If the unit digit of the positive integer n is 5, what is the tens dig

Question

If the unit digit of the positive integer n is 5, what is the tens digit of n?

(1) The tens digit of n + 5 is 7.
(2) The tens digit of n - 6 is 5.

Capakki · Answer

Unit digit is 5. So let the number be m5

S1: m5+5= 70
Adding 5 to unit digit's 5 would increase the tens digit's value of m5 by 1. As 7 is the tens digit of new number, orginal number will have 6 as its unit digit. 
Sufficient

S2: m5-6= 59
Going by the same logic as in S1, subtracting 6 from 5 at unit digit position will reduce the tens digit by 1. So unit digit of m5 is 5+1=6.
Sufficient.

Hence, both statements are individually sufficient. D

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yashikaaggarwal · Answer

N = 10A+B
Where A is tens digit and B is unit
B = 5(given)

We have to find A

Statement 1: tens digit of N+5 = 7
10a+5+5 Tens digit is 10(7)+0(5+5 = 10 ,where one carried forward)
10a+10 Tens digit is 70
10(a+1) = 70
A+1 = 7
A = 6
(Sufficient)

Statement 2: tens digit of N-6 = 5
10a+5-6 Tens digit is 10(5)+y
10a-1 Tens digit is 50+y
A will shift to its previous no. Resulting A-1
A-1 = 5
A = 6
(Sufficient)

Answer is D

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rajatchopra1994 · Answer

Explanation:

Given : Unit digit of the positive integer n is 5
To find: tens digit of n

Statement 1: The tens digit of n + 5 is 7
Number N + 5 , then tens digit is 7
& unit digit is 5 
So N+5 will given Zero at unit place.
So N tens digit will be 6

Sufficient

Statement 2: The tens digit of n - 6 is 5
5+1 = 6 will be N tens digit.
as -6 will take tens digit to previous number line

Sufficient

IMO-D

Feynmann01 · Answer

Statement 1)
if n+5 gives a tens digit of 7, then the only possible tens digits for n is 6 given that we start with n has a unit digit of 5

Statement 2)
by the same logic, statement alone is also sufficient since it gives the same kind of information

So answer C

Kinshook · Answer

Asked: If the unit digit of the positive integer n is 5, what is the tens digit of n?

(1) The tens digit of n + 5 is 7.
The tens digit of n is 6.
SUFFICIENT

(2) The tens digit of n - 6 is 5.
The tens digit of n is 6.
SUFFICIENT

IMO D

KaramveerBakshi · Answer

The number will be k5 where k is the tens digit. We need to find k.

Statements:

(1) The tens digit of n + 5 is 7.
If n = k5, when we add 5 we have (k+1)0 as n.
Now, k+1 = 7 OR k=6

Sufficient

(2) The tens digit of n - 6 is 5.
Similarly, if n=k5, when we subtract we get (K-1)9 as n.
Now, k-1 = 5 OR k = 6

Sufficient

Hence, the answer is Option (D).

sm1510 · Answer

found this question in the 6th test of GMAT Prep

Bunuel · Answer

_____________________
Added the tag. Thank you!

valeriacastro11 · Answer

Can someone explain me this step by step? i am not understanding the explanations

Janscho147 · Answer

HI, I hope I can help you with my explanation.

123.45

1= Hundreds
2= tens
3= units
"."
4= tenths
5= hundredths

(1) The tens digit of n + 5 is 7.

When you add 5 to n, the tens digit is 7. So n could be 65, 66, 67, 68, 69, 70, 71, 72, 73, 74. If you add 5, the numbers are all between 70-79, hence the statement is fulfilled.
But => As you can see, some "n" have a 6 as a tens digit and some others have a 7 as a tens digit. Therefore insufficient.

(2) The tens digit of n - 6 is 5.

If you subtract 6 from n, the tens digit is 5. So n could be 56, 57, 58, 59, 60, 61, 62, 63, 64, 65. If you subtract 6, the numbers are all between 50-59, which means they have a 5 as the tens digit, hence the statement is fulfilled.
But => As you can see, some "n" have a 5 as the tens digit and some have a 6 as the tens digit. Therefore insufficient.

If you combine the information from both statements, you can see that only 6 as a tens digit suffices both statements.

I hope I was able to help you.

Rajatpo · Answer

I am not understanding the explanations? can someone explain me in more detail? (step by step explaination)

Bunuel · Answer

If the unit digit of the positive integer n is 5, what is the tens digit of n?

(1) The tens digit of n + 5 is 7.

Given that the unit digit of n is 5, the unit digit of n + 5 would be 0. Consequently, n + 5 = 70 and n = 65, which implies the tens digit of n is 6. Sufficient.

(2) The tens digit of n - 6 is 5.

Given that the unit digit of n is 5, the unit digit of n - 6 would be 9. Consequently, n - 6 = 59 and n = 65, which implies the tens digit of n is 6. Sufficient.

Answer: D.

Rajatpo · Answer

Still confusing with calculations can you tell how calculations are there?

(2) The tens digit of n - 6 is 5.

Given that the unit digit of n is 5, the unit digit of n - 6 would be 9. Consequently, n - 6 = 59 and n = 65, which implies the tens digit of n is 6. Sufficient.

Bunuel · Answer

If a positive number ending in 5 has 6 subtracted from it, the resulting units digit will be 9. For example, 25 - 6 results in 19.

Rajatpo · Answer

If a positive number ending in 5 has 6 subtracted from it, the resulting units digit will be 9. ---understood

n - 6 = 59 
how 59 come? and why

Bunuel · Answer

The stem says: the unit digit of n is 5.
(2) says: the tens digit of n - 6 is 5.

Given that the unit digit of n is 5,  the unit digit of n - 6 would be 9 . Since also given that  the tens digit of n - 6 is 5 , then n = 59.

I hope now it's clear!

Rajatpo · Answer

Thanks a lot got it.

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If the unit digit of the positive integer n is 5, what is the tens dig

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