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If the tick marks on the number line above are equally spaced, which o
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18 Jan 2024, 02:33
18 Jan 2024, 02:33
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If the tick marks on the number line above are equally spaced, which of the following is correct about the value of x?
Indicate all correct options.
(A) \(x = −3^{11}\)
(B) \(x = −2 (3^{10})\)
(C) \(x^3<x\)
(D) \(x^5>x^3\)
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If the tick marks on the number line above are equally spaced, which o
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18 Jan 2024, 16:17
18 Jan 2024, 16:17
First, we have to find what the distance between \(3^{11}\) and \(3^{10}\) is, so that we can find the distance between each tick mark.
\(3^{11} - 3^{10} = (3^{10})(3) - 3^{10} = 3^{10}(3 - 1) = 2 * 3^{10}\)
Key: When there are large powers, you're most likely not expected to brute force calculate the actual values. Rather, you're expected to know how to factor the exponentiation. In this case, we factored out \(3^{10}\).
Since there are 2 spaces between the \(3^{11}\) and \(3^{10}\) ticks, the value of each space is \(3^{10}\).
Thus, the value of x is \(3^{11} - 5(3^{10})\).
Just like how we previously factored out \(3^{10}\),
\(3^{11} - 5(3^{10}) = 3^{10}(3) - 5(3^{10}) = -2(3^{10})\). This is option B.
We also now know that x is a negative number. Negative numbers raised to odd powers remain negative. So, \(x^3\) is going to be MORE negative than x. Thus, option C is also correct.
\(3^{11} - 3^{10} = (3^{10})(3) - 3^{10} = 3^{10}(3 - 1) = 2 * 3^{10}\)
Key: When there are large powers, you're most likely not expected to brute force calculate the actual values. Rather, you're expected to know how to factor the exponentiation. In this case, we factored out \(3^{10}\).
Since there are 2 spaces between the \(3^{11}\) and \(3^{10}\) ticks, the value of each space is \(3^{10}\).
Thus, the value of x is \(3^{11} - 5(3^{10})\).
Just like how we previously factored out \(3^{10}\),
\(3^{11} - 5(3^{10}) = 3^{10}(3) - 5(3^{10}) = -2(3^{10})\). This is option B.
We also now know that x is a negative number. Negative numbers raised to odd powers remain negative. So, \(x^3\) is going to be MORE negative than x. Thus, option C is also correct.
gmatclubot
If the tick marks on the number line above are equally spaced, which o [#permalink]
18 Jan 2024, 16:17
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