Latest elitmus Aptitude Question SOLUTION: how many integer below 100 whose reciprocal are recurring a)90 b)92 c)85 d)75

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how many integer below 100 whose reciprocal are recurring
a)90
b)92
c)85
d)75

Asked In elitmus ARBIND NAYAK (9 years ago)

Unsolved Read Solution (11)

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Read Solution (11) :

Gaurav Dhimankar  (9 years ago)

As The fraction will terminate or non-recurring if and only if the denominator has for prime divisors only 2 & 5, that is, if and only if the denominator has the form: 2^n * 5^m
Possible Combination of No. < 100 of form 2^n * 5^0 = 1,2,4,8,16,32,64
Possible Combination of No. < 100 of form 2^0 * 5^m = 5,25 ( 1 is already taken)
Possible Combination of No. < 100 if we relate above two 10(5*2),20(5*4),40(5*8),80(5*16) & 50(25*2)
So total 14 Numbers possible which can be Non - Recurring
Thus Ans is (99 - 14 ) = 85 positive Integer below 100 whose reciprocal are Recurring.

Is this solution Helpfull? Yes (86) | No (1)  

Purnendu Giri  (9 years ago)

Ans: 85
non recurring no. are 1,2,4,8,16,32,64 and 5,10,20,40,80, and 25,50..

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T.VIGNESWARA REDDY  (9 years ago)

75 substract of all 2 and 5 mutiples 6+19=25 100-25=75

Is this solution Helpfull? Yes (3) | No (14)  

T.VIGNESWARA REDDY  (9 years ago)

ALL NON RECURING NUMBERS ARE 2 POWERS 1,2,4,8,16,32,64(TOTAL 7)
ALL 5 MULTIPLIES 5,10,20,25,40,50,80 (TOTAL 7)
(REMOVING ALL 3,7,11,13,17,19 MULTIPLES) I.E (15,30,35,45,55,60,65,70,75,85,90,95)
1/3=0.33333
1/7=0.14285
1/11=0.099
1/13=0.76123076
SO 99-14=85

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Manish  (9 years ago)

Ans :92
Check for each numbers remainders when it divides 1.

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aditya saraswat  (9 years ago)

Ans:85
no. are 2,4,6..........
and 5,10,20......
and 25,50.....

Is this solution Helpfull? Yes (1) | No (4)  

Gaurav Dhimankar  (9 years ago)

As The fraction will terminate or non-recurring if and only if the denominator has for prime divisors only 2 & 5, that is, if and only if
the denominator has the form: 2^n * 5^m

Possible Combination of No. < 100 of form 2^n * 5^0 = 1,2,4,8,16,32,64
Possible combination of No.

Is this solution Helpfull? Yes (1) | No   

sanjay kumar gupta  (8 years ago)

reciprocal of all prime no. doesnot give recurring decimal...4 ex. ---1/17=588235294176.....it is not terminated nor recurred ...so how could i consider ds typ of no.

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Raj Kumar Ray  (9 years ago)

@reddyl.... but suppose 30.. it is divisible by 5 but 1/30 is recurring decimel... i guess this will be 85

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Manish  (9 years ago)

These numbers 1,5,10,20,25,50,80 wont provide Recurring decimals on reciprocal.
All the Numbers Xcept these will do..
So total number less than 100 that will provide recurring decimals after inverse must be
(99-7) = 92
I hope this could be helpful.

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Vishal Kumar  (9 years ago)

I think it should be 86.All non recurring numbers are 1,2,4,5,8,10,16,20,25,32,40,50,64,75.
I know its not in options but can any1 give example apart from this?

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