n is a positive integer that lies between 100 and 200, exclusive, and

Question

n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5?

(1) n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number.

(2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.

chetan2u · Answer

n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5?

I. n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n is a prime number.
So, sum of digits is 9 or 18.. first digit is 1... Number is 1xy..
Number could be 135 or 171
Insufficient

II. The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.
Hundred digit is 1, so tens digit will be 1+2=3..
Thus, units digit can be 3+2=5 or 3-2=1, but units digit can be only 5, as digit cannot be repeated, so number is 135..
Sufficient

B

OhsostudiousMJ · Answer

Hi chetan2u ,
Referring to the highlighted part, the question's asked if the last digit is 5, and it is not given. Hence, the number can be 153 or 135. Am I understanding this right?

And so, from 1 and 2, it can be concluded that 135 is the number and hence, imo,  C is the answer .

chetan2u · Answer

No, the number can only be 135..
It is given that the difference in hundreds and tens digit is 2, so 153 would mean the difference is 5-1=4..
Thus the number is 135..3-1=5-3=2
B

OhsostudiousMJ · Answer

Ah yes! Indeed! Thank you so much!!

Diya52 · Answer

Hi  chetan2u ,

If the digits cannot be repeated can the number be 171 as you showed in the example of statement 1?

Posted from my mobile device

neha283 · Answer

That is correct, it is not 171, it should be 198. So the 2 numbers between 100 and 200 exclusive that are divisible by 9 and whose units and tens digits when reversed result in a prime number are 135 and 198.

sanjayparihar16 · Answer

Hi Chetan,

This explanation needs an edit.

For statement 1 - The number cannot be 171 as digits cannot be repeated, it should be 198 (prime number in that case will be 89)

cheeseypeesy · Answer

Hi, confused as statement 1 says that n is divisible by 9 and the 2-digit number formed by inverting the units and tens digit of n  is a prime number . Doesn't this mean that the 2-digit number is a prime number? 35 from 135 is not a prime number and any number ending in 5 is not a prime?

Bunuel · Answer

35 is not a prime number but 53, the number you get by reversing the digits is. That's what the question means.

n is a positive integer that lies between 100 and 200, exclusive, and

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