Given : x = (y-z)^2
(i) Statement 1
yz=13
There is no information on limitations to y and z i.e. whether they are decimals, integers, etc. So a quick way can be to plug in a few numbers to evaluate this answer choice.
1. y=13,z=1 (y-z)=12 and hence x^2=144
2. y=-13,z=-1 (y-z)=-14 and hence x^2=196
We can go on to decimals (y=6.5 and z=2) but it is pretty much not needed. Statement (i) is insufficient.
(ii). Statement 2
We get y and z are non-zero integers. The value of x will change as y and z change. Hence statement (ii) is insufficient.
Both statements together, we can see that x can take a value of 144 or 196.
Thus answer is E i.e. both statements together are not sufficient.
confused
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adthedaddy
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I think there one typo in the reply given by anujan007.
In Statement 1,
When yz=13 then for following two conditions,
y=13 , z= 1; (y-z)=(13-1)=12 => (y-z)^2 = x^2 = 12^2 = 144
y=-13, z=-1; (y-z)=[-13-(-1)] = [-13+1] = (-12) => x^2 = (-12)^2 = 144
Thus in either case, we get the same value of x, i.e. 144
Thus, statement is "SUFICIENT"
Statement 2 is insufficient because there is no clarity on the values.
Thus, Ans = "A"
In Statement 1,
When yz=13 then for following two conditions,
y=13 , z= 1; (y-z)=(13-1)=12 => (y-z)^2 = x^2 = 12^2 = 144
y=-13, z=-1; (y-z)=[-13-(-1)] = [-13+1] = (-12) => x^2 = (-12)^2 = 144
Thus in either case, we get the same value of x, i.e. 144
Thus, statement is "SUFICIENT"
Statement 2 is insufficient because there is no clarity on the values.
Thus, Ans = "A"
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Brent@GMATPrepNow
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Statement 1:AJWILL wrote:Given that X=(Y-Z)^2 . What is the value of X?
(1) the product of Y and Z is 13
(2) Y and Z are non zero integers.
If YZ = 13, there are many possible values for Y and Z. Here are two cases:
Y=1 and Z=13, in which case X=(Y-Z)^2 = (1-13)^2 = 144
Y=2 and Z=6.5, in which case X=(Y-Z)^2 = (2-6.5)^2 = 20.25
Since we cannot determine the value of x, statement 1 in not sufficient
Statement 2:
No help here
Since we cannot determine the value of x, statement 2 in not sufficient
Statements 1&2:
If YZ = 13 AND Y and Z are both integers there are only 2 cases:
Y=1 and Z=13, in which case X=(Y-Z)^2 = =(1-13)^2 = 144
Y=13 and Z=1, in which case X=(Y-Z)^2 = =(13-1)^2 = 144
Since x must equal 144, the statements combined are sufficient
Answer = C
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Brent
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Let the statements guide you.AJWILL wrote:Given that X=(Y-Z)^2 . What is the value of X?
(1) the product of Y and Z is 13
(2) Y and Z are non zero integers.
Statement 2: Y and Z are nonzero INTEGERS.
Why does statement 2 require that Y and Z be integers?
Because this restriction likely has an effect upon Statement 1.
Implication: be sure to consider NON-INTEGER values when evaluating statement 1.
Statement 1: The product of Y and Z is 13.
It's possible that Y=13 and Z=1 or that Y=13,000 and Z=1/1000.
Since each combination will yield a different value for X, INSUFFICIENT.
Statement 2: Y and Z are non zero integers.
Since Y and Z can be any combination of nonzero integers, there is no way to determine the value of X.
INSUFFICIENT.
Statements 1 and 2 combined:
There are only 4 options for Y-Z:
Y-Z = 13-1 = 12.
Y-Z = 1-13 = -12.
Y-Z = -13-(-1) = -12.
Y-Z = -1-(-13) = 12.
Since 12² = (-12)² = 144, in each case X = 144.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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