What is the least five-digit positive integer which when divided by 8,

Question

What is the least five-digit positive integer which when divided by 8, 12, 16 and 20 leaves remainders 1, 5, 9 and 13, respectively ?

(A) 10093
(B) 10073 
(C) 10013
(D) 10003 
(E) 10001

PrajayM · Accepted Answer

Quick solving way

A number is divisible by 8 if the last three digits of the number are divisible by 8. Here we want the number to leave a remainder of 1 when divided by 8. So divide the last 3 digits of all answer choices by 8 and you will see only option B gives a remainder of 1.

sj296 · Answer

Since 8 - 1 = 7
 12- 5 = 7
 16 - 9 = 7
 20 - 13 = 7

We will subtract 7 from the least five-digit number divisible by LCM (8, 12, 16, 20) to get the required number
 
Smallest five-digit number = 10000

Let us divide this by the L.C.M of 8, 12, 16, and 20

L.C.M of 8, 12, 16, and 20 = 240

Dividing 10000 by 240 leaves a remainder 160, Subtract 160 from 10000 
=> 100000 - 160 = 9840

So this means 9840 is divisible by 240.

So, least five-digit number = 9840+240 = 10080 (which will also be divisible by 240, 8, 12, 16, and 20)

So the answer is 10080 - 7 = 10073. OA should be B

emotionalaatma · Answer

Out of the 5 available answers, Only B and C leaves remainder of 13 when divided by 20. (Since division by 20 is more easy and fast to calculate)

So eliminate all other options, not between B and C, only B leaves remainder 1 when divisible by 8.

so Eliminate c.

Answer is B.

AmitK55 · Answer

I quickly solved it using this elimination method:
For any large number to be divisible by 8, the last 3 digits must be divisible by 8 or if there's a 000 at the end, which means 10,000 is divisible by 8 (remainder=0). Further, it is given to us that dividing the 5 digit number by 8 gives a remainder of 1, purely on this information we can eliminate a few options:

A : 10093-1 => not divisible by 8
C: 10013-1 => not divisible by 8
D: 10003-1 => again not divisible by 8
(All these options give remainder >1 when divided by 8)

Now, we're left with B and E, we know that 10,001 gives a remainder of 1 when divided by 8. Lets check with other information given to us, now 10,001 does not give a remainder of 13 when divided by 20, so we can eliminate that. We're left with option E, which is our answer, as (10073-1) is divisible by 8 and (10073-13) is divisible by 20.

Thanks, let me know if there is a faster way or if I can improve my method.

BrushMyQuant · Answer

Positive integer which when divided by 20 leaves remainder 13

=> Last two digits of the number - 13 should be divisible by 20

(A) 10093 
=> Last two digits - 13 = 93 - 13 = 80
Divisible by 20 =>   KEEP

(B) 10073  
=> Last two digits - 13 = 73 - 13 = 60
Divisible by 20 =>   KEEP

(C) 10013 
=> Last two digits - 13 = 13 - 13 = 00
Divisible by 20 =>   KEEP

(D) 10003  
=> Last two digits - 13 = 10003 - 13 = 90
NOT Divisible by 20 =>   ELIMINATE

(E) 10001  
=> Last two digits - 13 = 10001 - 13 = 88
NOT Divisible by 20 =>    ELIMINATE

Positive integer which when divided by 8 leaves remainder 1

=> Remainder of last three digits by 8 = 1

(A) 10093 
=> Remainder of 093 by 8 = 5  ≠ 1 =>    ELIMINATE

(B) 10073  
=> Remainder of 073 by 8 =  1 =>    KEEP

(C) 10013 
=> Remainder of 013 by 8 = 5  ≠ 1 =>    ELIMINATE

So,  Answer will be B 
Hope it helps!

Watch the following video to MASTER Divisibility Rules

https://www.youtube.com/watch?v=D9ZWVUyvFvM

What is the least five-digit positive integer which when divided by 8,

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