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# A three-digit number k, the units digit is non-zero, what is

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A three-digit number k, the units digit is non-zero, what is [#permalink]

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05 Oct 2005, 03:03
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A three-digit number k, the units digit is non-zero, what is the tens digit?

(1) The tens digit of k+9 is 3.
(2) The tens digit of k+4 is 2.
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05 Oct 2005, 04:08
I'd pick A.

1, sufficient, we know that the unit digits is non-zero.
So, the tens digit has to be 2. Just pick some numbers here.

unit digit = 1, T=Tens digit.
9
+T1
-------
30

9
+T9
-------
30
T has to be 2

2, insufficient, two values for T

4
+T1
-------
25 -> T is 2

4
+T9
-------
23 -> T is 1

hmm...The numbers 9 and 4 in the above examples should be straight above the unit digits.

Last edited by macca on 05 Oct 2005, 04:10, edited 1 time in total.
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05 Oct 2005, 04:10
I also got 'A' but what if 'k' is negative....???
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05 Oct 2005, 04:29
Vivek!

I think you're right. k could be negative. It's not stated that k is positive.
And the answer is probably E in that case.

1,
if k > 0 -> tens digit = 2
if k< 0 -> tens digit = 4 or 3

2,
if k>0 -> tens digit = 2 or 1
if k<0 -> tens digit = 3,2

Both together, -> insufficient
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05 Oct 2005, 05:10
From statement 1, we know that the tens digit of K+9 is 3. However, we're also told that the last digit of k is non-zero. So the last digit cannot be 1.

If the units digit is from 2-9, if we add 9, we will have a carry over of 1 to the tens digit position. In order to get 3 in the tens position, the original number must be holding a 2 in the tens position.

Statement 1 is therefore sufficient.

From statement 2, we know the tens digit of K+4 is 2. However, we're also told the last digit of k is non-zero, so the last digit cannot be 6. It can be 1-5, 7-9. If the units digit is 1-5, the tens digit is 2. If the units digit is 7-9, the units digit is 1. Since we have two possible solutions, Statement 2 is not sufficient.

Ans: A.
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05 Oct 2005, 05:11
macca wrote:
Vivek!

I think you're right. k could be negative. It's not stated that k is positive.
And the answer is probably E in that case.

1,
if k > 0 -> tens digit = 2
if k< 0 -> tens digit = 4 or 3

2,
if k>0 -> tens digit = 2 or 1
if k<0 -> tens digit = 3,2

Both together, -> insufficient

oops Did not consider the negative case.
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05 Oct 2005, 06:06
Thanks for the expln. guys. ywilfred, your reasoning makes it very easy to understand.
Well the OA is strangely A. Strangely coz vivek makes a valid point!!
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05 Oct 2005, 07:52
I would have chosen A as well because I did not think about the possibility of k being negative. How do you prevent yourself from overanalyzing a question like this? The negative case is a valid point...
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05 Oct 2005, 07:57
rahulraao wrote:
Thanks for the expln. guys. ywilfred, your reasoning makes it very easy to understand.
Well the OA is strangely A. Strangely coz vivek makes a valid point!!

Just out of curiosity, what is the source of this question? I doubt the OG would allow you to second guess the nature of the question (in this case, we're left wondering if the 3 digit number could be negative)
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05 Oct 2005, 18:07
This is a question from Math Test 3 0r 4 from Scoretop.com's free online tests.
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05 Oct 2005, 18:14
I got it as A too!
So, being wrong sometimes has its advantages too... or am I wrong?
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05 Oct 2005, 18:17
anandsebastin wrote:
I got it as A too!
So, being wrong sometimes has its advantages too... or am I wrong?

A is the OA given for this question. The only question was whether the 3 digit number can be negative, that's all. But I suppose ETS or Pearson will set questions that does not leave you in any doubt.
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05 Oct 2005, 18:19
MsStephanie wrote:
I would have chosen A as well because I did not think about the possibility of k being negative. How do you prevent yourself from overanalyzing a question like this? The negative case is a valid point...

I have exactly same question as you. I hope real test will not have questions with open scope.
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05 Oct 2005, 21:28
rahul, macca, MsStephanie, anand, duttsit....

ywilfred has a point.
So far, I have not seen any question by ETS (in OG or any other source) having any doubtful answer but at the same time I have seen couple of controversial questions in other non-ETS material. I think we should be careful, not to take our mistakes too seriously in such a material, just learn & move ahead...
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05 Oct 2005, 21:43
Ok.

Just wanted to put one of my learnings...
Whenever there is a DS question, which just says "a number",

Don't forget to check,

1) Can it be an integer
2) Can it be a floating ppoint number (or a fraction)
3) Can it be a zero (sometimes I made mistakes by ignoring it to be a zero)

& in each of 1) & 2) above,

a) can it be a negative (integer/float)
b) can it be a positive (integer/float)
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05 Oct 2005, 21:53
vivek123 wrote:
Ok.

Just wanted to put one of my learnings...
Whenever there is a DS question, which just says "a number",

Don't forget to check,

1) Can it be an integer
2) Can it be a floating ppoint number (or a fraction)
3) Can it be a zero (sometimes I made mistakes by ignoring it to be a zero)

& in each of 1) & 2) above,

a) can it be a negative (integer/float)
b) can it be a positive (integer/float)

Good roundup, Vivek.... and floating point number.. hmm.. computer engineering?
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06 Oct 2005, 21:15
ha ha ha... yeah! I'm a computer bug!
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08 Oct 2005, 04:25
Oh my god!! What in good heavens is a floating point number???

This forum can indeed be intimidating sometimes!
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08 Oct 2005, 04:25
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