If 'P' is the greatest number.that divides 9086, 12326 and 23126 leaving the same remainder in each

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10 Oct 2022 Number System

If 'P' is the greatest number.that divides 9086, 12326 and 23126 leaving the same remainder in each case. What is the sum of digits in P ?

OPtion

1) 4
2) 8
3) 6
4) 7
5) 5
6) 3
7) 9
8) 12
9) 14
10) None of these

Solution

Difference of given numbers:
12326 - 9086 = 3240
23126 -12326 = 10800
23126 - 9086 = 14040
Required number (P) = HCF of 3240, 10800 and 14040 = 1080
Hence required sum 1+0+8+0 = 9
Correct Option 7)

Correct Option: 7 Best Solution (1)

G.S.Kantharao   1 year AGO

Let 9086=ab+r
12326=cd+r
23126=ef+r
(cd+r)-(ab+r)=12326-9086=3240
(ef+r)-(cd+r)=23126-12326=10800
(ef+r)-(cd+r)=23126-9086=14040
So the H.C.F of 3240,10800,14040 is 360 which is the highest number leaves the same remainder.
Now 3+6+0=9 is the required answer.
My option is 7👈

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