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Bunuel
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If m is a two-digit positive integer and 2*m is a three-digit positive 24 Nov 2022, 02:30
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85% (hard)

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46% (02:32) correct 54% (02:21) wrong based on 50 sessions

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If m is a two-digit positive integer and 2*m is a three-digit positive integer, what is the units digit of m ?

(1) The units digit of 2*m is 4.
(2) The units digit of m equals to to the tens digit of 2m



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If m is a two-digit positive integer and 2*m is a three-digit positive 24 Nov 2022, 03:04
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Bunuel
If m is a two-digit positive integer and 2*m is a three-digit positive integer, what is the units digit of m ?

(1) The units digit of 2*m is 4.
(2) The units digit of m equals to to the tens digit of 2m

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Given

m is a two digit positive integer.
2m is a three digit positive integer. Inference: \(50\leq{m}\leq{99}\)
Statement 1

The units digit of 2*m is 4.

The unit digit of m can be 2 or 7.

As we are getting two answers for the value of the unit digit, this statement doesn't help and we can eliminate A and D.

Statement 2

The units digit of m equals to to the tens digit of 2m

Case 1: m = 50; 2m = 100
Case 2: m = 75; 2m = 150

As we are getting two answers for the value of the unit digit, this statement doesn't help and we can eliminate B

Combined

The units digit of 2*m is 4.
The units digit of m equals to to the tens digit of 2m

Case 1: m = 87; 2m = 174
Case 2: m = 62; 2m = 124

The statements combined don't help. Option E.
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If m is a two-digit positive integer and 2*m is a three-digit positive 24 Nov 2022, 10:11
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given m is a + '2' digit number amd 2*m is three digit number
target what is units digit of 'm'
least value of m is 50 and max value is 99
#1
The units digit of 2*m is 4
m ; 52 , 57,62,67... so on
insufficient
#2
The units digit of m equals to to the tens digit of 2m
m = 62 ; 2m ; 124
m=74 ; 2m ; 148
insufficient
from 1 &2
unit digit is 2,7
m=62, 87
insufficient
option E


Bunuel
If m is a two-digit positive integer and 2*m is a three-digit positive integer, what is the units digit of m ?

(1) The units digit of 2*m is 4.
(2) The units digit of m equals to to the tens digit of 2m



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If m is a two-digit positive integer and 2*m is a three-digit positive 24 Nov 2022, 23:29
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[quote="Bunuel"]If m is a two-digit positive integer and 2*m is a three-digit positive integer, what is the units digit of m ?

(1) The units digit of 2*m is 4.
(2) The units digit of m equals to to the tens digit of 2m



[textarea]

m is a two-digit positive integer and 2*m is a three-digit positive integer => m is between 50 and 99, both included

(1) The units digit of 2*m is 4.
unit digit can be 2 or 7 => 52, 72, 77 are all possible .. no unique solution ---> Insufficient
(2) The units digit of m equals to to the tens digit of 2m
m is a two-digit positive integer and 2*m is a three-digit positive integer => three digit positive integer will be even numbers between 100 and 198, both included.
unit digit of m and tens digit of 2m can be both even or odd.
Let number be 10a+b, then 2m will be 20a+2b.
Case 1: If b is between 0-4, tens digit will be unit digit of 2a => units digit of 2a will be even => unit digit of m, ie b will be even => b = 0,2,4 => corresponding unit digit of 2a will be 5, 6, 7=> possible m will be 50, 62, 74


Case 2: if b is between 5-9, tens digit will be unit digit of 2a+1 => units digit of 2a+1 will be odd => unit digit of m, ie b will be odd => b = 5,7,9 => corresponding digit of a will be 7,8,9 => possible m will be 75, 87, 99

Many values of m is possible => Insufficient

Combine both
62 and 87 satisfies both => m has two values --> Insufficient

Ans E
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