The simple way is
For any 100 numbers range, the total no.of integers which satisfy given condition == 27. (How? Just see below the answer?)
From the question, the range of numbers is 700 to 999.
so,
700 to 799 === 27 integers
800 to 899 === 27 integers
900 to 999 === 27 integers
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Total === 81 integers
As question asked for the no.of 3-digit integers greater than 700. So, we have to exclude the integer 700.
Total - 1 == 81 - 1 == 80
Ans: 80
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I'm interested to take some numbers ranging from 100 to 199
I'd like to rewrite this number 100 as in a format
H- Hundredth-digit + T - Tenth-digit + U - Unit's/One's- digit i.e., (H*100 + T*10 + U*1).
We can write as,
1*100 + 0*10 + 0*1
H remains constant for the range of numbers from 100 to 199. We have to check 3 conditions here,
1. If H=1, T - (0-9), U=1 === 101,111,121,131,141,151,161,171,181,191 = total 10 integers, but 111 is not satisfying given condition. Then, we are left with 9 integers.
2. If H=1, T=1, U= (0-9) === then we have 10 possibilities, but 111 is not satisfying the given condition. then left with 9 integers.
3. If H=1, T=(0-9), U=(0-9) & T=U ==== 10 possibilities, but 111 is not satisfying the given condition. then left with 9 integers.
So, that we can conclude for any 100 3-digit numbers, the no.of integers which satisfy condition is 27.
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By seeing the explanation, it might look like it will take more time. Actually, to make you understand, I have tried my level best to explain you well. Once we get used to, then it won't take much time. However, we are checking the possibilities for the given range & giving answer.
HTH, GOOD LUCK & Have a gr8 day,
Thanks,
Rajesh,
Loves GMAT....!!!!
