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For F.S 2, we know that n-8 = 4X. Thus, n = 4X+8. Adding 8 on both sides, we get n+8 = 4X+16. Now, as the tens digit of n+8 is 6, therefore, X can only range from 4 to 9. Thus, the maximum value of n = 49+8 = 57 and the minimum value of n = 44+8 = 52.

The tens digit of n = 5. Sufficient.
_________________

Re: If n is a positive integer and the tens digit of n+8 is 6, w [#permalink]

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19 Aug 2013, 03:21

1

This post received KUDOS

fozzzy wrote:

Could you elaborate a bit more it isn't very clear. I approached this question differently. Let n = abc

abc + 8 in this scenarios b is 6 so c = 0,1,2,3 then we don't get a carryover b=6 but if c=4-9(range) then we get a carryover so b=5

Given statement 1 is sufficient since there will be carryover so c=5

Statement 2

abc - 8 then in this case b=4 if c=9,8 then there is no carryover in that case c=4 but if c=0-7(range) then b=5

but my question in using this approach c can only be 4,5,6,7 ( I know its irrelevant for this question but I'm asking this for conceptual clarity?)

So can someone explain this part

Could you state exactly which part was not clear?

Anyways, here is another approach : From F.S 2, we know that \(40\leq{n-8}\leq{49} \to 48\leq{n}\leq{57}\)

Also, the question stem states that : \(60\leq{n+8}\leq{69} \to 52\leq{n}\leq{61}\)

The common intersection of both the in-equalities is \(\to 52\leq{n}\leq{57}\). So , yes, "c" as in your example can range only from 2 to 7.

Hope this is clear.

Note: When I say \(52\leq{n}\leq{57}\), it doesn't mean that n is a 2 digit number. It is just a scalable inequality for its last 2 digits.
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Ques :- If n is a positive integer and the tens digit of n+8 is 6, what is the tens digit of n?

Tens digit of n+8 is 6, So lets assume that n+8 is 6b, where b is units digit. We are asked the tens digit of n. that means ques is indirectly asking that if we subtract 8 from 6b (i.e. from n+8) would the tens digit reduce from 6 to 5?

Further examination would tell us that if b takes any value from 0 to 7 tens digit will become 5 (i.e. will change) and it b takes value of 8 or 9 tens digit will remain same because when smaller units digit subtracted from larger units digit, the subtraction would not affect the tens digit.

So the question is basically asking us What is the units digit of n?

(1) The units digit of n is a prime number :- Units digit is one from 1,2,5,7. All these values are below 8. So we can say tens digit of n is 5. Sufficient

(2) The tens digit of n-8 is 4 :- This is tricky. (n+8) and (n-8) have difference of 16. n+8 has tens digit as 6 and n-8 has tens digit as 4. So these numbers must be of the form 6b (59<6b<70) and 4a (39<4a<50) The only pairs of the numbers that obeys above conditions and differed by 16 are as follows 44 and 60 45 and 61 46 and 62 47 and 63 48 and 64 49 and 65 In all the cases we can see the units digit of all 6b (i.e. of n+8) lies between 0 and 5. That means it is below 8. So tens digit of n is 5. Sufficient

Re: If n is a positive integer and the tens digit of n+8 is 6, w [#permalink]

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12 Feb 2014, 10:11

Narenn wrote:

Yeah, You were correct. Ten's digit should be 5. There was a typing mistake, which I just corrected.

Thanks

There's no need for all this. From statement 2 we have that n - 8 tens digit 4. We had that n+8 tens digit 6. Therefore, only tens digit that is possible is 5, since both are 16 apart.

Re: If n is a positive integer and the tens digit of n+8 is 6, w [#permalink]

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13 Aug 2014, 00:05

Let ....yx be he number n where y is ten's digit and x is unit'd digit.

Given information : ten's digit of (n+8) =6 It means two possibilites :- <1> y=6 ,x=0,1 <2>y=5,x>=2 Now let's go to options:-

<A> Unit digit is a prime number It means x=2 or 3 or 5 or 7 This imples y=5 Hence ,ten's digit of n can be uniquely determined as 5 <B> ten's digit of (n-8)=4 It means two possibilities :- <1> y=4,x=8,9 <2> y=5,x=1,2,3,4,5,6,7 This means y=5 as from given information y=5 or 6.

Hence , option D ,Each statement is suffiecient alone

Guys I think the answer should be B. For A what about 28+8 or 38+8 we can never find out what the tens digit is.what do you say?

Notice that we are told that the tens digit of n+8 is 6. In your examples, the tens digit of 28+8=36 is 3, not 6 and the tens digit of 38+8=46 is 4, not 6. Also, the first statement says that the units digit of n is a prime number, and 8 (the units digit of 28 and 38), is NOT a prime.