BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Data Sufficiency Questions

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 22
Joined: Sat Jan 01, 2011 2:58 am
Thanked: 1 times

Data Sufficiency Questions

by Anamaiy » Mon Mar 14, 2011 10:05 am
Guys it would be great if you can help me out with the solutions of these Data Sufficiency questions:

Are x and y both positive ?
(1). 2x-2y = 1
(2). x/y > 1

What fraction of this year graduation students at a certain college are males ?
(1). Of this year graduating students, 33% of the males and 20% of the females transferred from another college/
(2). Of this year's graduating students, 25% transferred from another college.

Is m+z > 0 ?
(1). m-3z > 0
(2). 4z-m > 0

Are at least 10% of the people in country X who are 65 years or older and employed ?
(1). In country X, 11.3% of the population is 65 years or older.
(2). In country X, of the population 65 years or older, 20% of the men and 10% of the woman are employed.

On the number line, distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line ?
(1). xyz < 0
(2). xy < 0
Top
Source: — Problem Solving |
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Mar 14, 2011 11:22 am
Are x,y>0
st(1) x=1/2+y Not Sufficient, since we don't know the signs of x and y, they could be both -ve OR +ve;
st(2) x/y>1, |x|>|y|; x and y can be both -ve OR +ve, hence Not Sufficient;
Combined st(1&2): x=1/2+y, since |x|>|y| and x,y can be both +ve OR -ve --> If x,y<0 then x lies LHS from y, i.e. x<y which is impossible for x=1/2+y, hence x,y>0 and x>y. Our answer is yes x,y>0 Sufficient

IOM C
Anamaiy wrote:Guys it would be great if you can help me out with the solutions of these Data Sufficiency questions:

Are x and y both positive ?
(1). 2x-2y = 1
(2). x/y > 1
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
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Mar 14, 2011 11:59 am
Find ratio, males/graduating students-? OR M/S-?
st(1) 0.33M+0.2F=TS(transferred from another college), no information about males in this college -Not Sufficient;
st(2) 0.25S=TS, no information about males -Not Sufficient;
Combined st(1&2): 0.25(M+F)=0.33M+0.2F and M+F=100, by solving for M we can find ratio M/S -Sufficient

IOM C
Anamaiy wrote: What fraction of this year graduation students at a certain college are males ?
(1). Of this year graduating students, 33% of the males and 20% of the females transferred from another college/
(2). Of this year's graduating students, 25% transferred from another college.
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
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Mar 14, 2011 12:20 pm
Is m>-z ?
st(1) m>3z, Not Sufficient as we have no information about signs of m and z (-ve OR +ve);
st(2) 4z>m, Not Sufficient, as two cases are possible m=<4z when (m+z>0) and m>4z when (m+z<0)
Combined st(1&2): [m-3z] + [4z-m]>0, z>0; If z is +ve, i.e. z>0 then m-3z>0 means that m is also +ve! Our answer is Yes (m+z>0) Sufficient

IOM C
Anamaiy wrote: Is m+z > 0 ?
(1). m-3z > 0
(2). 4z-m > 0
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
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Mon Mar 14, 2011 1:03 pm
Question(1) IMO -E
statement1= x-y=1/2 ( x and y can be both +ve or -ve, but cant have diff signs)

Statement 2= x/y>1 ( again same sign)
combining= we cant say if both are +ive or -ve.

Question (2) IMO- c
0.33m+0.20f=m+f/4 ----(1)
m+f=100-------(2)
hence m and f can be obtained and hence m/m+f

Question (3)IMO- c

stmnt1- m-3z>0
m/3>z (insufficient since m and z can be +ve or -ve)

stmnt2- 4z-m>0
z>m/4 (Insufficient since m and z can be +ve or -ve)

combining.
add ineqalities. z>0 ( +ve) as per stmnt (1) m>3z ( if z is +ve them m will be positive too) hence m+n will be +ve

Question (4) IMO- B
stmnt1- insufficient
stmnt2- sufficient
say men be M and women be W. hence the total figure is

( 20 % of M + 10 % of W )
------------------------------
( M + W )

this gives a weighted average whose value will always be greater than 10 and less than 20.

Question (5)IMO- E

stmnt1- XYZ < 0.
1 negative or
all 3 negatives.

all can be on the left (-ve x axis)

So A is insufficient.
stmnt 2
XY < 0.
only one -ve
any one can be on the -ve axis.but z can lie anywhere. eg- x 0 z y or z x 0 y. (insufficient)

combining-
from stmnt 2 only one can be -ve hence when we combine both statements one of x, y are -ve and rest two have to be +ve to maintain (xyz<0)
hence if x is -ve then x 0 z y
if y -ve then y 0 x z
hence E
Top
Master | Next Rank: 500 Posts
Posts: 423
Joined: Fri Jun 11, 2010 7:59 am
Location: Seattle, WA
Thanked: 86 times
Followed by:2 members

by srcc25anu » Mon Mar 14, 2011 2:06 pm
Q5. IMO it should be C
stat 2 says xy <0 i.e. x and y have opp signs no indication of Z (Not Sufficient)

stat 1 says xyz < 0 that is either one or all three are -ve. (not sufficient)

using both statements:
xy < 0, that is x and y have diff signs. and xyz = -ve that is z = positive

.__y________x___Z_____

and zero lies between y and x. therefore we can answer using both statements.
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Mon Mar 14, 2011 2:21 pm
yes anu you are correct that zero will lie between x and y. however as per the original poster- the question is does Z lie between x and y. you can see there are two scenarios possible here

if x is -ve then x 0 z y
if y -ve then y 0 x z

hope that helps
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Mar 14, 2011 2:40 pm
you marked E.

