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Data sufficiency: Units and tens digit ...

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by imane81 » Mon Jan 18, 2010 6:43 pm
Please could you help in this one


If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?
(1) The tens digit of k + 9 is 3.
(2) The tens digit of k + 4 is 2.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

thanks!
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Source: — Data Sufficiency |
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by Pharo » Mon Jan 18, 2010 11:46 pm
write the number k as abc where a,b,c are the digits.

for statement 1 : when you add 9 to abc, you first add 9 to c. Since c is non zero, no matter what it is, it will make the addition end up with a 2 digits number. That means, you will have to carry 1 to b or mathematically, b's new value will be b+1. (So, the original b was 2; 3-1 = 2.)

for example say c = 1 , then c + 9 = 10 so abc + 9 becomes a(b+1)0

for statement 2 : since we do not know if adding 4 will result in a carry over to b, this statement is useless by itself.

So the answer is A .
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by mehravikas » Tue Jan 19, 2010 8:17 pm
Let K = ABC, where A is the 100th digit, B is the 10s digit, and C is the units digit. From the question we know that C <> 0

Statement 1 - ABC + 9 = 3, If C <> 0 then C + 9 will be > 10, and will carry a power of one to B therefore we know what b = 2 - Sufficient
Statement 2 - ABC + 4 = 2, If C = 8, then B = 1, If C = 3, then B = 2 - Insufficient
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