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Difficulty:
65%
(hard)
Question Stats:
54% (01:48) correct
46%
(01:39)
wrong
based on 161
sessions
History
Date
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Which of the following fractions is the greatest?
(A) \(\frac{1999}{3001}\)
(B) \(\frac{201}{301}\)
(C) \(\frac{19}{32}\\
\)
(D) \(\frac{4}{7}\)
(E) \(\frac{2}{3}\\
\)
(A) \(\frac{1999}{3001}\)
(B) \(\frac{201}{301}\)
(C) \(\frac{19}{32}\\
\)
(D) \(\frac{4}{7}\)
(E) \(\frac{2}{3}\\
\)
IanStewart
Expert
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 13 Sep 2026
Posts: 4,146
Location: United States
GMAT 1: 780 Q51 V47
Expert reply
GMAT 1: 780 Q51 V47
Posts: 4,146
We can compare most of the answers directly with 2/3. For A,
1999/3001 < 2000/3001 < 2000/3000 = 2/3
(if our numbers are positive, then when we increase the numerator or decrease the denominator of a fraction, we're making the fraction's value larger). Similarly for C,
19/32 < 20/32 < 20/30 = 2/3
and for D:
4/7 < 4/6 = 2/3
So we just need to compare 2/3 and 201/301. Again if you have positive numbers, then if you add identical things to the numerator and denominator of a fraction, the value of that fraction will move towards 1. So 200/300 < 201/301. Or, if that principle is unfamiliar, you can also get a common denominator, which isn't too bad with these specific numbers: 2/3 = (2/3)(301/301) = 602/(3)(301), while 201/301 =(201/301)(3/3) = 603/(3)(301), so 201/301 is largest and the answer is B.
_________________
1999/3001 < 2000/3001 < 2000/3000 = 2/3
(if our numbers are positive, then when we increase the numerator or decrease the denominator of a fraction, we're making the fraction's value larger). Similarly for C,
19/32 < 20/32 < 20/30 = 2/3
and for D:
4/7 < 4/6 = 2/3
So we just need to compare 2/3 and 201/301. Again if you have positive numbers, then if you add identical things to the numerator and denominator of a fraction, the value of that fraction will move towards 1. So 200/300 < 201/301. Or, if that principle is unfamiliar, you can also get a common denominator, which isn't too bad with these specific numbers: 2/3 = (2/3)(301/301) = 602/(3)(301), while 201/301 =(201/301)(3/3) = 603/(3)(301), so 201/301 is largest and the answer is B.
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ScottTargetTestPrep
Expert
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 14 Sep 2026
Posts: 22,739
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Posts: 22,739
sjuniv32
Solution:
We see that each fraction is approximately 2/3, with the last one equal to exactly 2/3. So let’s compare each of the first four fractions to 2/3, using the bow tie method. We see that:
A) 1999/3001 > 2/3 ?
3(1999) > 2(3001) ?
5997 > 6002 ? → No
B) 201/301 > 2/3 ?
3(201) > 2(301) ?
603 > 602 ? → Yes
C) 19/32 > 2/3 ?
3(19) > 2(32) ?
57 > 64 ? → No
D) 4/7 > 2/3 ?
4(3) > 2(7) ?
12 > 14? → No
Since only 201/301 is greater than 2/3, then 201/301 is the greatest.
Answer: B
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