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

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Joined: 18 Feb 2019
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n is a positive integer that lies between 100 and 200, exclusive, and  [#permalink]

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14 Apr 2019, 06:14
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Difficulty:

95% (hard)

Question Stats:

40% (02:38) correct 60% (02:47) wrong based on 43 sessions

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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.

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.
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Posts: 7981
Re: n is a positive integer that lies between 100 and 200, exclusive, and  [#permalink]

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14 Apr 2019, 10:30
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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n is a positive integer that lies between 100 and 200, exclusive, and  [#permalink]

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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]

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15 Apr 2019, 00:13
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]

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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]

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15 Apr 2019, 02:37
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
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Re: n is a positive integer that lies between 100 and 200, exclusive, and  [#permalink]

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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?

Posted from my mobile device

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] 15 Apr 2019, 03:21
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