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Suppose N and 4N each represent a three digit positive integer, and

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Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 00:16
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Suppose N and 4N each represent a three digit positive integer, and that the sum of the digits of N is 12. What is the greatest possible value of 4N?

(A) 732
(B) 846
(C) 984
(D) 1203
(E) 1512
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C
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 00:30
Since N is an integer, 4N is a multiple of 4 and 4N is a three digit integer (4N is at least 400 and at most 996)

Eliminate (B) (D) & (E)

4N can be 732 and 984 and so its greatest possible value is 984

Answer is (C)

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Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   Updated on: 22 Apr 2020, 07:21
Another way of working this out is to plug numbers. Since the math is quite simple it's possible to reach the answer very quickly.

Looking for the greatest possible 4N is equivalent to looking for the greatest possible N
We know that 4N is a 3 digit number therefore N < 250. The highest of which will be in the form of 24X with X 0-9

The only other constraint is that the sum of digits is 12, therefore 246 is by definition the highest solution.
4N = 4 x 246 = 984

Answer (C) 984

Originally posted by MBABackstage on 22 Apr 2020, 01:49.
Last edited by MBABackstage on 22 Apr 2020, 07:21, edited 1 time in total.
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 06:52
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MBABackstage wrote:
Another way of working this out is to plug numbers. Since the math is quite simple it's possible to reach the answer very quickly.

Looking for the greatest possible 4N is equivalent to looking for the greatest possible N
We know that 4N is a 3 digit number therefore N < 250. The highest of which will be in the form of 24X with X 0-9

The only other constraint is that the sum of digits is 12, therefore 246 is by definition the highest solution.
4N = 4 x 236 = 984

Answer (C) 984


Dear MBABackstage,
Thank you for your solution, just a small typo here, we have 236 instead of 246, hope you will correct it to prevent confusion. Thank you.
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 07:21
well spotted and thanks stne !
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 12:21
I am not sure i understood the line of reasonong. SUm of digits of n is 12 , so 282=12 , so is 822 =12.

Can somebody please explain the above line of thought
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink] New post   22 Apr 2020, 12:26
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Subhrajyoti wrote:
I am not sure i understood the line of reasonong. SUm of digits of n is 12 , so 282=12 , so is 822 =12.

Can somebody please explain the above line of thought


We are told that both N and 4N are three digit numbers. If N is 282 or 822, then 4N will not be a three digit number.
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Re: Suppose N and 4N each represent a three digit positive integer, and [#permalink]
22 Apr 2020, 12:26
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