Grid with sums
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2w + y + x = 6-------I
w + y + 2x = 3-------II
Subtract the 2 equations, we get w-x =3 or w = 3+x
we have to find
3x + w = n
Substitute the value of w
3x + x + 3 = n
4x+3 = n
plug the answer choices.
4x + 3 = 6, x = 3/4 not an integer - eliminate
4x + 3 = 7 , x = 1 integer--answer
4x + 3 = 8, x = 5/4 not an integer - eliminate
4x + 3 = 9, x = x=6/4 or 3/2 not an integer - eliminate
4x + 3 = 10, x = 7/4 not an integer - eliminate
Hence B.
If B is the answer, my solution goes against 1 condition in the question stem.
Z<W<X<Y
if W is less than X, then how come i am getting W=X+3 or is it that W is negative. If W is negative then X also has to to be negative.
Is there something that i am missing.
w + y + 2x = 3-------II
Subtract the 2 equations, we get w-x =3 or w = 3+x
we have to find
3x + w = n
Substitute the value of w
3x + x + 3 = n
4x+3 = n
plug the answer choices.
4x + 3 = 6, x = 3/4 not an integer - eliminate
4x + 3 = 7 , x = 1 integer--answer
4x + 3 = 8, x = 5/4 not an integer - eliminate
4x + 3 = 9, x = x=6/4 or 3/2 not an integer - eliminate
4x + 3 = 10, x = 7/4 not an integer - eliminate
Hence B.
If B is the answer, my solution goes against 1 condition in the question stem.
Z<W<X<Y
if W is less than X, then how come i am getting W=X+3 or is it that W is negative. If W is negative then X also has to to be negative.
Is there something that i am missing.
No rest for the Wicked....
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Can someone please hlep me underatand this?
w = x+3 like PC said
I am working wiht 2 other equations and getting x as a non intger(I must be missing something also wiht the problem constraints and whats given)
x+w+2z = -2 I
x+2y+w = 5 II
w+2y+z = 7 III
Subtract III from II
x-z = -2
z = x+2
Sub z=x+2 in I
x+w+2(x+2) = -2
3x+w=-6 IV
w-x = 3 V
Subtract V FROM IV
4X =-9
X = -9/4???
May be I messed up the grid....
w = x+3 like PC said
I am working wiht 2 other equations and getting x as a non intger(I must be missing something also wiht the problem constraints and whats given)
x+w+2z = -2 I
x+2y+w = 5 II
w+2y+z = 7 III
Subtract III from II
x-z = -2
z = x+2
Sub z=x+2 in I
x+w+2(x+2) = -2
3x+w=-6 IV
w-x = 3 V
Subtract V FROM IV
4X =-9
X = -9/4???
May be I messed up the grid....
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Wow, am I ever sloppy.
The letter in the top right corner is wrong. It should have been a Z.
I have corrected it here.
Having said that, I recommend that you do not solve this system for W, X, Y, and Z. Solving 4 equations with 4 unknowns is beyond the scope of the GMAT.
As you probably guessed, there is a quick (10-second) way to solve this question.
A thousand apologies for posting the wrong question.
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x+w+2z = -2----------I
2z+w+y = 0 or 2z = -w -y
substitute the value in the first equation
x + w - w -y = -2 or x-y = -2-------II
2x + w + z = 3
2x + y + z = 9
Subtract both the equations
y-w = 6 or y = w+6-------III
substitute III in II
x - w -6 = -2
x = 4+w
n=3x + w
n = 12 + 3w +w = 12+ 4w
12 + 4w = n
plug in the answer options
12 + 4w = 6, w= -3/2 not an integer
12 + 4w = 7, w= -5/4, not an integer
12 + 4w = 8, w= -1, integer
12 + 4w = 9, w= -3/4, not an integer
12 + 4w = 10, w=-1/2, not an integer
Hence Answer is C.
2z+w+y = 0 or 2z = -w -y
substitute the value in the first equation
x + w - w -y = -2 or x-y = -2-------II
2x + w + z = 3
2x + y + z = 9
Subtract both the equations
y-w = 6 or y = w+6-------III
substitute III in II
x - w -6 = -2
x = 4+w
n=3x + w
n = 12 + 3w +w = 12+ 4w
12 + 4w = n
plug in the answer options
12 + 4w = 6, w= -3/2 not an integer
12 + 4w = 7, w= -5/4, not an integer
12 + 4w = 8, w= -1, integer
12 + 4w = 9, w= -3/4, not an integer
12 + 4w = 10, w=-1/2, not an integer
Hence Answer is C.
No rest for the Wicked....
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This one is quite evil.
The sums of the 4 rows are given, so if we add all 4 of those sums (3+6+9+0=18) we will get the sum of all 16 numbers in the grid.
If we add the 4 column sums, we better get the same sum since we are adding the same 16 numbers.
So, we can conclude that (-2)+7+n+5 = 18
Solve for n to get n=8
Told you it was evil
The sums of the 4 rows are given, so if we add all 4 of those sums (3+6+9+0=18) we will get the sum of all 16 numbers in the grid.
If we add the 4 column sums, we better get the same sum since we are adding the same 16 numbers.
So, we can conclude that (-2)+7+n+5 = 18
Solve for n to get n=8
Told you it was evil
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Nice question, but Awesome solution.Brent Hanneson wrote:This one is quite evil.
The sums of the 4 rows are given, so if we add all 4 of those sums (3+6+9+0=18) we will get the sum of all 16 numbers in the grid.
If we add the 4 column sums, we better get the same sum since we are adding the same 16 numbers.
So, we can conclude that (-2)+7+n+5 = 18
Solve for n to get n=8
Told you it was evil
Thanks.
No rest for the Wicked....
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The solution is way too cool. Thanks Brent.
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GMATPREP1 - 550 (Oct 08)
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MGMAT CAT1 - 670 (Jan 09)
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