Given that the units digit of 14*N is same as the tens digit of 20*M

Question

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

gmatophobia · Answer

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

chetan2u · Answer

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

chetan2u · Answer

Perfectly fine answer. 
But M could also end in 7 as 20*7=140, that is the tens digit is 4. Of course the answer would not change as 4*7 also gives unit digit as 8.

bumpbot · Answer

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Given that the units digit of 14N is same as the tens digit of 20M

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