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Praetorian
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[#48] 2 Min. Challenge: Fractions 13 May 2004, 08:19
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Level: Intermediate

Time yourself and Solve under 2 minutes.

Which of the five fractions is largest?

(A)
25038876541 / 25038876543
(B)
25038876543/ 25038876545
(C)
25038876545/ 25038876547
(D)
25038876547/ 25038876549
(E)
25038876549/ 25038876551



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[#48] 2 Min. Challenge: Fractions 13 May 2004, 08:38
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E for me as well but I will hold the explanation till others attempt
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[#48] 2 Min. Challenge: Fractions 13 May 2004, 08:53
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x/(x+2) (x+2)/(x+4) (x+4)/(x+6) (x+6)/(x+8) (x+8)/(x+10)

Substract 1.

-2/(x+2) -2/(x+4) -2/(x+6) -2/(x+8) -2/(x+10)

As x is positive, -2/(x+10) is closer to Zero than any others; hence the answer is E
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[#48] 2 Min. Challenge: Fractions 13 May 2004, 09:04
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(A)
25038876541 / 25038876543 = 1 - 2 / 25038876543
(B)
25038876543/ 25038876545 = 1 - 2 / 25038876545
(C)
25038876545/ 25038876547 = 1 - 2 / 25038876547
(D)
25038876547/ 25038876549 = 1 - 2 / 25038876549
(E)
25038876549/ 25038876551 = 1 - 2 / 25038876551

2 / 25038876551 is smallest fraction
Hence 1 - 2 / 25038876551 is biggest
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[#48] 2 Min. Challenge: Fractions 13 May 2004, 14:27
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Praetorian
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Level: Intermediate

Time yourself and Solve under 2 minutes.

Which of the five fractions is largest?

(A)
25038876541 / 25038876543
(B)
25038876543/ 25038876545
(C)
25038876545/ 25038876547
(D)
25038876547/ 25038876549
(E)
25038876549/ 25038876551
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Answer is E, I'm pretty sure my explanation is correct...but feel free to point out any mistakes.

For any fraction, if you add the same number to the numerator and the denominator, the fraction gets larger (i.e. 1/2 < (1 + 1)/(2 + 1) < (1+1+1)/(2+1+1) or 1/2 < 2/3 < 3/4)

in this case your simply adding 2 to the numerator and denominator in each case

For simplicity sake
Let 25038876541 = x
Let 25038876543 = y

(1) x/y
(2) (x+2)/(y+2)
(3) (x+4)/(y+4)
(4) (x+6)/(y+6)
(5) (x+8)/(y+8)

The one that adds the most to both the numerator and the denominator equally is the largest, therfore E is the largest.
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[#48] 2 Min. Challenge: Fractions 15 May 2004, 04:50
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Indeed, the answer is E.



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Hi there,
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Thank you for understanding, and happy exploring!