What is the value of x ?

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Thu Aug 15, 2019 5:26 am

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Each Statement is clearly insufficient alone. Using both, you might notice that Statement 1 resembles the Pythagorean Theorem - we have x^2 + y^2 = 5^2. If you're familiar with the 3-4-5- triangle, you might see two solutions to this equation immediately -- we could have x=3 and y=4, or x=4 and y=3. Both of those solutions work in Statement 2. We'll also have negative solutions: x = -3 and y = -4, or x = -4 and y = -3. So we can't tell what x is, and the answer is E.

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pm; Followed by:5 members

by deloitte247 » Fri Aug 16, 2019 2:50 pm

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What is the value of x?
$$Statement\ 1:\ x^2+y^2=25$$
$$x^2=25-y^2$$
$$x=\sqrt{25-y^2}\ but\ value\ of\ y\ is\ unknown$$
Hence, we cannot evaluate x. Statement 1 is NOT SUFFICIENT
$$Statement\ 2:\ xy=12$$
$$x=\frac{12}{y}\ but\ value\ of\ y\ is\ unknown$$
Hence, we cannot evaluate x. Statement 2 is NOT SUFFICIENT
Combining both statements together
$$1=>\ x^2+y^2=25\ \ \ \ \ =>x=\sqrt{25-y^2}$$
$$2=>\ xy=12\ \ =>\ x=\frac{12}{y}$$
None of the statement provides the value of y. Hence, we cannot evaluate x.

Therefore, both statements together are NOT SUFFICIENT.

Answer = E

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