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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
(A) 732
(B) 846
(C) 984
(D) 1203
(E) 1512
firas92
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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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Eliminate (B) (D) & (E)
4N can be 732 and 984 and so its greatest possible value is 984
Answer is (C)
Posted from my mobile device
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GraemeGmatPanda
Joined: 13 Apr 2020
Last visit: 08 Sep 2026
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Schools: LBS '16 (A$)
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Updated on: 22 Apr 2020, 06:21
Originally posted by GraemeGmatPanda on 22 Apr 2020, 00:49.
Last edited by GraemeGmatPanda on 22 Apr 2020, 06:21, edited 1 time in total.
Last edited by GraemeGmatPanda on 22 Apr 2020, 06:21, edited 1 time in total.
Another way of working this out is to plug numbers. Since the math is quite simple it's possible to reach the answer very quickly.
Looking for the greatest possible 4N is equivalent to looking for the greatest possible N
We know that 4N is a 3 digit number therefore N < 250. The highest of which will be in the form of 24X with X 0-9
The only other constraint is that the sum of digits is 12, therefore 246 is by definition the highest solution.
4N = 4 x 246 = 984
Answer (C) 984
_________________
Looking for the greatest possible 4N is equivalent to looking for the greatest possible N
We know that 4N is a 3 digit number therefore N < 250. The highest of which will be in the form of 24X with X 0-9
The only other constraint is that the sum of digits is 12, therefore 246 is by definition the highest solution.
4N = 4 x 246 = 984
Answer (C) 984
_________________
Graeme
Coach & Founder of GMAT Panda
Coach & Founder of GMAT Panda
MBABackstage
Dear MBABackstage,
Thank you for your solution, just a small typo here, we have 236 instead of 246, hope you will correct it to prevent confusion. Thank you.
_________________
- Stne
GraemeGmatPanda
Joined: 13 Apr 2020
Last visit: 08 Sep 2026
Posts: 102
Location: United Kingdom
Concentration: Marketing
Schools: LBS '16 (A$)
Products:
Schools: LBS '16 (A$)
Posts: 102
Posts: 70
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
Can somebody please explain the above line of thought
Subhrajyoti
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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