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28 Oct 2021, 04:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:38) correct
27%
(01:42)
wrong
based on 439
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How many integers from 101 to 800, inclusive, remains the value unchanged when the digits were reversed?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
28 Oct 2021, 04:23
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Bunuel
This means we are looking for palindrome numbers.
Number is of the form XYX.
X can be anything from 1 to 7, so 7 ways.
No restrictions on Y, so 10 ways.
Total 7*10*1=70, we count 1 way for the second X as it will be same as first digit.
C
28 Jun 2023, 14:07
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Two possible cases:
xyx or xxx
First case:
The first digit must be greater than 0, or otherwise we will not have a 3 digit number. Additionally, since we need the digit to repeat, it needs to be less than 8 (since our set stops before 808).
So we have 7 possible choices for the first slot.
In the second slot, we do not want to repeat the first digit, and we also want to add 0 back in -> 9 total choices
In the third slot, it has to be the repeat of the first, so there is only 1 choice possible
total ways: 7*6*1=63
Second case xxx:
In this case, we can only have 1 choice for the first slot and the rrest must be all the same digit
7 total ways
total possible ways: 63+7=70
C
xyx or xxx
First case:
The first digit must be greater than 0, or otherwise we will not have a 3 digit number. Additionally, since we need the digit to repeat, it needs to be less than 8 (since our set stops before 808).
So we have 7 possible choices for the first slot.
In the second slot, we do not want to repeat the first digit, and we also want to add 0 back in -> 9 total choices
In the third slot, it has to be the repeat of the first, so there is only 1 choice possible
total ways: 7*6*1=63
Second case xxx:
In this case, we can only have 1 choice for the first slot and the rrest must be all the same digit
7 total ways
total possible ways: 63+7=70
C
