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19 Sep 2023, 00:33
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A
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Difficulty:
55%
(hard)
Question Stats:
68% (02:17) correct
32%
(02:21)
wrong
based on 153
sessions
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Given that the units digit of 14*N is same as the tens digit of 20*M, where N and M are positive integers. If the unit’s digit of 3*N is 8, then what is the unit’s digit of 4*M?
A. 8
B. 6
C. 4
D. 2
E. 0
A. 8
B. 6
C. 4
D. 2
E. 0
19 Sep 2023, 00:59
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Bunuel
From the question premise - If the units digit of 3*N is 8
The units digit of 3*N = 3 * Unit Digit of N
The units digit of N is an integer between 0 and 9, inclusive.
0 * 3 = 0
1 * 3 = 3
2 * 3 = 6
3 * 3 = 9
4 * 3 = 2
5 * 3 = 6
6 * 3 = 8
7 * 3 = 1
8 * 3 = 4
9 * 3 = 7
We can conclude that the units digit of N = 6
From the question premise - the units digit of 14*N is same as the tens digit of 20*M
Units digit of 14 * N = 14 * Units digit of N = 14 * 6 = 4
Therefore tens digit of 20*M = 4
The tens digit of 20*M is formed by the multiplication of 2 * the units digit of M, hence we can conclude that the units digit of M = 2
Units digit of 4*M = 4 * 2 = 8
Option A
19 Sep 2023, 01:08
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Bunuel
Unit’s digit of 3*N is 8
Only possibility is that N has a unit digit of 6.
Unit’s digit of 14*N is
14*z6 will end in 4.
Ten’s digit of 20*M, therefore, is also 4.
The unit digit of 20*M or 2*M*10 will be 0, and ten’s digit will be nothing but unit digit given by 2*M.
2*M ends in 4, so 2*(2*M) will end in 2*4 or 8.
A
