Halimah_O wrote:If w, y and z are positive integers, and w = y - z, is w a perfect square?
1) y+z is a perfect square
2) z is even
Target question: Is w a perfect square?
IMPORTANT: Including the variable w in this question makes it look trickier than it is.
Notice that we could just as easily ask, "Is y-z a perfect square?" and IGNORE the w altogether. So, let's do that by REPHRASING our target question...
REPHRASED target question: Is y-z a perfect square?
Given: y and z are positive integers
Statement 1: y+z is a perfect square
This statement doesn't
FEEL sufficient, so I'll TEST some values.
There are several values of z and z that satisfy statement 1. Here are two:
Case a: y = 5 and z = 4. Here, 5 + 4 = 9, and 9 is a perfect square. In this case
y-z = 5-4 = 1, and 1 IS a perfect square
Case b: y = 7 and z = 2. Here, 7 + 2 = 9, and 9 is a perfect square. In this case
y-z = 7-2 = 5, and 5 is NOT a perfect square
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: z is even
No information about y.
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are still several values of y and z that satisfy BOTH statements. Here are two:
Case a: y = 5 and z = 4. Here, 5 + 4 = 9, and 9 is a perfect square. In this case
y-z = 5-4 = 1, and 1 IS a perfect square
Case b: y = 7 and z = 2. Here, 7 + 2 = 9, and 9 is a perfect square. In this case
y-z = 7-2 = 5, and 5 is NOT a perfect square
Since we cannot answer the
REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
RELATED VIDEO
REPHRASED target question:
https://www.gmatprepnow.com/module/gmat ... video/1100
