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Updated on: 04 Sep 2014, 14:33
Originally posted by manish2014 on 04 Sep 2014, 14:10.
Last edited by Bunuel on 04 Sep 2014, 14:33, edited 1 time in total.
Last edited by Bunuel on 04 Sep 2014, 14:33, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
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Question Stats:
60% (03:25) correct
40%
(03:00)
wrong
based on 316
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How many three digit even numbers N can be formed that are divisible by 9 such that both N and N^2 have the same units digits?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
04 Sep 2014, 14:40
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manish2014
How many three digit even numbers N can be formed that are divisible by 9 such that both N and N^2 have the same units digits?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
For an even number to have the same units digit as its square, it must have the units digit of 0 (0^2 = 0) or 6 (6^2 = 6). Thus the units digit of N must be 0 or 6.
For a number to be divisible by 9, the sum of its digit must be divisible by 9.
If the units digit of N is 0, then N could be:
900;
810, 180;
720, 270;
630, 360;
540, 450;
990.
10 numbers.
If the units digit of N is 6, then N could be:
306;
216, 126;
936, 396;
846, 486;
756, 576;
666.
10 numbers.
Total = 10 + 10 = 20.
Answer: A.
P.S. Pleas provide OA when posting and do NOT shorten or reword the question in ANY way.
General Discussion
subhamgarg91
GMAT 2: 750 Q51 V40
Posts: 24
07 Dec 2015, 06:15
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manish2014
How many three digit even numbers N can be formed that are divisible by 9 such that both N and N^2 have the same units digits?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Unit digit can be "0" or "6"
CASE 1 - When unit digit is "0"
Sum of digits should be divisible by 9
If sum of digits is 9 then first two digits can be -
9,0
1,8 or 8,1
2,7 or 7,2
3,6 or 6,3
4,5 or 5,4
if sum of digits is 18 then -
9,9
CASE 2 - When unit digit is "6"
If sum of digits is 9 then first two digits can be -
3,0
1,2 or 2,1
if sum of digits is 18 then -
9,3 or 3,9
8,4 or 4,8
7,5 or 5,7
6,6
Total = 9 + 1 + 3 + 7 = 20
