Date sufficiency
M is two a digit number and 2m is a three digit number, what’s the unit digit of m?
1)the unit number of 2m is 4;
2)the unit number of m is the same as the tens number of 2m;
My solution:
According to 1) the unit number of m can be 2 or 7;
According to 2), m can be 62,74,86,98;
Putting 1) and 2) together, m can only be 62. Therefore, the unit digit of m is 2.
1) and 2) together are sufficient to solve the problem.
Does anyone have any other ideas about this problem?
Thank you very much!
One tough Data Sufficiency Problem
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It took me over 2 minutes, but I did come up with a methodical way of solving this problem:
m = __ __ and 2m = __ __ __ where each spot is a digit
1) the unit number of 2m is 4
use all the combinations of 2 and another digit and see which have 4 in the units place: 2(2) = 4 and 2(7) = 14 so you cannot tell if the units digit of m is 7 or 2. INSUFF.
2) the unit number of m is the same as the tens number of 2m
set it up like a multiplication where x is the units digit:
__ X * 2 = __ X __
you can choose many values for X and just set the tens digit to work out so that U is also. For example, if I choose x = 1 then I can make 1 the tens digit of m so that 2 will be the tens digit of m or I can choose x = 4 and make the tens digit of m also 4. In any case, there are many values for the units digit of m. INSUFF. [Edit: I just realized my example choices do not work because 2m is not a three digit number, but you can choose a value higher than 5 for the tens digit of m and the logic still works out the same]
3) One point here is to note that for a two digit number to become a 3 digit number when multiplied by 2, the two digit number must be over 50 (e.g. 2 * 30 will not be a three digit number). This helps reduce the domain of possible testing values (i.e. saves time). Update the diagram in (2) to include data from (1):
__ X * 2 = __ X 4
From (1), we know X can be 2 or 7 so now we can update with the two cases:
__ 2 * 2 = __ 2 4
__ 7 * 2 = __ 7 4
To satisfy the first, we can pick 6 for the tens digit: 62 * 2 = 124
To satisfy the first, we can pick 8 for the tens digit: 87 * 2 = 174
Both these values for 2m satisfy all conditions, but there still two values for the units digit of m: 2 and 7.
INSUFF.
m = __ __ and 2m = __ __ __ where each spot is a digit
1) the unit number of 2m is 4
use all the combinations of 2 and another digit and see which have 4 in the units place: 2(2) = 4 and 2(7) = 14 so you cannot tell if the units digit of m is 7 or 2. INSUFF.
2) the unit number of m is the same as the tens number of 2m
set it up like a multiplication where x is the units digit:
__ X * 2 = __ X __
you can choose many values for X and just set the tens digit to work out so that U is also. For example, if I choose x = 1 then I can make 1 the tens digit of m so that 2 will be the tens digit of m or I can choose x = 4 and make the tens digit of m also 4. In any case, there are many values for the units digit of m. INSUFF. [Edit: I just realized my example choices do not work because 2m is not a three digit number, but you can choose a value higher than 5 for the tens digit of m and the logic still works out the same]
3) One point here is to note that for a two digit number to become a 3 digit number when multiplied by 2, the two digit number must be over 50 (e.g. 2 * 30 will not be a three digit number). This helps reduce the domain of possible testing values (i.e. saves time). Update the diagram in (2) to include data from (1):
__ X * 2 = __ X 4
From (1), we know X can be 2 or 7 so now we can update with the two cases:
__ 2 * 2 = __ 2 4
__ 7 * 2 = __ 7 4
To satisfy the first, we can pick 6 for the tens digit: 62 * 2 = 124
To satisfy the first, we can pick 8 for the tens digit: 87 * 2 = 174
Both these values for 2m satisfy all conditions, but there still two values for the units digit of m: 2 and 7.
INSUFF.
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Wow, great explanation mayonnai5e!
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Hi mayonnai5e,
Well certainly your explanation is very good & the answer should be E, I solved like this
m is a 2 digit nos
2m is 3 digit
m can be between 50 -99
&
2m can be between 100 & 198
let m =ab so 2m =1xy
stmt 1: INSUFF
stmt 2: 2m =1by
so 100 + 10b +y = 2(10a +b)
so 8b = 20a -100 -y
now here a can vary between 5-9 & y between 0-9
so multiple values will be possible for b
INSUFF
Combine
y=4
so 8b = 20a -100 -4
8b = 20a -104
here a can be between 6,8 so b will have values 2,7
INSUFF so E
Well certainly your explanation is very good & the answer should be E, I solved like this
m is a 2 digit nos
2m is 3 digit
m can be between 50 -99
&
2m can be between 100 & 198
let m =ab so 2m =1xy
stmt 1: INSUFF
stmt 2: 2m =1by
so 100 + 10b +y = 2(10a +b)
so 8b = 20a -100 -y
now here a can vary between 5-9 & y between 0-9
so multiple values will be possible for b
INSUFF
Combine
y=4
so 8b = 20a -100 -4
8b = 20a -104
here a can be between 6,8 so b will have values 2,7
INSUFF so E
Regards
Samir
Samir