
Manager
Joined: 16 Feb 2017
Posts: 90
Own Kudos [?]: 46 [0]
Given Kudos: 56
Location: India
Concentration: Finance, Strategy
GPA: 3.69
Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
What is the concept of multiplying two inequalities? WHy can we not mltiply the two here? And if we do, how to go about it? Bunuel JeffTargetTestPrep ScottTargetTestPrep nick1816
Director
Joined: 20 Apr 2022
Posts: 602
Own Kudos [?]: 348 [0]
Given Kudos: 335
Location: India
GPA: 3.64
Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
What is the concept of multiplying two inequalities? WHy can we not mltiply the two here? And if we do, how to go about it? Bunuel JeffTargetTestPrep ScottTargetTestPrep nick1816 KarishmaB avigutman ThatDudeKnows
Tutor
Joined: 11 May 2022
Posts: 1081
Own Kudos [?]: 743 [1]
Given Kudos: 81
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Kudos
Elite097 wrote:
What is the concept of multiplying two inequalities? WHy can we not mltiply the two here? And if we do, how to go about it? Bunuel JeffTargetTestPrep ScottTargetTestPrep nick1816 KarishmaB avigutman ThatDudeKnows

One of the most common things that the GMAT tests on inequalities is whether you know/remember to reverse the sign when you multiply by a negative number. If everything in both inequalities is greater than 0, you're safe. But if anything is less than 0 (or could be less than 0), there's no clean way to handle reversing the sign(s) (or even knowing whether to reverse the signs.

a>b>0 and p>r>0 --> ap*br>0 Yes

0>a>b and p>0>r (or any other set up whereby we have a negative or possible negative) --> Can't do it
Tutor
Joined: 17 Jul 2019
Posts: 1303
Own Kudos [?]: 1759 [1]
Given Kudos: 66
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
1
Kudos
Elite097 wrote:
What is the concept of multiplying two inequalities? WHy can we not mltiply the two here? And if we do, how to go about

I sense that you're looking for a rule here, Elite097, but, well, it's complicated.
Unlike additive reasoning, with which we can safely infer that the sum of two bigger terms will be greater than the sum of two smaller terms (a.k.a. adding inequalities), multiplicative reasoning behaves differently depending on the positioning of the terms relative to -1, 0, and 1.
The inequalities in this problem allow x and y to be located on either side of those key tick marks on the number line, so we should probably avoid multiplying them.
Non-Human User
Joined: 09 Sep 2013
Posts: 34421
Own Kudos [?]: 865 [0]
Given Kudos: 0
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64 [#permalink]
Moderator:
Math Expert
94940 posts