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Is x = 0 ? 1. xy = x2. x + y = ySource: GMAT Club Tests - hardest GMAT questions Please explain why statement 1 is insufficient.
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gmat4life wrote: Is x=0?
1. xy=x
2. x+y=y
Please explain why statement 1 is insufficient. Now xy=x means xy-x=0 or x(1-y)=0 For the equation x(1-y)=0 to hold good, either x has to be 0 or y has to be 1. It can very well be that x=0 and y=1 at the same time. We are not sure. So since it is not clear if x=0 or not, this statement is not sufficient. Now in statement 2. x+y=y clearly shows x=0. So it must be B HTH
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Thanks for a good explanation! +1 amitdgr wrote: gmat4life wrote: Is x=0?
1. xy=x
2. x+y=y
Please explain why statement 1 is insufficient. Now xy=x means xy-x=0 or x(1-y)=0 For the equation x(1-y)=0 to hold good, either x has to be 0 or y has to be 1. It can very well be that x=0 and y=1 at the same time. We are not sure. So since it is not clear if x=0 or not, this statement is not sufficient. Now in statement 2. x+y=y clearly shows x=0. So it must be B HTH _________________
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This question goes to show that when you have been looking at 700 level questions too long, you try and pick holes in something as simple as x = y - y ....
on the other hand, its good to finally get a question right!
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For the first option, lets assume Y = 1. So whatever the value of x, the product of XY is always X.
X * 1 = X (For any values of X). So, option 1 is ruled out..
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for statement 1 : x*y=x if x=0 and y=1 then 0*1=0 ; satisfies if x=2 and y=1 then 2*1=2 ; satisfies thus statement 1 is insufficient to say that x is 0 for statement 2: x+y=y if x=0 and y=any integer then 0+y = y ; satisfies if x=2(or any int but not zero) and y=any int then x+y=y is not satisfying thus statement 2 is sufficient to say that x=0 SO B But what would be the answer if the second statement was : x + y = x ??
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Hi Jimmy86; if (2) where: x + y = x --> y = 0 [no information about x after subtracting x from both sides] combining (1) & (2) [x*y=x; x+y=x]: x(0) = x for all values of x, x*0 is always a zero. So, we can say x (the result of the multiplication) is a zero. IMO C
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If X+Y=X, then I go for E.. we have options, x * y = x and x + y = x. Combining 1 and 2, (x + y) * y = x, xy + y^2 = x y (x + y) = x and so, x will be zero only if Y is also 0 or else the condition is not satisfied. So, IMO its E. jimmy86 wrote: for statement 1 :
x*y=x
if x=0 and y=1 then 0*1=0 ; satisfies
if x=2 and y=1 then 2*1=2 ; satisfies
thus statement 1 is insufficient to say that x is 0
for statement 2:
x+y=y
if x=0 and y=any integer then 0+y = y ; satisfies
if x=2(or any int but not zero) and y=any int then x+y=y is not satisfying
thus statement 2 is sufficient to say that x=0
SO B
But what would be the answer if the second statement was : x + y = x ??
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[quote="sivai87"]If X+Y=X, then I go for E..
we have options,
x * y = x and
x + y = x.
Combining 1 and 2,
(x + y) * y = x,
xy + y^2 = x
y (x + y) = x and so, x will be zero only if Y is also 0 or else the condition is not satisfied. So, IMO its E. I agree... its E. in case statement 2 : x+y = x x=-1 , y=0 gives -1+0 = -1 ; satisfies x=0 , y= 0 gives 0+0 = 0 ; satisfies we see x is not necessarily 0. Insufficient And combining y(x+y)=x if x=0 ; y=0 then 0*(0+0)=0 ; satisfies if x=1/2 ; y=1/2 then 1/2*(1/2+1/2)=1/2 ; satisfies So x is not necessarily 0.Insufficient Thus IMO its E But what if the question states that x is an integer. Then i suppose the only value that of x that satisfies y(x+y)=x is x=0. and answer would be C(not sure, feel i am missing something)
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Supasubi wrote: This question goes to show that when you have been looking at 700 level questions too long, you try and pick holes in something as simple as x = y - y ....
on the other hand, its good to finally get a question right! Haha yes! I definitely know what you mean. You're so traumatized from every question trying to trick you, that you're reluctant to believe that the answer could be sufficient with something as easy as X=Y-Y. I stared at it for a good 30 seconds trying to pick it apart too. That's hilarious.
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(2) if y = x - x, then, it is sufficient to say y = "0". plug in y (0) into (1) [x*y = x] or x = x*y x = x*0 RHS = x*0 = 0 for any value of a number, 0 times that number = 0 So, RHS is always "0" LHS = x LHS = RHS --> x = RHS x = 0 Sufficient So, C IMO....except am doing something stupid somewhere. Please correct me.
