Quote:
If N = 16 × 10^(-p) and −4 < p < 4, how many different integer values of p will make N a perfect square?
A. 0
B. 2
C. 3
D. 5
E. 7
SOUMYAJIT_ wrote:
B.
-2 & 0.
2 will make it 4^2*10^-2.. which isn't a perfect square ? What am I missing ?
Bolded part - .16 can be a perfect square if the latter's definition is "a rational number multiplied by itself." ... Which seems to be the issue.
If -p = 2, we get p = -2, and 16 x
10\(^{-2}\) = .16 --> .4 * .4
If -p = (-2), we have p = 2. 16 *
10\(^2\) = 1600 = 40 * 40
My solution: If N = 16 × 10^(-p) and −4 < p < 4, how many different integer values of p will make N a perfect square?1. -p has to be -3, -2, -1, 0, 1, 2, or 3
2. Check the integers
16 x
10\(^{-(-3)}\) =16 * 1000 . . . 1000 is not a perfect square. Incorrect.
16 x
10\(^{-(-2)}\) = 1600. 40*40 = 1600. Correct
16 x
10\(^{-(-1)}\) = 16 * 10. 10 is not a perfect square. Incorrect
16 x
\(10^{-(-1)(0)}\) =
\(10^0\) = 16 * 1 = 16. 16 = 4*4. Correct.
16 *
\(10^{-1}\) = 1.6, or
1\(\frac{6}{10}\), or
\(\frac{16}{10}\), whose denominator is not a perfect square. Incorrect.
16 *
10\(^{-2}\) = .16 =
(.4)\(^2\). Also, .16 =
\(\frac{16}{100}\). Numerator and denominator are perfect squares. Correct.
16 *
10\(^{-3}\) = .016 = \(\frac{16}{1000}\). 1000 is not a perfect square. Incorrect.
3. -p = -2, 0, and 2. There are three integer values of -p that will make N a perfect square.
Answer Cbrianne5 , I have the same question as you do, though I answered the question as if the definition of perfect square were expanded beyond integers. I wonder if GMAT adheres to the definition of perfect square as the product of a rational number multiplied by itself? Even in the Math Theory section on the forum, a perfect square is defined as "A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an perfect square."
https://gmatclub.com/forum/math-number-theory-88376.htmlEdited to use -p correctly. Answer unchanged. _________________
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