Inqualities

Expert replies

Previous Topic Next Topic

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Mon Mar 21, 2011 7:21 am

If 3x + 2y > 20, is 4x + y > 20 ?

(1) x > y + 1
(2) y < 5

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon Mar 21, 2011 7:21 am

force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Mon Mar 21, 2011 7:47 am

IMO A

question says 3x+2y>20
stmnt 1 (sufficient)

x>y+1
( multiplying by 2 and adding to stem)

x>4.4 and y>3.2
which gives us 4x+y>20 ( for all values)

stmnt 2 (insufficient)

y<5 (can have various values)

Like this post

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Mon Mar 21, 2011 9:06 am

I got Y<5 is sufficient here...

using A

if x > Y+1 then x~= y+2
3(y+2)+2y>20 => 5y+6>20
y ~= 3 x=5

is 4x+y>20 yes

IMO D here

Like this post

srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Mon Mar 21, 2011 11:18 am

i tried to plot the above inequalities on a graph and feel its E (cannot be solved even by both statements)

any more explanations on this one???

Like this post

force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Mon Mar 21, 2011 11:35 am

Hi Anu i really feel Stmnt A will give you the answer.

BTW Kevin what is the OA????

Like this post

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Mon Mar 21, 2011 12:51 pm

hi guys
got A here, my reasoning
if 3x+2y>20 does 4x+y>20
(1) x-y>1, here summing both 3x+2y>20 and x-y>1. gives us 4x+y>21, thus if 4x+y>21, 4x+y must be greater that 20
suff
(2)y<5 insuff to prove this, again sum 3x+2y>20, and y<5, this lead us to 3x+y>15
x=5, y=1 then 3*5+1=16>15, and 4x+y=4*5+1=21>20 the answer is yes
x=1,y=15, then 3*1+15=18>15, but 4*1+15=19<20 the answer is no
insuff

Like this post

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Mar 21, 2011 7:41 pm

srcc25anu wrote:i tried to plot the above inequalities on a graph and feel its E (cannot be solved even by both statements)

any more explanations on this one???

If 3x + 2y > 20, is 4x + y > 20 ?

(1) x > y + 1
(2) y < 5

Solution:
Consider first (1) alone.
It says x > y + 1.
Or x - y > 1.------------(a)
The main question says that 3x + 2y > 20.------------(b)
Adding (a) and (b) we get that 4x + y > 21.
This means that 4x+2y > 20.
Or (1) alone is sufficient.
Next consider (2) alone.
It says that y < 5.
Or -5y > -25.----------(c)
Now, 3x + 2y > 20 implies that 12x + 8y > 80.---------(d)
Adding (c) and (d), we get that 12x + 3y > 55.
Or 4x + y > 18 1/3.
This is not sufficient to tell us whether 4x + y > 20 or not.
Or (2) alone is not sufficient.

The correct answer is (A)

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Mar 21, 2011 8:55 pm

Statement (1) x>y+1, x-y>1
3x + 2y > 20 Plus x-y>1 ---> 4x+y>21 Sufficient;

Statement (2) y<5 OR -y>-5 Plus 3x + 2y > 20 ---> 3x+y>15. Verifying x ---> -y>-5 Plus 3x+y>15 x>10/3
Not Sufficient

IOM A

kevincanspain wrote:If 3x + 2y > 20, is 4x + y > 20 ?

(1) x > y + 1
(2) y < 5

My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

Like this post

HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Mon Mar 21, 2011 10:11 pm

Let me use Y<5 one more time with Y= 4, Y= -2, (Y= 6 and Y = 20)

at y = 4 ; 3x+2y>20 will give x>4 => 4x+y > 20 satisfies
at y = -2; 3x+2y>20 will give x>8 => 4x+y > 20 satisfies
at y = 6; 3x+2y>20 will give x>3 => 4x+y >20 is not satisfied
at y =20; x is -ve so 4x is more negitive... so not satisfied

So Y< 5 is doing good.. what am I missing Night reader/Anurag

Like this post

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Mar 21, 2011 10:56 pm

nobody said that y can't be 4 and x can't be >4

conditions given y<5 and x>10/3 and in fact y could be -2,000,000 and/or x could be 2,000,000
the discomfort (trouble/problem/issue/question/doubt) with your ascertainment about y=4 and x>4 is fixing areas which are fixed already that is 5<y and x>10/3. We need 100% validation, BUT here it's missing; the ranges are not fixed the way we like OR you like. x could be less OR greater than (20-15) ... the missing quantity RHS

HSPA wrote:Let me use Y<5 one more time with Y= 4, Y= -2, (Y= 6 and Y = 20)

at y = 4 ; 3x+2y>20 will give x>4 => 4x+y > 20 satisfies
at y = -2; 3x+2y>20 will give x>8 => 4x+y > 20 satisfies
at y = 6; 3x+2y>20 will give x>3 => 4x+y >20 is not satisfied
at y =20; x is -ve so 4x is more negitive... so not satisfied

So Y< 5 is doing good.. what am I missing Night reader/Anurag

Like this post

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Mar 21, 2011 11:26 pm

HSPA wrote:Let me use Y<5 one more time with Y= 4, Y= -2, (Y= 6 and Y = 20)

at y = 4 ; 3x+2y>20 will give x>4 => 4x+y > 20 satisfies
at y = -2; 3x+2y>20 will give x>8 => 4x+y > 20 satisfies
at y = 6; 3x+2y>20 will give x>3 => 4x+y >20 is not satisfied
at y =20; x is -ve so 4x is more negitive... so not satisfied

So Y< 5 is doing good.. what am I missing Night reader/Anurag

Your calculations show that the further y grow from 5, the more certain you are that 4x+y is indeed greater than 20. At y=-2, 4x alone is already at 32. Do the opposite: try using a 4<y<5 (get y closer to 5)

at y = 4.5 ; 3x+2y>20 will give x>11/3 => 4x+y will not necessarily satisfy >20

Geva
Senior Instructor
Master GMAT
1-888-780-GMAT
https://www.mastergmat.com

Like this post

kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

by kevincanspain » Tue Mar 22, 2011 2:55 am

kevincanspain wrote:If 3x + 2y > 20, is 4x + y > 20 ?

(1) x > y + 1
(2) y < 5

4x + y > 20 if 4x + y >= 3x + 2y i.e x >= y

If x < y, 4x + y < 3x + 2y, and 4x + y may be less than, greater than or equal to 20

(1) IF x > y + 1, x > y SUFF
(2) If y < 5 , since x > (20 - 2y)/3, x > 10/3.

If y is slightly less than 5 and x slightly greater than 10/3, 4x + y will be close to 40/3 + 5 = 55/3 < 20

However, if y < 0, x> 0 and the answer would be yes

NOT SUFF

Arurag's comments on (2) are very nice!

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review