Latest Elitmus Aptitude Question SOLUTION: how many numbers are there from 100 to 1000 in which sum of any two digit equal to the third digit..?

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(#M40017818) ELITMUS Numerical Ability question Keep an EYE

how many numbers are there from 100 to 1000 in which sum of any two digit equal to the third digit..?

Asked In Elitmus vaibhav sharma (11 years ago)

Unsolved Read Solution (11)

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sandeep kumar  (11 years ago)

sum of any 2digits equal to 3rd
such 3digit no. with 0 in it are
101(101,110),202,303,404,505,606,707,808,909(2 ways each)
similarly
112,224,336,448(3ways each)
remaining
123 235 347 459
134 246 358
145 257 369
156 268
167 279
178
189
each can be written in 6 ways

so total nos are 9*2+4*3+16*6=18+12+96=126

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dharmendra  (11 years ago)

in series of 100->101,112,123,134,145,156,167,178,189
no =9
in series of 200->202,213,224,235,246,257,268,279
n0=8
similarly for other
so
9+8+7+6+5+4+3+2+1=45

Is this solution Helpfull? Yes (7) | No (22)  

Smita  (11 years ago)

so total numbers will be 9*2+4*3+16*6= 18+12+96=126

Is this solution Helpfull? Yes (3) | No (2)  

Smita  (11 years ago)

@ Vani,

Pls check cases when three numbers are different and no zero (0) is used..

U hv considered
Quote
for different digits(with out 0): 1 can be sum up with 7 numbers ,2 with 6......8 with 1 ,9 with 0 number ...total:7*7+1/2=28 numbers(like 2+1,3+2.....different numbers )
these can be written in 28*3! ways=168 ways

unquote.

I think u r considering same number multiple times.

like 189
when taking 3! of numbers with 189, u hv considered 189,198,891,819,918,981
and same numbers u hv considered with numbers having 8.
in case of 257 , u have considered same set of numbers 3 times in case of 2,5 and 7 and again taking 3! for each case.

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Mihir  (11 years ago)

116 Nos.

Here sum of any two digit equal to the third digit.
number like 101,110,112,121,211 ..... 945,954 are to be considered.

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phani  (11 years ago)

same numbers like:1+1=2 ,2+2,3+3,4+4 each number can be written in 3!/2! =3 ways

4 numbers 4*3=12----(1)

for different digits(with out 0): 1 can be sum up with 7 numbers ,2 with 6......8 with 1 ,9 with 0 number ...total:7*7+1/2=28 numbers(like 2+1,3+2.....different numbers )
these can be written in 28*3! ways=168 ways-----(2)

with 0:1+0,2+0..... 9 numbers with each number in 2 ways

9*2=18 ways---(3)

total :168+18+12=198 numbers

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ankit singh  (11 years ago)

@ all my ans 66 is correct because i have attempted 6 question in in quants in my elitmus xam and all were correct so there should be no confusion

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Karan  (11 years ago)

@ Ankit,

Pls clarify what do u mean by ..
2,3,5.... 4ways ...I think 6 ways 235,253,352,325,523,532
3,3,6 2ways .... 3 ways are possible...336,363,633
4,5,9 2ways ...... 6 ways .. 459,495,549,594,945,954
..
and some other similar cases ?

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deepika  (11 years ago)

10
one in each row of 10 no.(for e.g. 101 from 100 to 110 and so on )

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ankit singh  (11 years ago)

1,0,1 2ways
1,1,2 3ways
1,2,3
6ways
1,3,4

6ways
1,4,5 4ways
1,5,6 2ways
1,6,7 2ways
1,7,8 2ways
1,8,9 2ways
2,02 2ways
2,2,4 3ways
2,3,5 4ways
2,4,6 4ways
2,5,7 2ways
2,6,8 2ways
2,7,9 2ways
303 2ways
3,3,6 2ways
3,4,7 4ways
3,5,8 2ways
3,6,9 2ways
4,0,4 2ways
4,4,8 2ways
4,5,9 2ways
total 66 such numbers

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Vikash Sahu  (9 years ago)

ans...1665

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