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

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n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   14 Apr 2019, 06:14
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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.­
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   15 Apr 2019, 02:37
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Hi chetan2u,

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

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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   14 Apr 2019, 10:30
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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
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   15 Apr 2019, 00:06
chetan2u wrote:
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


Hichetan2u,
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.
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   15 Apr 2019, 00:13
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OhsostudiousMJ wrote:
chetan2u wrote:
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


Hichetan2u,
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.


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
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   15 Apr 2019, 00:30
chetan2u wrote:
OhsostudiousMJ wrote:
chetan2u wrote:
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


Hichetan2u,
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.


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


Ah yes! Indeed! Thank you so much!!
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   15 Apr 2019, 03:21
dhritidutta wrote:
Hi chetan2u,

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

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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.
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   19 Feb 2023, 19:26
chetan2u wrote:
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


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)
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   09 Apr 2024, 07:40
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?
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink] New post   09 Apr 2024, 07:52
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Saobsm wrote:
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.­

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?

­35 is not a prime number but 53, the number you get by reversing the digits is. That's what the question means.
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Re: n is a positive integer that lies between 100 and 200, exclusive, and [#permalink]
09 Apr 2024, 07:52
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