Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 05 Jun 2009
Posts: 73

Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
Updated on: 21 Sep 2019, 17:08
Question Stats:
67% (01:44) correct 33% (01:58) wrong based on 575 sessions
HideShow timer Statistics
Is \(xy < 6\) ? (1) \(x < 3\) and \(y < 2\) (2) \(\frac{1}{2} < x < \frac{2}{3}\) and \(y^2 < 64\) DS76602.01
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sacmanitin on 24 Oct 2009, 05:36.
Last edited by Bunuel on 21 Sep 2019, 17:08, edited 2 times in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 58449

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
09 Apr 2012, 12:31
9. Inequalities For more check Ultimate GMAT Quantitative Megathread
_________________




Director
Joined: 01 Apr 2008
Posts: 648
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]
Show Tags
24 Oct 2009, 05:46
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.




Math Expert
Joined: 02 Sep 2009
Posts: 58449

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
06 Nov 2010, 21:50
Geronimo wrote: I don't really agree with OG's answer. What about you ? Is xy<6 ? (1) x<3 and y<2 (2) 1/2 < x < 2/3 and y^2<64 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 YES. Not sufficient. (2) \(\frac{1}{2}<x<\frac{2}{3}\) and \(y^2<64\), which is equivalent to \(8<y<8\) (not y<8, y>8. as written above) > 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. Answer: B.
_________________



Manager
Joined: 14 Feb 2011
Posts: 144

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
28 Feb 2011, 02:56
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: 58449

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
28 Feb 2011, 03:05
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: 115
Location: India
Concentration: Technology, Entrepreneurship

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
02 Mar 2011, 00:13
How does y^2 <64 become y<8 and y>8?



Retired Moderator
Joined: 20 Dec 2010
Posts: 1578

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
02 Mar 2011, 00:27
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: 59

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
09 Apr 2012, 12:41
Bunuel, your explanations are so easy to understand. Thanks!
_________________
http://mymbadreamz.blogspot.com



Intern
Joined: 24 Apr 2013
Posts: 44

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
28 May 2013, 15:14
Bunuel wrote: mymbadreamz 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. Answer: B. 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: 58449

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
28 May 2013, 15:23
madzstar wrote: Bunuel wrote: mymbadreamz 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. Answer: B. 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: 80
Location: Australia
GMAT Date: 04012014

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
Updated on: 01 Feb 2014, 14:04
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. Answer B;
_________________
Kudos (+1) if you find this post helpful.
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
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
Show Tags
19 Oct 2016, 06:07
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 Alone1/2 < 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. Answer: B
_________________
5star 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.



VP
Joined: 14 Feb 2017
Posts: 1196
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
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]
Show Tags
30 Sep 2019, 16:06
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
_________________
Goal: Q49, V41
+1 Kudos if I have helped you




Re: Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2/3 and y^2 < 64
[#permalink]
30 Sep 2019, 16:06






