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One tough Data Sufficiency Problem

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One tough Data Sufficiency Problem

by Jinger » Tue Oct 09, 2007 10:43 am
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!
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by achandwa » Tue Oct 09, 2007 12:03 pm
You missed the possibility that m=50 from ii) but it's inconsequential.
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by Jinger » Tue Oct 09, 2007 1:20 pm
I agree with you. m=50 is also a possible value for 2). Thanks for pointing it out.
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by mayonnai5e » Wed Oct 10, 2007 8:24 am
Is the OA E? That's what I came up with.
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by Jinger » Wed Oct 10, 2007 2:02 pm
I found the question on another website and the answer is E. How did you come up with the answer?
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by mayonnai5e » Wed Oct 10, 2007 2:54 pm
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.
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by Jinger » Wed Oct 10, 2007 5:12 pm
Thank you so much for the detailed explanation. I see where I made the mistake. I am pretty confused by the wording of the question.
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by beatthegmat » Wed Oct 10, 2007 7:35 pm
Wow, great explanation mayonnai5e!
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by samirpandeyit62 » Thu Oct 11, 2007 2:24 am
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
Regards
Samir
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