XAT 2011 Question 85

Question 85

The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?

Solution

The meter skips all the numbers in which there is a 5

From, (1 to 99) -> 5 occurs 10 times in tens place and 10 times in units place (which also includes 55)

=> Total occurrence = $$10 + 10 - 1 = 19$$

Similarly from (100 to 199), from (200 to 299)..., from (400 to 499) , from (600 to 699),...from (900 to 999)

It occurs = $$8 \times 19 = 152$$

Now, from (500 to 599), there are 100 numbers, => micromanometer reading can change from 499 to 600.

Thus, total numbers skipped from (1 to 999) = $$19 + 152 + 100 = 271$$

Similarly, from (1000 to 1999) = 271

and from (2000 to 2999) = 271

Also, 3005 and 3015 are also skipped

=> Total number of skips = $$271 + 271 + 271 + 2 = 815$$

$$\therefore$$ Actual pressure = $$3016 - 815 = 2201$$



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