SAT One-variable data Question

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Question 1 · Hard · MathNovember 2025 Batch 3 · Q11One-variable data: distributions and measures of center and spread · 0 solved

a,26,29,b,33,49,c For the given data set, the data values are listed in ascending order, where a, b, and c are constants. For this data set, the mean is 36, the median is 29, and the range is 72. What is the value of c? $y = 3 (\frac{a}{6})^{x + c} - b$ How many times does the graph of the given equation in the xy-plane cross the X-axis, where a,b,and c are positive constants such that $a > 6$ and $b > c$ ?

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Strategy

For an x-intercept question, set y equal to 0 and rewrite the equation so you can study whether the resulting function can hit that value. Then use the shape of the exponential: if the base is greater than 1, it is monotonic, so it can cross a horizontal level at most once unless the equation has been changed by additional terms.

Hints (open one at a time)

Hint 1

Start by asking where the graph hits the x-axis: that means y is 0.

Hint 2

Rewrite the equation so the exponential term is isolated on one side, then think about how many x-values can satisfy that equation.

Hint 3

A monotonic exponential can match a given positive level only once; check whether the transformed equation allows that level to be reached more than once.

Step-by-step Explanation

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