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DS: what is the tens digit of k

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DS: what is the tens digit of k

by navami » Tue Aug 30, 2011 10:59 pm
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.


[spoiler]OA : A
_ _ _ -->if units digit is non zero, the minimum value of it should be 1 and maximum 9. now if we add 9 with that minimum of maximum value there is +1 as carry which should get added to the tens digit. [/spoiler]
This time no looking back!!!
Navami
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Source: — Data Sufficiency |
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by bubbliiiiiiii » Tue Aug 30, 2011 11:08 pm
good question .. tricky one. :)

what is the source? Is it from some CAT software?
Regards,

Pranay
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by jbivins » Wed Aug 31, 2011 6:35 pm
I tried to think of this in terms of inequalities.


saw k=ABC

(1) tells us ABC
+ 9
=A3C (i know its not really c any more since 4 was added but who cares)
it can only be three if the following inequality is met
A21<=ABC<=A31 (so the ten's digit could be 2 or 3, but wait! the units digit is non zero so the ten's digit has to equal 2!)

(2) Same Methodology

ABC
+ 4
=A2C
only if
A16<=ABC<=A26
so the ten's digit could be 1 or 2. This one is useless.

I believe the answer is A.

I first I thought it was d but then I read the question more carefully and saw that the units digit was non-zero. My biggest problem is not reading the questions carefully enough.


Some of my formatting isn't working. I'm new here....
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by prateek_guy2004 » Thu Sep 01, 2011 2:58 am
Yeah even i thought its D...but the answer is A
Don't look for the incorrect things that you have done rather look for remedies....

https://www.beatthegmat.com/motivation-t90253.html
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by GMATGuruNY » Thu Sep 01, 2011 3:08 am
I posted a solution here:

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by AbhiJ » Thu Sep 01, 2011 3:31 am
Its a tricky one, no doubt. Lets call unit digit as U and tens digit as T.
As U <> 0, so U must be one of 1, 2,3..9.

From A.) K+9 has T=3, Now whatever be the value of U from 1-9, T of 'K' will always be 2.

Hence sufficient.

From B.) K+4 has T=2, Now if U = 6,7,8,9; T of 'K' will be 1.
But if U = 1,2,3,4,5; T of 'K' will be 2.
Thus depending on value of U we cannot be sure of T of 'K'

Not sufficient.
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by saketk » Thu Sep 01, 2011 10:31 am
navami wrote: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.


[spoiler]OA : A
_ _ _ -->if units digit is non zero, the minimum value of it should be 1 and maximum 9. now if we add 9 with that minimum of maximum value there is +1 as carry which should get added to the tens digit. [/spoiler]
This should be straight...

As we know that the unit digit is non-zero...therefore we can use a number ending with 1,2,... 9
Statement A:-
Adding 9 gives us 3 as the tens digit. Adding 9 to any number from 1....9 will carry 1 to the next digit.. therefore the answer will be 2 (2+1 =3) -- SUFFICIENT

Statement B-- adding 4 to a number will NOT necessarily carry 1 to the tens digit.. Therefore, Statement B is INSUFFICIENT.

Answer: -- A
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