GPL Mathematical Skills | Number System

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Q. No. 49:	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

Solution Answer: A card number = 996, PIN = x, Remainder = 123 Thus, (996 * x)/997 = 123 x = 874(From options).

Q. No. 50:	The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, what is the original number ?
A :	74
B :	63
C :	85
D :	Cannot be determined

Solution Answer: D Let the number be xy. The number = 10x+y On interchanging the digits of the number = 10y+x => 10x+y - 10y-x = 27 => x-y = 3 Now, y is not equal to zero and the set of digits satisfying the condition are :- (9,6), (8,5), (7,4), (6,3), (5,2), (4,1) We can't reach on the distinct answer.

Q. No. 51:	If x and y are any natural numbers, then which of the following is an odd number ?
A :	x^y + y^x (x-y)(x^y +x)
B :	x^y (x+y)(x^y +x)
C :	y^x (x² -y)(x^y -x)
D :	None of these

Solution Answer: A x and y are natural numbers. We know that of any natural number p. pⁿ +p is even And, pⁿ -p is even. When we multiply an even number to any natural number the resultant number is even.