Aptitude - Percentage - Discussion

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number = 14.

I.E.

100% -------> 70 number.

X --------> 14.

(100x14) / 70 = 20%.

How to find those 14 numbers in between 1-70 is there any shortcut to find it?

We cannot keep 2 digits at a time at a unit place, right. so there should be 1 or 9.

11, 19 is a prime number. So why they are included in squares?

Why not 12, 13, 14, . , 18? All have 1 in them! It is told 1 OR 9. Not 1 AND 9?

But they asking 1 or 9 (if they asking instead of this 1 and 9). What will be the answer?

What if larger numbers are given?

Eg: 1 to 10000. We cannot count manually all the numbers right, Is there any shortcut?

Thanks for your clear solution @Tabi.

Look again for the definition of "unit's digit".

If we have (for the sake of example) --> 180.
Then:
1 on '1'80 = hundreds digit.
8 on 1'8'0 = tens digit.
0 on 18'0' = units digit.

Therefore, numbers that fulfill the question "What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?" is numbers that have either '1' or '9' on its "units digit".

Disclaimer: 10, or 12, 13, 14, 15, 16, 17 and 18 did not make it to the answer because even though they have '1' on its component, that '1'is not a "units digit" since our definition above.

The correct numbers are: 1, 9 , 11, 19, 21, 29 , 31, 39, 41, 49, 51, 59, 61, 69.

*Counted -> 14 numbers out of 70's.

Percentage = (14/70)*100% = 20%.
Answer : C

Y is less than 117 by 19, means; Either y =117 - 19 or 117 - y = 19.

I'm confused with this. Please answer this.