Somehow I find both to satisfy the statements. Please help me find where I am getting it wrong.
I simplified the equations as:
x-y = 1/2
x>y
Somewhere I'm getting it wrong!
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Are x and y both positive? (GMATPrep)
This topic has expert replies
-
clawhammer
- Master | Next Rank: 500 Posts
- Posts: 132
- Joined: Sun Aug 15, 2010 10:08 am
- Thanked: 3 times
- Followed by:1 members
For this question (attached), I first assumed x=1/4, y=-1/4; then x=1. y =1/2.
Somehow I find both to satisfy the statements. Please help me find where I am getting it wrong.
I simplified the equations as:
x-y = 1/2
x>y
Somewhere I'm getting it wrong!
Somehow I find both to satisfy the statements. Please help me find where I am getting it wrong.
I simplified the equations as:
x-y = 1/2
x>y
Somewhere I'm getting it wrong!
-
beat_gmat_09
- Master | Next Rank: 500 Posts
- Posts: 437
- Joined: Sat Nov 22, 2008 5:06 am
- Location: India
- Thanked: 50 times
- Followed by:1 members
- GMAT Score:580
statement 1 simplification is correct. (x-y) = 1/2
For statement 2 remember when you are not given about the sign of variables you can multiply them in inequalities, but you have to consider +ve and -ve cases.
you only considered +ve case.
x/y*y > 1*y this is true when y is +ve, for this statement both the statements have to be considered, y<0 and y>0
when y is -ve :
x/(y) * (y) < (1) (y) ........ note the inequality sign has to be changed.
x < y ...... x is negative as x is less than -y
both statements are not sufficient.
Combining 1 & 2
x-y=1/2 and from statement 2 you know that x > y (both are positive as y is positive in this case) and x < y (both are negative as y is negative in this case)
case 1 - x and y both positive.
from statement 1, x - y =1/2 , this will hold true as x>y , no need to plug numbers.
case 2 - x and y both negative.
from statement 1, x - y =1/2, in this case x < y the difference cannot be +ve hence this is not true. Discard y -ve and x -ve case. Case 1 remains, x and y both are +ve.
Thus 1 & 2 are sufficient.
For statement 2 remember when you are not given about the sign of variables you can multiply them in inequalities, but you have to consider +ve and -ve cases.
you only considered +ve case.
x/y*y > 1*y this is true when y is +ve, for this statement both the statements have to be considered, y<0 and y>0
when y is -ve :
x/(y) * (y) < (1) (y) ........ note the inequality sign has to be changed.
x < y ...... x is negative as x is less than -y
both statements are not sufficient.
Combining 1 & 2
x-y=1/2 and from statement 2 you know that x > y (both are positive as y is positive in this case) and x < y (both are negative as y is negative in this case)
case 1 - x and y both positive.
from statement 1, x - y =1/2 , this will hold true as x>y , no need to plug numbers.
case 2 - x and y both negative.
from statement 1, x - y =1/2, in this case x < y the difference cannot be +ve hence this is not true. Discard y -ve and x -ve case. Case 1 remains, x and y both are +ve.
Thus 1 & 2 are sufficient.
Hope is the dream of a man awake
-
goyalsau
- Legendary Member
- Posts: 866
- Joined: Mon Aug 02, 2010 6:46 pm
- Location: Gwalior, India
- Thanked: 31 times
I ) x - y = 1/2
If we assume x = 1/4 , y = - 1/4 Answer will be 1/2 (as you say ) { one is positive and another one is negative }
If we assume x = 3/2 y = 2/2 Answer will be 1/2 (as you say ) { Both are positive }
In sufficient
II ) X/Y > 1
Either Both are positive or Both Negative & X should always be Greater then Y
We can re write it as X > Y
Again put the same values in both the cases x > y ,
In sufficient,
Now Combining Both statements,
x - y = 1/2 { Regardless of sign Absolute value of x is greater than y Because sign will cancel out, }
Considering +ve sign First,
For any value of X which is higher than the value of Y , X - Y will always we positive,
Considering -ve sign ( Consider Absolute values )
For any -ve value of X if we add any thing which is smaller than X result will always be -ve
Like -3/4 + 1/4 = -2/4 WE are adding Because x - y
-7/8 + 6/8 = -1/8
So the result will always be - ve Hence for x-y to be +ve Both x and y should be +ve
If we assume x = 1/4 , y = - 1/4 Answer will be 1/2 (as you say ) { one is positive and another one is negative }
If we assume x = 3/2 y = 2/2 Answer will be 1/2 (as you say ) { Both are positive }
In sufficient
II ) X/Y > 1
Either Both are positive or Both Negative & X should always be Greater then Y
We can re write it as X > Y
Again put the same values in both the cases x > y ,
In sufficient,
Now Combining Both statements,
x - y = 1/2 { Regardless of sign Absolute value of x is greater than y Because sign will cancel out, }
Considering +ve sign First,
For any value of X which is higher than the value of Y , X - Y will always we positive,
Considering -ve sign ( Consider Absolute values )
For any -ve value of X if we add any thing which is smaller than X result will always be -ve
Like -3/4 + 1/4 = -2/4 WE are adding Because x - y
-7/8 + 6/8 = -1/8
So the result will always be - ve Hence for x-y to be +ve Both x and y should be +ve
Saurabh Goyal
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
[email protected]
-------------------------
EveryBody Wants to Win But Nobody wants to prepare for Win.
