Fractions

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# Fractions

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The sum of the reciprocals of four different natural numbers is 1.85. Which of the following could be the sum of the four numbers?

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1.85 can be split into

1.000 1
+.500 1/2
+.25   1/4
+.1     1/10
--------
1.85

Hence 1+2+4+10=17

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Natural numbers from 1 to n are written on board.One of the numbers was erased and the new average becomes 600/17. Find the erased number ?

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Ans: 69

If there were n numbers before, then now there will n-1 numbers left.

Now, if average is 600/17, that means n-1 is multiple of 17.

With Hit & Trial, I come out with n-1=68 as the sum will be 69X70/2=2415.

And as per average, sum of n-1 numbers will be: (600/17)X68=2400.

Therefore, missing number is 2415-2400=15.

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How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits
is allowed?
(a) 499 (b) 500 (c) 375 (d) 376 (e) 501

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How many 5-digit numbers can be formed with the first digit as 1 and last digit as 5, which are not divisible by 3?
a)300  b)600  c)666  d)667

This post was modified 3 years ago 2 times by Amrita Mirchandani

@amritamirchandani
The divisibility rule of 3 says that the sum of digits should be divisible by 3.

1abc5
1 + 5 + a + b + c i. e
6 + a + b + c should be a multiple of three.

Or we can say three digit number abc should be divisible by 3. Hence from 000 , 003 , 006 , ....., 999 . abc can take 334 values. So 1000 -334 = 666 such numbers.

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