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# PS Fractions #13 from section 24 out 21-30 PS set

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Intern
Joined: 10 Jun 2008
Posts: 3
PS Fractions #13 from section 24 out 21-30 PS set [#permalink]

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30 Nov 2008, 03:38
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Hello All,

Please help me with this problem. I've been trying to solve this forever . I'm so tempted to use the calculator but I know I can't.

13. Of the following sums, which is the greatest?

A) (1/sqrt2) + (1/sqrt3) + (1/sqrt4) + (1/sqrt5)

B) (1/2^2) + (1/3^2) + (1/4^2) + (1/5^2)

C) (1/2^2) + (1/2^3) + (1/2^4) + 1/2^5)

D) (1) - (1/2) + (1/3) - (1/4)

E) (1/2) + (1/3) + (1/4) + (1/5)

How would you solve this in less than 2 mins?

Manager
Joined: 23 Nov 2008
Posts: 79
Re: PS Fractions #13 from section 24 out 21-30 PS set [#permalink]

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30 Nov 2008, 04:04
1
KUDOS
I'd do it by elimination:

13. Of the following sums, which is the greatest?
A) (1/sqrt2) + (1/sqrt3) + (1/sqrt4) + (1/sqrt5)
B) (1/2^2) + (1/3^2) + (1/4^2) + (1/5^2)....def less than choice E, so out
C) (1/2^2) + (1/2^3) + (1/2^4) + 1/2^5)....def less than choice E, so out
D) (1) - (1/2) + (1/3) - (1/4)
E) (1/2) + (1/3) + (1/4) + (1/5)...def less than choice A, so out (sqrt of a number will always be smaller than the number, and since its in the denominator, it makes the whole number larger)

That leaves A and D:
simplying them:
D) 1/2 + 1/12 = 7/12
A) sqrt2/2 + sqrt3/3 + sqrt4/4 + sqrt5/5 = (6sqrt2 + 4sqrt3 + 3sqrt4)/12 + sqrt5/5 => we can see its greater than D.

Hence, A
Manager
Joined: 18 Nov 2008
Posts: 115
Re: PS Fractions #13 from section 24 out 21-30 PS set [#permalink]

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30 Nov 2008, 05:50
1
KUDOS
Quote:
I'd do it by elimination:

13. Of the following sums, which is the greatest?
A) (1/sqrt2) + (1/sqrt3) + (1/sqrt4) + (1/sqrt5)
B) (1/2^2) + (1/3^2) + (1/4^2) + (1/5^2)....def less than choice E, so out
C) (1/2^2) + (1/2^3) + (1/2^4) + 1/2^5)....def less than choice E, so out
D) (1) - (1/2) + (1/3) - (1/4)
E) (1/2) + (1/3) + (1/4) + (1/5)...def less than choice A, so out (sqrt of a number will always be smaller than the number, and since its in the denominator, it makes the whole number larger)

That leaves A and D:
simplying them:
D) 1/2 + 1/12 = 7/12
A) sqrt2/2 + sqrt3/3 + sqrt4/4 + sqrt5/5 = (6sqrt2 + 4sqrt3 + 3sqrt4)/12 + sqrt5/5 => we can see its greater than D.

Hence, A

Agree with you, there may be no other way.. How can we do it in 2 min?

1) (about 30 sec) We should see the similiraty between answer choices, A,B,C and E all are sums of four numbers with 1 as a numerator and with different denominators. The largest of them has the least values of denominators and, therefore it's A.
2) (about 30 sec) D = 7/12
3) (max. 1 min) D = 7/12 = 1/2 + 1/12; A = 1/sqrt4 + (sum of 3 numbers) = 1/2 + sum of 3 numbers, that is obviously greater than 1/12.

Manager
Joined: 08 Aug 2008
Posts: 229
Re: PS Fractions #13 from section 24 out 21-30 PS set [#permalink]

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30 Nov 2008, 05:57
1
KUDOS
look at it this way:-
$$2^3 > 2^2 >2 > sqrt(2)$$

so $$1/sqrt(2) > 1/2 >1/2^2 > 1/2^3$$

hence we are only left with A and D.
clearly D<1<A.

HTH.
Intern
Joined: 10 Jun 2008
Posts: 3
Re: PS Fractions #13 from section 24 out 21-30 PS set [#permalink]

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30 Nov 2008, 05:59
Thank you!! I got it now. I appreciate all your help.
Twilight, Atletikos and Parsun84....you all rock!!
OA is A.
Re: PS Fractions #13 from section 24 out 21-30 PS set   [#permalink] 30 Nov 2008, 05:59
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