Number System
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Q.

A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.

He was afraid of forgetting his PIN. He wrote down the number 123 in his diary to remember his PIN. He also wrote out the way to calculate 123 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 123".

Once, Prafull saw his diary in which Pinaki wrote this number 123. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?

 A.

874

 B.

875

 C.

876

 D.

877

 Hide Ans

Solution:
Option(A) is correct

card number $= 996$, PIN $= x$, Remainder $= 123$

Thus, $\dfrac{(996 × x)}{997} = 123$

$x =$ 874 (From options).


(7) Comment(s)


ABHIJEET
 ()

X=pin 996 = Credit no.

the proper answer should be like this:

996 x X = 997k + 123

996 x X = (996 + 1)k + 123

996 x X = 996k + (k+123)

Now the RHS should be divisible by 996

so k = 873

finally,

996 x X = 996(k+1)

so from deduction

x = k+1 = 873 + 1 = 874


ABHIJEET
 ()

to clear up the first step

it is provided in the question that the product is divisible by 997 and leaves a remainder 123..

as like 25 when divided by 6 leaves remainder 1,

we can also write 25 = 6k + 1 , here k being 4


Kenneth
 ()

This question is wrong



Vinit Patil
 ()

The question is correct

(996xPN)/997 = R(123)

the reamainder from 996 is -1 hence , the remainder from PN would be -123

therefore, 997-123 = 874

PN= Pin number



Pcfg
 ()

The question is wrong. It should be quotient is 123 not remainder



PRATYUSH ANAND
 ()

Hi 2 all,

I think Eqation should be-

$996 \times X= 997Y +123$

where,

$X=$ Pin no.

and $Y=$ Quotient.

Admin Please bring solutions with proper approach and if possible without taking option help as far as possible.



Anoop Tiwari
 ()

I think it should be

Remainder $\dfrac{996\times x}{997}= 123$ as mentioned in the question???