Each of 200 electrical switches controls a separate light bulb.

Question

Each of 200 electrical switches controls a separate light bulb. How many of the switches are in the off position?

(1) Forty percent of the bulbs are glowing.
(2) Five percent of the bulbs are burnt out.

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Dereno · Answer

There are 200 Electric Bulbs, each connected to a distinct switch.

We need to find the number of bulbs in OFF condition = ?

Statement 1:

(1) Forty percent of the bulbs are glowing.

40%*(200) = 80 bulbs are glowing.

Which means, there might be ATLEAST 80 switches ON, so that 80 Bulbs are glowing.

There might be some bulbs, which is NOT GLOWING ( burnt bulbs) , but the switch can be ON.

Hence, we cannot ascertain the number of switches that is OFF ( only based on the not bulbs that’s glowing).

Numbers of switches OFF can take a max value of 120.

Insufficient

Statement 2:

(2) Five percent of the bulbs are burnt out.

If 5%*(200) bulbs are burnt out = 10 bulbs.

These 10 bulbs belong to two classes-

switch ON , but bulb not glowing (BURNT)

switch OFF, but bulb BURNT.

Hence,  Insufficient

Combining both statements 1 and 2, we get

SWITCH OFF = 110 + cases of OFF switches, but BURNT

This category - cases of OFF switches, but BURNT , can take max 10 and minimum 0.

The values can be from 120 to 110 (both Inclusive).

Hence,  Insufficient

Option E

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