If the units digit of the three-digit positive integer k is nonzero, what is the tens digit of k?

k=abc, c not zero, 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.
_________________

The answer is A.

Consider Statement 1:pick numbers to resolve it, if unit digit of k takes from 1 to 9, then adding nine would increase the tens digit by 1, hence it should be 2..sufficient to answer the question

Consider statement 2: if unit digit takes anything between 1 t0 5 , then on adding 4 tens digit remains the same. so in this case it would be 2, but if unit digit take from 6 to 9, tens digit would increase by 1, so this case its 1.

hence statement 1 alone is sufficient but not 2

Lets say k=x,y,z.

All of x, y and z are in the range of 1-9 (Given). Find Tens Digit ie y.

Stmt 1 Says: K + 9 = gives a number with 3 as the tens digit.
With that we can safely say that the Tens digit of k has to be 2. For eg let k be 121. Adding 9 will give 130. Similiarly, if k = 129, adding 9 will give 138. If we have k = 111, adding 9 will give 120 which goes against the stmt.

Stmt 2 : Not Suff as explained by alwynjoseph.

Hence, A.

[quote="tarek99"]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.


k= xyz , z is not 0 what is y??

from 1
xyz
+ 009
-------
z is not 0 thus surely we carried one to add to y thus y = 2...suff

from 2
xyz
+ 004
-------

if 0<z<6 y = 3 if 6<=z<=9 thus y = 2 .............insuff

A, hi Tarek , i think it is easier to visualize it this way, hope it helps.

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.

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.

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

Consider

x y z
+ + 9

Minimum value of z is 1. Maximum value of z is 9
In both cases if 9 is added to z, it will produce 1 as carry over to y (tens digit)
If y becomes 3 after the addition, then it was 2 before the addition

Statement 1-----sufficient

Statement 2 is clearly insufficient, as we could have a carry from the Units digit and not have a carry (with the addition of 4). Each will give different result

Hope this is simply put

Unit digit has to be atleast 1.
1: k+9 so there will be a carry of 1 in tens digit always hence tens digit in original number is 2 hence sufficient.
2: k+4 can't say on carry to tens digit as unit digit of original number can be >6 or <6 hence insufficient.

Therefor A.
Whats the OA.

I am unable to follow your reasoning.Could you please explain in detail ,how you infer that the tens digit is 2 in stmt 1.

Thanks Bunuel.. good explanation.

Well, I plugged some numbers and got A.
I) If k+9=38 (can't be 39 as k would have 0 as unit digit and also unit digit of k+9 can be from 0 to 8) then k=38-9=29 so the 10th digit for k is 2, that was if unit digit of k+9 is max which is 8. If, I take k+9=30 then k=21 and similarly for k+9=34, k would be 25 so the 10th digit is still 2. Same goes for 130 to 138 and 230 to 238 and so on.
Hence A is sufficient, so cross out answer choices B,C, and E.
Now we are left with options A & D. T check whether D can be an answer or not, we'll have to check out 2nd information.
II) If k+4=28 (can't be 24 as this way we'll get 0 as unit digit for k) then k=24 and 10th digit for k is 2. Now if we take k+4 less than 24 suppose k+4=23 then k=19 and 10th digit for k is 1. So we can't be sure either 10th digit for k is 1 or 2, Hence Insufficient. Same goes for if k+4 is in hundreds or more. Now cross out D option and we are left with only option A.
So Answer is A
Hope it helps!

The question is fine I think.

Going by stmt 1: k+9 giving 3 in the tenths place would mean any number with two in the tenths place can give this. Sufficient.
Going by stmt 2: k+4 giving 2 in tenths place would mean any number between 1 and 5 in the hundreds place would return the same number in the tenths place. Any number between 6 and 9 in the hundreds place would return the next value. Therefore insufficient.
_________________

Hope this helps.

i think A is the answer.
if the units digit is non -zero, then no matter what it is, if u plus 9 , u will get 1. 1 +x =3 then the tens digit is 2
st2 cant help us to determine the tens digit
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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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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.
_________________

I miss the nonzero..
be extra aware of the questions

1) let number be 121,122,123,124,125,.....129
if 9 is added the tens digit changes to 3 therefore tens digit is 3. A/D
2) let number be 119 then adding 4 makes tens digit 2 but on other hand taking number 121 and adding 4 makes tens digit again 2 so insufficient.

A is the answer