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Difficulty:
95%
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Question Stats:
22% (02:17) correct
78%
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based on 117
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Laser diodes and micro-controllers are among the components used to make a tracking system. During the past year, the cost of a laser diode (L) increased by x percent, and the cost of a micro-controller (M) decreased by y percent. If a tracking system is assembled using equal numbers of diodes and micro-controllers, and the cost of all other components remained the same during the past year, then the cost of a tracking system changed by what percent?
1. The ratio of L to M is equal to the reciprocal of the ratio of x to y.
2. The increase in the cost of a laser diode was the same as the decrease in the cost of a micro-controller.
1. The ratio of L to M is equal to the reciprocal of the ratio of x to y.
2. The increase in the cost of a laser diode was the same as the decrease in the cost of a micro-controller.
06 Oct 2020, 09:39
Kudos
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Vishh13
I have no idea why anyone would word Statement 1 that way, but all it says is that L/M = y/x, so Lx = My. If that's true, then Lx/100 = My/100. Now L(x/100) is the increase in the price of one laser diode, and M(y/100) is the decrease in the cost of one micro-controller. If the increase in the cost of each diode equals the decrease in the cost of each controller, then if we use the same number of each component, the overall cost will be the same as it was last year. So the overall cost didn't change, and Statement 1 is sufficient.
Statement 2 tells us the same thing in a simpler way, so the answer is D.
06 Oct 2020, 21:09
Kudos
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Laser diodes and micro-controllers are among the components used to make a tracking system. During the past year, the cost of a laser diode (L) increased by x percent, and the cost of a micro-controller (M) decreased by y percent. If a tracking system is assembled using equal numbers of diodes and micro-controllers, and the cost of all other components remained the same during the past year, then the cost of a tracking system changed by what percent?
Tracking system cost (TS)= Cost of Laser Diode * No. of Laser Diode + Cost of MC * No. of MC
Before Price Change, \(TS_{old}\)= L * n + M * n ( Given equal no. of laser diode and MC)
After Price Change, \(TS_{new}\)= \(L(1+\frac{x}{100}) * n + M(1-\frac{y}{100}) * n \)
Let n=1
\(TS_{old}\)= L + M
\(TS_{new}\)= \(L(1+\frac{x}{100}) + M(1-\frac{y}{100}) \)
Change in Percent=\(\frac{TS_{new} - TS_{old}}{TS_{old}} *100\)
Change in Percent= \(L(1+x/100)*M(1-y/100) - L - M / (L + M) *100\)
Change in Percent =\(\frac{ Lx-My}{L+M}\)
1. The ratio of L to M is equal to the reciprocal of the ratio of x to y.
\(\frac{L}{M}=\frac{y}{x}\)
Lx=My
Change in Percent = 0
This statement is sufficient
2. The increase in the cost of a laser diode was the same as the decrease in the cost of a micro-controller.
\(L(1+\frac{x}{100}) = M(1-\frac{y}{100}) \)
\(L + \frac{Lx}{100} = M - \frac{My}{100}\)
This statement is insufficient.
Answer should be A
But the given choice is D
IS I am making some mistake? Bunuel please tell
Tracking system cost (TS)= Cost of Laser Diode * No. of Laser Diode + Cost of MC * No. of MC
Before Price Change, \(TS_{old}\)= L * n + M * n ( Given equal no. of laser diode and MC)
After Price Change, \(TS_{new}\)= \(L(1+\frac{x}{100}) * n + M(1-\frac{y}{100}) * n \)
Let n=1
\(TS_{old}\)= L + M
\(TS_{new}\)= \(L(1+\frac{x}{100}) + M(1-\frac{y}{100}) \)
Change in Percent=\(\frac{TS_{new} - TS_{old}}{TS_{old}} *100\)
Change in Percent= \(L(1+x/100)*M(1-y/100) - L - M / (L + M) *100\)
Change in Percent =\(\frac{ Lx-My}{L+M}\)
1. The ratio of L to M is equal to the reciprocal of the ratio of x to y.
\(\frac{L}{M}=\frac{y}{x}\)
Lx=My
Change in Percent = 0
This statement is sufficient
2. The increase in the cost of a laser diode was the same as the decrease in the cost of a micro-controller.
\(L(1+\frac{x}{100}) = M(1-\frac{y}{100}) \)
\(L + \frac{Lx}{100} = M - \frac{My}{100}\)
This statement is insufficient.
Answer should be A
But the given choice is D
IS I am making some mistake? Bunuel please tell
