Determine the RANGE of the sum.
There are 10 fractions in total.
The smallest fraction is 1/100.
The greatest fraction is 1/91.
If all 10 fractions were 1/100, then S = 10(1/100) = 1/10.
Since 9 of the fractions are actually GREATER THAN 1/100, S must be GREATER THAN 1/10.
If all 10 fractions were 1/90, then S = 10(1/90) = 1/9.
Since all 10 fractions are actually LESS THAN 1/90, S must be LESS THAN 1/9.
Thus:
1/10 < S < 1/9.
Of the 3 options, only III is less than S.
The correct answer is C.
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Hi maakya,
In these types of questions, it's important to remember that the GMAT does NOT expect you to calculate that sum. Instead, you're supposed to use estimation and some logic to eliminate answer choices.
To start, we're asked to think about the sum of the fractions: 1/91 + 1/92 + 1/93.....+ 1/100.
Since there are 10 fractions, IF.... they were all equal to 1/90 exactly (which they are NOT, we know that they are all SMALLER than 1/90), then the sum would be 10/90 = 1/9. Since all 10 fractions are LESS than 1/90, the sum is LESS than 1/9.
In that same way....IF.... all of the fractions were exactly 1/100 (which they are NOT, we know that 9 of them are GREATER than 1/100), then the sum would be 10/100 = 1/10. Since those 9 fractions are GREATER than 1/100, the sum is GREATER than 1/10.
With these deductions, only Roman Numeral 3 is less than the sum.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
In these types of questions, it's important to remember that the GMAT does NOT expect you to calculate that sum. Instead, you're supposed to use estimation and some logic to eliminate answer choices.
To start, we're asked to think about the sum of the fractions: 1/91 + 1/92 + 1/93.....+ 1/100.
Since there are 10 fractions, IF.... they were all equal to 1/90 exactly (which they are NOT, we know that they are all SMALLER than 1/90), then the sum would be 10/90 = 1/9. Since all 10 fractions are LESS than 1/90, the sum is LESS than 1/9.
In that same way....IF.... all of the fractions were exactly 1/100 (which they are NOT, we know that 9 of them are GREATER than 1/100), then the sum would be 10/100 = 1/10. Since those 9 fractions are GREATER than 1/100, the sum is GREATER than 1/10.
With these deductions, only Roman Numeral 3 is less than the sum.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
