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06 Sep 2019, 07:24
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (01:47) correct
33%
(01:07)
wrong
based on 39
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What is the value of \(x + y^2\) ?
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
Source: Nova GMAT
06 Sep 2019, 10:54
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1) Not sufficient.
X=3,2,5,... Y=4,5,2,...
2) X²+Y²=25
X=3,4,-3,-4,...Y=4,3,-4,-3
Option E
Posted from my mobile device
X=3,2,5,... Y=4,5,2,...
2) X²+Y²=25
X=3,4,-3,-4,...Y=4,3,-4,-3
Option E
Posted from my mobile device
08 Sep 2019, 12:20
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SajjadAhmad
What is the value of \(x + y^2\) ?
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
(1) \(x + y = 7\)
(2) \(x^2 + y^2 = 25\)
Source: Nova GMAT
Glancing over the problem, my immediate thought is about positives and negatives, since I'm seeing a lot of squares. There are only two variables, and the numbers are pretty small, so it's probably smart to test cases, being very careful to test both positive and negative numbers if the statement looks sufficient, and to plug the cases back into the question itself.
Statement 1: x + y = 7.
This is an easier one to test - you could use any numbers that sum to 7. Start with x = 0, y = 7. Then, x + y^2 = 0 + 7^2 = 49, so the answer to the question is 49.
But if x = 7, y = 0, then x + y^2 = 7. The question has two different answers, so this statement is insufficient.
Statement 2: What stands out is that 25 is also a perfect square, 5^2. In geometry, there's a Pythagorean triple, 3^2 + 4^2 = 5^2. If you recall this, you'll know that x = 3, y = 4 is a good case. So is x = 4, y = 3.
If x = 3 and y = 4, then x + y^2 = 3 + 4^2 = 3 + 16 = 19, so the answer to the question is 19.
If x = 4 and y = 3, then x + y^2 = 4 + 3^2 = 4 + 9 = 13, so the answer to the question is 13.
The question has two different answers, so this statement is insufficient.
Statements 1 and 2 together:
3 + 4 sums to 7, so both of the cases we tested for statement 2 will also work for statement 1. Therefore, since there were two different answers, the two statements are insufficient together and the answer to the question is (E). We didn't end up having to use negatives after all, since it was possible to prove the statements insufficient without them!
