Latest Elitmus Aptitude Question SOLUTION: In between 2000 and 2199 how many numbers are there who are perfect square?? (like 2194=2+1+9+4=16 which is a perfect square)

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In between 2000 and 2199 how many numbers are there who are perfect square?? (like 2194=2+1+9+4=16 which is a perfect square)

Asked In Elitmus Rozzer (10 years ago)

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RAKESH  (9 years ago)

from 2000 to 2099 => 20xy
sum of 1st two digit is 2, for no. to be perfect square (x+y)= 2,7,14
x+y=2, (x,y)=(0,2),(2,0),(1,1) => 3 no.s
x+y=7, (x,y)= (0,7),(1,6),...,(7,0) => 8 no.s
x+y=14, (x,y)= (5,9),(6,8),(7,7),(8,6),(9,5) => 5 no.s

from 2100 to 2199 => 21xy
sum of 1st two digit is 3, for no. to be perfect square (x+y)= 1,6,13
x+y=1, (x,y)=(0,1),(1,0) => 2 no.s
x+y=6, (x,y)=(0,6),(1,5),...,(6,0) => 7 no.s
x+y=13, (x,y)=(4,9),(5,8),...,(9,4) => 6 no.s

total no.s = 3 + 8 + 5 + 2 + 7 + 6 = 31

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NIHARIKA KUMARI  (10 years ago)

Ans: There are 31 nos between 2000 and 2199 which are perfect square,,
Solutions:
As 2194= 2 +1+9+4=16, Similarly 2002=2+0+0+2=4 (a perfect square),2007,2011,2016,2020,2025,2034,2043,2052,2059,2061,2068,2070,2077,2086,
2095,2101,2106,2110,2115,2124,2133,2142,2149,2151,2158,2160,2167,2176,2185,
2194.....total 31 numbers...

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Amit kumar jha  (10 years ago)

sqare starting from 4 to 16 ie 4,9,16
for 4 = 2 1 1 0,2 0 1 1,2 1 0 1, 2 0 2 0, 2 0 0 2, = total 5
for 9= 2 1 1 5, 2 1 5 1, 2 1 6 0, 2 1 0 6, 2 1 2 4, 2 1 4 2,2 1 3 3,
2 0 6 1, 2 0 1 6,2 0 4 3, 2 0 3 4,2 0 5 2,2 0 2 5,2 0 7 0,2 0 0 7 =15
for 16= 2 1 9 4, 2 1 4 9= 2
tatal 22 numbers possible

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shilpy  (9 years ago)

@rakesh question is for 4digit number but u consider for 3digit

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Abhinav khare  (9 years ago)

ans is 22
just try for the combinations with sum of no. as 2,3,4,5 because the greates no. possible is 2999 and hence greatest suare must be equal or less then 29

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