-
clawhammer
- Master | Next Rank: 500 Posts
- Posts: 132
- Joined: Sun Aug 15, 2010 10:08 am
- Thanked: 3 times
- Followed by:1 members
Thanks a lot guys. You all make complete sense. I wish I could be good at digging deep fast enough under time pressure.
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
Though goyalsau and beat_gmat_09 provided effective and easy solution to the question, I want to provide some insight into the question. Picking numbers and cross checking the statements is a very common strategy to attack GMAT problems. But don't practice them directly. If you are going for that method then you've to choose the numbers carefully! My suggestion is: First go through the basics, Strengthen your concepts and then go for the shortcuts. If your concepts are clear, you'll never make a wrong assumption.
Statement 1: 2x - 2y = 1
Implies (x - y) = 1/2. This means the only case that is not possible is x negative and y positive. In that case the LHS will be negative always! So the possible cases are (with examples),
Not sufficient.
Statement 2: (x/y) > 1
Again this implies any one of the following two cases,
1 & 2 Together: Statement 2 limits the number of possible cases to two. Let's analyze them again with the help of statement 1.
Sufficient.
The correct answer is C.
Statement 1: 2x - 2y = 1
Implies (x - y) = 1/2. This means the only case that is not possible is x negative and y positive. In that case the LHS will be negative always! So the possible cases are (with examples),
- (1) x positive, y positive (x = 4.5, y = 4)
(2) x positive, y negative (x = 0.25, y = -0.25)
(3) x = 0.5, y = 0
(4) x = 0 , y = -0.5
(5) x negative, y negative (x = -4, y = -4.5)
Not sufficient.
Statement 2: (x/y) > 1
Again this implies any one of the following two cases,
- (1) Both of them are positive and x > y
(2) Both of them are negative and x < y
1 & 2 Together: Statement 2 limits the number of possible cases to two. Let's analyze them again with the help of statement 1.
- (1) Both of them are positive and x > y => (x - y) = 0.5 is possible.
(2) Both of them are negative and x < y => (x - y) will be always negative. Not possible.
Sufficient.
The correct answer is C.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
-
clawhammer
- Master | Next Rank: 500 Posts
- Posts: 132
- Joined: Sun Aug 15, 2010 10:08 am
- Thanked: 3 times
- Followed by:1 members
Thanks Rahul.Rahul@gurome wrote:First go through the basics, Strengthen your concepts and then go for the shortcuts. If your concepts are clear, you'll never make a wrong assumption.
Statement 2: (x/y) > 1
Again this implies any one of the following two cases,Not sufficient.
- (1) Both of them are positive and x > y
(2) Both of them are negative and x < y
Clearly this part about abt statement 2 was something I didn't remember. If you gave me x/y = 1. i would have definitely noticed both can be + or -. But I must learn to treat inequalities like equations and remember the basics!
-
beat_gmat_09
- Master | Next Rank: 500 Posts
- Posts: 437
- Joined: Sat Nov 22, 2008 5:06 am
- Location: India
- Thanked: 50 times
- Followed by:1 members
- GMAT Score:580
-3/-3.5 = -3/(-7/2) = +6/+7 < 1tomada wrote:I'm a bit confused by this one. Maybe someone can help me understand where I'm erring in my reasoning.
If I let X= -3 and Y= -3.5, the first equation is satisfied: 2(-3) - 2(-3.5) = -6 -(-7) = +1.
Then, the second equation is satisfied because (-3)/(-3.5) > 1
(alternative way of saying this is that -3 > -3.5)
Can someone explain how this isn't a viable scenario?
x/y > 1 from statement 2.
Hope this helps.