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@Gmatbull.. Buddy, I dont think u went wrong... I believe I am somewhere wrong.. The first mistake i made was, in substitution... I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X.. But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient... And I am not sure how to proceed further... Can anyone help me pls... gmatbull wrote: (2) if y = x - x, then, it is sufficient to say y = "0".
plug in y (0) into (1) [x*y = x]
or x = x*y
x = x*0
RHS = x*0 = 0
for any value of a number, 0 times that number = 0
So, RHS is always "0"
LHS = x
LHS = RHS
--> x = RHS
x = 0
Sufficient
So, C IMO....except am doing something stupid somewhere.
Please correct me.
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sivai87 wrote: @Gmatbull..
The first mistake i made was, in substitution...
I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X..
But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient...
And I am not sure how to proceed further...
I think you seem to make the expression difficult to yourself. First, realize that (2) has simplified the job: from x+y = x, you know y = 0. (x+y) * y = (x+y) ==> (x+y)0 = x+0 0 = x +0 0 = x you still arrive at C.
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@ GMAT BULL Is X = 0? 1) X * Y = X 2) X + Y = X The statements 1 and 2 are contradicting to each other.. Option 1 says that, X * Y = X which tends to give Y = 1, But option 2 gives, X + Y = X, and So Y = 0. I believe such questions wont appear in GMAT and so less to worry about this question... gmatbull wrote: sivai87 wrote: @Gmatbull..
The first mistake i made was, in substitution...
I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X..
But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient...
And I am not sure how to proceed further...
I think you seem to make the expression difficult to yourself. First, realize that (2) has simplified the job: from x+y = x, you know y = 0. (x+y) * y = (x+y) ==> (x+y)0 = x+0 0 = x +0 0 = x you still arrive at C. |
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sivai87 wrote: @ GMAT BULL Is X = 0? 1) X * Y = X 2) X + Y = X The statements 1 and 2 are contradicting to each other.. Option 1 says that, X * Y = X which tends to give Y = 1, But option 2 gives, X + Y = X, and So Y = 0. I believe such questions wont appear in GMAT and so less to worry about this question... Not so. First of all statement (2) is x+y=y and not x+y=x. Next, (1) xy=x --> x(y-1)=0 --> either x=0 (and y can take any value) OR y=1 (and x can take any value). So we can not say that y=1 from this statement. If the question were:Is x = 0? (1) xy = x(2) x+y=x (Note that this statement is changed) Then the answer would be C: (1) xy=x --> x(y-1)=0 --> either x=0 (and y can take any value) OR y=1 (and x can take any value). Not sufficient. (2) x+y=x --> y=0. Not sufficient to answer whether x=0. (1)+(2) As from (2) y=0\neq{1} then according to (1) x=0. Sufficient. So for this revised question answer would be C. Hope it helps.
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answer is B statement 1 XY=X means y=1 but X can take any value not sufficient statement 2 x + y = Y means X = y-y or X=0 sufficient
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Bunuel wrote: sivai87 wrote: @ GMAT BULL Is X = 0? 1) X * Y = X 2) X + Y = X The statements 1 and 2 are contradicting to each other.. Option 1 says that, X * Y = X which tends to give Y = 1, But option 2 gives, X + Y = X, and So Y = 0. I believe such questions wont appear in GMAT and so less to worry about this question... Not so. First of all statement (2) is x+y=y and not x+y=x. Next, (1) xy=x --> x(y-1)=0 --> either x=0 (and y can take any value) OR y=1 (and x can take any value). So we can not say that y=1 from this statement. If the question were:Is x = 0? (1) xy = x(2) x+y=x (Note that this statement is changed) Then the answer would be C: (1) xy=x --> x(y-1)=0 --> either x=0 (and y can take any value) OR y=1 (and x can take any value). Not sufficient. (2) x+y=x --> y=0. Not sufficient to answer whether x=0. (1)+(2) As from (2) y=0\neq{1} then according to (1) x=0. Sufficient. So for this revised question answer would be C. Hope it helps. I seem to recall that you can't add/subtract variables from both sides of the equation unless you know the sign of the variables. But the question doesn't tell you the sign of x or y so I don't think the problem can be approached this way. I think the only way to answer the question is to plug in numbers for x and y then check to see if the equation holds.
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St 1: xy = x. Either x=0 and y can take any value OR x can be any value and y=1. So insufficient. St2 x+y = Y => X=0, Y can be anything. Hence Sufficient. OA is B.
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CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned
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B.
1 tells us that y=1 and 2 tells us that x=0.
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Quote: Is x = 0 ?
1. xy = x
2. x + y = y
For Option1, which of the below method need to be followed? Method1 ---- xy = x ----> xy-x = 0 ----> x(y-1) = 0 ----> x = 0, y = 1 ---- I thought this method is always true in determining a valueMethod2 ---- xy = x - Substitute values x=0 & ycan be any value? or x can be any value and y=1?
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