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If the units digit of the three-digit positive integer k is

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If the units digit of the three-digit positive integer k is [#permalink] New post 17 Oct 2009, 19:28
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 May 2013, 03:51, edited 2 times in total.
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Re: DS number problem [#permalink] New post 17 Oct 2009, 19:44
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The answer is A.

We know the following:

(a) k is a 3 digit positive integer
(b) The units digit of k is NOT zero

Statement 1: The tens digit of k + 9 is 3.

If k + 9 has a tens digit of X, the only way k has a tens digit of X as well is if the units digit of k is zero. Since we know the units digit of k is NOT zero, the tens digit of k MUST be 2.

Sufficient.

Statement 2: Then tens digit of k+4 is 2.

The tens digit of k can be 1 or 2. Insufficient.
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Re: DS number problem [#permalink] New post 18 Oct 2009, 00:01
will go with A

Lets consider k = 100x + 10y +z where z is units digit and y is tens digit
we know z is not equal to zero i.e z is b/w 1 and 9 inclusive
we need to find y

1. tens digit of k + 9 is 3 ie z+9 will give the new value of y
since z+9 gives y = 3 then y=2 before 9 is added to z (z is 1 to 9 inclusive) . hence suff

2. tens digit of k + 4 is 2
now if z= 6 or 7 or 8 or 9 then on adding 4, y value will get incremented by 1 so value of y (before adding 4 ) is 1
but if z is b/w 1 to 5 (inclusive) then value of y will not change and y will be equal to 2
hence insuff
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Re: If the units digit of the three-digit positive integer k is [#permalink] New post 29 Jan 2012, 06:32
Let k =abc (c ≠ 0) question is b= ?

(1) As c ≠ 0, so b+9 means k+9, if k+9 then b = 3. it is possible if b = 2 only
[123 + 9 = 132, 122+9= 131]
sufficient
(2) k+4 = b = 2, 118+4 = 122, b = 1
123 = 127 b= 2
Insufficient.
Ans. A
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Re: If the units digit of the three-digit positive integer k is [#permalink] New post 29 Jan 2012, 06:40
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If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

Given that: k=abc and c is nonzero. Question b=?

(1) The tens digit of k + 9 is 3:
abc
+9
---
a3x

Tens digit of k+9, which is 3, gains 1 unit from c+9 (as c is not zero), hence b+1=3 --> b=2. Sufficient.

(2) The tens digit of k + 4 is 2
abc
+4
---
a2x

Tens digit of k + 4, which is 2, may or may not gain 1 unit from c+4, hence either b+1=2 or b+0=2. Two different values for b. Not sufficient.

Answer: A.

Hope it's clear.
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Re: If the units digit of the three-digit positive integer k is [#permalink] New post 22 Aug 2013, 04:20
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Re: If the units digit of the three-digit positive integer k is   [#permalink] 22 Aug 2013, 04:20
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