Hope is the dream of a man awake
-
beat_gmat_09
- Master | Next Rank: 500 Posts
- Posts: 437
- Joined: Sat Nov 22, 2008 5:06 am
- Location: India
- Thanked: 50 times
- Followed by:1 members
- GMAT Score:580
Were you asking for a explanation or are yourself giving one (in earlier post and now)tomada wrote:Unfortunately, that doesn't help, because -3/-3.5 > 1. I realize that a negative number divided by a negative number is a positive number, so you're saying that -3/-3.5 = 3/3.5. However, when doing that, you need to change the direction of the inequality sign. We know that 3 < 3.5. However, -3 > -3.5. So, when you go from -3/-3.5 to 6/7, you need to change the direction of the inequality sign.
I hope that helps.
In the above case you need not change the direction of sign.
Remember when the numerator and denominator both are -ve the result of division is always +ve, so there is no question of multiplying the inequality sign with negative number and to change the direction of inequality sign.
your numbers i.e. -3 and -3.5 do not fit the solution (when both the statements are combined)
because statement 2 does not pass as 6/7 < 1 and the reason it is less than 1 is aforementioned (i.e. num and deno when -ve result is +ve, inequality sign needn't be changed)
Hope is the dream of a man awake
-
prateek_guy2004
- Master | Next Rank: 500 Posts
- Posts: 398
- Joined: Tue Jul 26, 2011 11:39 pm
- Location: India
- Thanked: 41 times
- Followed by:6 members
I understand statement 1 and 2 are not sufficient but why C.
Can you please explain how to conclude that both X and y are positive.....
Can you please explain how to conclude that both X and y are positive.....
Don't look for the incorrect things that you have done rather look for remedies....
https://www.beatthegmat.com/motivation-t90253.html
https://www.beatthegmat.com/motivation-t90253.html
-
knight247
- Legendary Member
- Posts: 504
- Joined: Tue Apr 19, 2011 1:40 pm
- Thanked: 114 times
- Followed by:11 members
1. 2x-2y=1
Lets pick numbers for this one.
Let x=2 y=1.5
2(2)-2(1.5)=4-3=1 Condition Satisfied. Also x and y are +ve
Now, let x=-1.5 and y=-2
2(-1.5)-2(-2)=-3+4=1 Condition is still satisfied but x and y are -ve. This statement gives conflicting answers hence INSUFFICIENT
2. x/y>1
Meaning either both are positive and x>y eg 5>3
Or
Both are negative and |x|>|y| eg -5<-3 yet -5/-3>1. Again we get conflicting values of x and y hence INSUFFICIENT.
Combining both we have that both x and y have the same signs. i.e. either both are +ve or both are -ve. And if both are -ve then |x|>|y|. Again by plugging number we can eliminate the possibility that they are both negative. If both are negative and |x|>|y| then 2x-2y=1 will always be negative. Try x=-8 and y=-2. Also, try x=-3 y=-2. So the possibility of both being negative is ruled out. Now use our original values x=2 y=1.5. The condition is met. Hence C
Lets pick numbers for this one.
Let x=2 y=1.5
2(2)-2(1.5)=4-3=1 Condition Satisfied. Also x and y are +ve
Now, let x=-1.5 and y=-2
2(-1.5)-2(-2)=-3+4=1 Condition is still satisfied but x and y are -ve. This statement gives conflicting answers hence INSUFFICIENT
2. x/y>1
Meaning either both are positive and x>y eg 5>3
Or
Both are negative and |x|>|y| eg -5<-3 yet -5/-3>1. Again we get conflicting values of x and y hence INSUFFICIENT.
Combining both we have that both x and y have the same signs. i.e. either both are +ve or both are -ve. And if both are -ve then |x|>|y|. Again by plugging number we can eliminate the possibility that they are both negative. If both are negative and |x|>|y| then 2x-2y=1 will always be negative. Try x=-8 and y=-2. Also, try x=-3 y=-2. So the possibility of both being negative is ruled out. Now use our original values x=2 y=1.5. The condition is met. Hence C
-
prateek_guy2004
- Master | Next Rank: 500 Posts
- Posts: 398
- Joined: Tue Jul 26, 2011 11:39 pm
- Location: India
- Thanked: 41 times
- Followed by:6 members
Hi knight247
Thanks mate good approach..was just confused about the concluding both statements together...but thanks for explaining .....
Chaw
Thanks mate good approach..was just confused about the concluding both statements together...but thanks for explaining .....
Chaw
Don't look for the incorrect things that you have done rather look for remedies....
https://www.beatthegmat.com/motivation-t90253.html
https://www.beatthegmat.com/motivation-t90253.html
