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AJWILL: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Fri Jul 13, 2012 1:35 amFollowed by: 1 member; Thanked: 1 times

by AJWILL » Wed Aug 08, 2012 5:33 am

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.

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anujan007: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat May 15, 2010 5:46 am; Thanked: 2 times

by anujan007 » Wed Aug 08, 2012 5:42 am

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.

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Wed Aug 08, 2012 8:54 am

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"

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 08, 2012 9:28 am

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 1:
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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Aug 08, 2012 9:51 am

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.

Let the statements guide you.
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 12Â² = (-12)Â² = 144, in each case X = 144.
SUFFICIENT.

The correct answer is C.

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