By mistake Lalit divided a number by (-264) instead of 264 and got 20 as answer. Find the number. How many integers would be there between the two quotients?
Answers
Answer:
If and are natural numbers, with non-zero, it can be proven that there exist unique integers and , such that and . The number is called the quotient, while is called the remainder.
GMAT Prep definition of the remainder:
If and are positive integers, there exists unique integers and , such that and . is called a quotient and is called a remainder.
Moreover many GMAT books say factor is a "positive divisor", .
I've never seen GMAT question asking the ramainder when dividend () is negative, but if we'll cancel this restriction (), and only this restriction, meaning that we'll leave the other one (), then division of by will result:
, --> , . Hence .
Given-By mistake Lalit divided a number by (-264) instead of 264 and got 20 as answer.
To Find the correct number and How many integer
would be there between the two quotients
Solution- When he divided by wrong number
Divisor = (-264), quotient= 20, remainder=0
Hence dividend = -264x20+0 = -5280
Hence he should have to divide the number (-5280) by the correct number 264
Divisor= 264, Dividend = (-5280)
Hence quotient = Dividend/Divisor= (-5280) /264= (-20)
Total numbers between -20 and 20 are -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19
Hence total 39 numbers are in between (-20) and 20
Answer (-5280), 39
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