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22 Oct 2020, 03:27
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C
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:
68% (01:31) correct
32%
(01:44)
wrong
based on 68
sessions
History
Date
Time
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Not Attempted Yet
How many numbers between 10 and 10000 have the digit ‘4’ in the unit’s place and the digit ‘2’ in the ten’s place?
(A) 90
(B) 99
(C) 100
(D) 190
(E) 1000
(A) 90
(B) 99
(C) 100
(D) 190
(E) 1000
22 Oct 2020, 04:47
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Sajjad1994
Quickest way..
We take a 4-digit number with 24 as the last two digits....._ _ 24 or XY24
Now both x and y can take any of the 10 values including 0.....We have included 0 so that we can get 2- and 3-digits number from these calculations..
10*10*1*1=100
Simplest way
check separately for 2-,3- and 4- digit numbers
a) 2-digit numbers
Only 1 possible - 24
b) 3-digit numbers — Y24
Y can take any of 9 digits from 1 to 9.
So 9 numbers
c) 4-digit numbers — XY24
X can take values 1-9 and Y can take 0-9
So 9*10=90
Total 1+9+90=100
C
24 Oct 2020, 22:50
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Since the unit's digit is 4 and ten's digit is 2, let XY24 be the number between 10 and 10000.
X can be 0 to 9. If 0, XY24 will be a three-digit or a two-digit number depending on Y. There are 10 possible values for X.
Similarly, Y can be 0 to 9. If Y is 0 and X is non-zero, XY24 will be a four-digit number. If both Y and X are zero, XY24 is 24.
There are 10 possible values for Y.
In all the cases, the number is within the range of 10 to 10000.
So there are 10*10 possible numbers(Option C) of the form XY24
X can be 0 to 9. If 0, XY24 will be a three-digit or a two-digit number depending on Y. There are 10 possible values for X.
Similarly, Y can be 0 to 9. If Y is 0 and X is non-zero, XY24 will be a four-digit number. If both Y and X are zero, XY24 is 24.
There are 10 possible values for Y.
In all the cases, the number is within the range of 10 to 10000.
So there are 10*10 possible numbers(Option C) of the form XY24
