The function $f$ is defined for each positive thre... | Free GMAT Practice Question | GMAT Panda

👋 Hi! I'm GMAT Panda. Ask me anything about this question, or click a button below to get started!

The function f is defined for each positive three-digit integer n by f (n) = 2^{x} 3^{y} 7^{z}, where x, y, and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f (m) = 14 f (v), then m - v =

Explanation	Calculations	Help
$We assign the hundreds digit of m to x_{m}, the tens digit of m to y_{m}, and the units digit of m to z_{m} . We assign the digits of v similarly with x_{v}, y_{v}, and z_{v} .$	$f (m) = 2^{x_{m}} \times 3^{y_{m}} \times 7^{z_{m}} f (v) = 2^{x_{v}} \times 3^{y_{v}} \times 7^{z_{v}}$
$We write the ratio of f (m) to f (v) in terms of the differences of their digits.$	$\frac{f ( m )}{f ( v )} = 2^{x_{m} - x_{v}} \times 3^{y_{m} - y_{v}} \times 7^{z_{m} - z_{v}}$
$We set this ratio equal to 14 and express 14 as a product of prime powers.$	$2^{x_{m} - x_{v}} \times 3^{y_{m} - y_{v}} \times 7^{z_{m} - z_{v}} = 2^{1} \times 7^{1}$
$We recognize that the equation has unknowns in exponents, so we apply Prime Matching to match each exponent on both sides.$	$x_{m} - x_{v} = 1 y_{m} - y_{v} = 0 z_{m} - z_{v} = 1$	Theory & Tactics Method Card ALG7 Click to view full details
$We express the difference between the two original numbers in terms of the digit differences.$	$m - v = 100 \times (x_{m} - x_{v}) + 10 \times (y_{m} - y_{v}) + (z_{m} - z_{v})$
$We substitute the values of the digit differences and find the result.$	$m - v = 100 \times 1 + 10 \times 0 + 1 = 100 + 1 = 101$

Scroll horizontally to view all columns

C

The function f is defined for each positive three-digit integer n by f (n) = 2^{x} 3^{y} 7^{z}, where x, y, and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f (m) = 14 f (v), then m - v =

Explanation	Calculations	Help
$We assign the hundreds digit of m to x_{m}, the tens digit of m to y_{m}, and the units digit of m to z_{m} . We assign the digits of v similarly with x_{v}, y_{v}, and z_{v} .$	$f (m) = 2^{x_{m}} \times 3^{y_{m}} \times 7^{z_{m}} f (v) = 2^{x_{v}} \times 3^{y_{v}} \times 7^{z_{v}}$
$We write the ratio of f (m) to f (v) in terms of the differences of their digits.$	$\frac{f ( m )}{f ( v )} = 2^{x_{m} - x_{v}} \times 3^{y_{m} - y_{v}} \times 7^{z_{m} - z_{v}}$
$We set this ratio equal to 14 and express 14 as a product of prime powers.$	$2^{x_{m} - x_{v}} \times 3^{y_{m} - y_{v}} \times 7^{z_{m} - z_{v}} = 2^{1} \times 7^{1}$
$We recognize that the equation has unknowns in exponents, so we apply Prime Matching to match each exponent on both sides.$	$x_{m} - x_{v} = 1 y_{m} - y_{v} = 0 z_{m} - z_{v} = 1$	Theory & Tactics Method Card ALG7 Click to view full details
$We express the difference between the two original numbers in terms of the digit differences.$	$m - v = 100 \times (x_{m} - x_{v}) + 10 \times (y_{m} - y_{v}) + (z_{m} - z_{v})$
$We substitute the values of the digit differences and find the result.$	$m - v = 100 \times 1 + 10 \times 0 + 1 = 100 + 1 = 101$

Scroll horizontally to view all columns

C