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18 May 2005, 13:59
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A certain calculator is able to display atmost 10 digits, so that any number with a total of more than 10 digits before and after the decimal point cannot be displayed accurately. If x and Y are positive integers less than 1000, can the result of dividing x by y be displayed accurately on the calculator 
:
A ) 105 < x < 108
B ) 3 < y < 6
( Explain your answers pals )
:
A ) 105 < x < 108
B ) 3 < y < 6
( Explain your answers pals )
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18 May 2005, 14:13
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B.
condition A isn't sufficient since dividing some numbers in the range by say 3 or 7 will result in irrational numbers (infinite number of decimals)
condition B. is perfect because we have and 5, 4 gives you up to 2 decimals, and 5 - up to 1
1/4 = .25 and 1/5 = 0.2, multiply any integer by them and you will see
condition A isn't sufficient since dividing some numbers in the range by say 3 or 7 will result in irrational numbers (infinite number of decimals)
condition B. is perfect because we have and 5, 4 gives you up to 2 decimals, and 5 - up to 1
1/4 = .25 and 1/5 = 0.2, multiply any integer by them and you will see
18 May 2005, 14:17
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If we have a non terminating (repeating or non repeating) decimal representation of the fraction, it can't be displayed accurately.
A. x is 106 or 107. For (say) 106, a denominator of 2 would display correctly (53), but a denominator of 3 would not (35.33333333333). Insufficient.
B. x is any value. y is 4 or 5. For any fraction (with a whole number as the numerator), a denominator of 4 would produce terminating decimal representation of (.0, .25, .5 or .75) and a denominator of 5 would produce a terminating decimal representation of (.0, .2, .4, .6, or .8), none of which is non terminating. Besides, the number of digits for the quotient for dividends upto 1000 doesn't exceed 3. Thus sufficient.
B.
A. x is 106 or 107. For (say) 106, a denominator of 2 would display correctly (53), but a denominator of 3 would not (35.33333333333). Insufficient.
B. x is any value. y is 4 or 5. For any fraction (with a whole number as the numerator), a denominator of 4 would produce terminating decimal representation of (.0, .25, .5 or .75) and a denominator of 5 would produce a terminating decimal representation of (.0, .2, .4, .6, or .8), none of which is non terminating. Besides, the number of digits for the quotient for dividends upto 1000 doesn't exceed 3. Thus sufficient.
B.