Combined st(1) x=1/2+y AND st(2) x/y>1

from st(1&2) if (1/2+y)/y>1 then (1/2y)>0 Hence 2y>0 AND y>0 //agree?
from st(1) x=1/2 +y Hence with positive y ---> x=1/2 + y {positive value of y} We can answer Not only x and y are positive, BUT even x>y // agree?

answer is C
force5 wrote:Question(1) IMO -E
statement1= x-y=1/2 ( x and y can be both +ve or -ve, but cant have diff signs)

Statement 2= x/y>1 ( again same sign)
combining= we cant say if both are +ive or -ve.
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
Top
Junior | Next Rank: 30 Posts
Posts: 22
Joined: Sat Jan 01, 2011 2:58 am
Thanked: 1 times

by Anamaiy » Mon Mar 14, 2011 8:44 pm
Thanks guys
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Mon Mar 14, 2011 11:48 pm
Question(1) IMO -E
statement1= x-y=1/2 ( x and y can be both +ve or -ve, but cant have diff signs)

Statement 2= x/y>1 ( again same sign)
combining= we cant say if both are +ive or -ve.

Guys please correct the 1st question- the answer should be C and not E.
Top
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Tue Mar 15, 2011 12:08 am
Are x and y both positive ?
(1). 2x-2y = 1
(2). x/y > 1


Let us first use the line equation first : 2x-2y=1 => y= x-0.5.. So we have line in quadrants 3,1,4
Now let us use option 2... x/y is positive and greater than 1.. this is giving quadrants 1 and 3

But the question is if both x and y are from quadrant 1...
Here answer shall be E...
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 261
Joined: Wed Mar 31, 2010 8:37 pm
Location: Varanasi
Thanked: 11 times
Followed by:3 members

by ankur.agrawal » Tue Mar 15, 2011 12:51 am
Combined st(1) x=1/2+y AND st(2) x/y>1

from st(1&2) if (1/2+y)/y>1 then (1/2y)>0 Hence 2y>0 AND y>0 //agree?
from st(1) x=1/2 +y Hence with positive y ---> x=1/2 + y {positive value of y} We can answer Not only x and y are positive, BUT even x>y // agree?

answer is C
How did (1/2y)>0 convert to 2y>0. { Are we taking reciprocal) ? Plz explain.
Top
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Tue Mar 15, 2011 7:25 am
Hi Ankur, since 1>0, then in order for 1/2y to be greater than 0 OR to be positive, 2y must be greater than 0 OR must be positive. Hence 2y>0
thanks
ankur.agrawal wrote:
Combined st(1) x=1/2+y AND st(2) x/y>1

from st(1&2) if (1/2+y)/y>1 then (1/2y)>0 Hence 2y>0 AND y>0 //agree?
from st(1) x=1/2 +y Hence with positive y ---> x=1/2 + y {positive value of y} We can answer Not only x and y are positive, BUT even x>y // agree?

answer is C
How did (1/2y)>0 convert to 2y>0. { Are we taking reciprocal) ? Plz explain.
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
Top
User avatar
Legendary Member
Posts: 582
Joined: Tue Mar 08, 2011 12:48 am
Thanked: 61 times
Followed by:6 members
GMAT Score:740

by force5 » Tue Mar 15, 2011 10:33 am
Are x and y both positive ?
(1). 2x-2y = 1
(2). x/y > 1


Let us first use the line equation first : 2x-2y=1 => y= x-0.5.. So we have line in quadrants 3,1,4
Now let us use option 2... x/y is positive and greater than 1.. this is giving quadrants 1 and 3

But the question is if both x and y are from quadrant 1...
Here answer shall be E...
Hi HSPA this is an excellent doubt. ......

you are correct till eliminating A and B . This is what it is when we think about C

as per stmnt 1 your line y=x-0.5 has a positive slope and -ve y intercept. ( its in 1, 3, 4 th quadrant)
how ever also see that for this line x is always greater than y ( when x=0, y =-0.5, when y =0, x=0.5)

From stmnt 2 x and y have same sign.
when both are positive ( x>y)
when both are negative ( x<y)

now combining both. x >y can only happen when both are positive.


Hope that helps dear ...............
Top
User avatar
Legendary Member
Posts: 1101
Joined: Fri Jan 28, 2011 7:26 am
Thanked: 47 times
Followed by:13 members
GMAT Score:640

by HSPA » Tue Mar 15, 2011 11:45 pm
Super force5... I sometimes forget to do the complete calculation... this is what is haunting me from days
i did the same in some other question which says by how much 12 should be reduced to get 4.5.. i kept 37.5%
Top
Post new topic Post Reply