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Let A, B, C, ...

Question

Let A, B, C,... X, Y, Z be positive numbers such that AC = B, BD = C... XZ = Y. Given that A+B = 1988, find the maximum value of Y+Z?

994

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1988

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√1988

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3976

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Solution

The correct option is B 1988
Let A = x and C = y

Then B = xy

$D = \frac{1}{x}$

$E = \frac{1}{x y}$

$F = \frac{1}{y}$

G = x

H = xy

I = y

So we see that this is a sequence with a period six. So A = Y and B = Z.

Given A+B = 1988, so maximum value of Y+Z = 1988.

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Let A, B, C,... X, Y, Z be positive numbers such that AC = B, BD = C... XZ = Y. Given that A+B = 1988, find the maximum value of Y+Z?

The correct option is B 1988Let A = x and C = y Then B = xy D=1x E=1xy F=1y G = x H = xy I = y So we see that this is a sequence with a period six. So A = Y and B = Z. Given A+B = 1988, so maximum value of Y+Z = 1988.

The correct option is B 1988
Let A = x and C = y

Then B = xy

$D = \frac{1}{x}$

$E = \frac{1}{x y}$

$F = \frac{1}{y}$

G = x

H = xy

I = y

So we see that this is a sequence with a period six. So A = Y and B = Z.

Given A+B = 1988, so maximum value of Y+Z = 1988.