Which of the following represents the greatest value? A) : PS Archive
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# Which of the following represents the greatest value? A)

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Which of the following represents the greatest value? A) [#permalink]

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15 Mar 2006, 04:34
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Which of the following represents the greatest value?

A) √2/√3 + √3/√4 + √4/√5 + √5/√6

B) 2/3 + 3/4 + 4/5 + 5/6

C) 2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2

D) 1 - 1/3 + 4/5 - 3/4

E) 1 - 3/4 + 4/5 + 1/3

The answer is pretty simple, but what I don't understand is how one can quickly determine which on of A and E is the greatest??

SVP
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15 Mar 2006, 07:06
Which of the following represents the greatest value?

A) √2/√3 + √3/√4 + √4/√5 + √5/√6

B) 2/3 + 3/4 + 4/5 + 5/6

C) 2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2

D) 1 - 1/3 + 4/5 - 3/4

E) 1 - 3/4 + 4/5 + 1/3

The answer is pretty simple, but what I don't understand is how one can quickly determine which on of A and E is the greatest??

Notice that C= (2/3)^2 + (3/4)^2 + (4/5) ^2 + (5/6) ^2
because 2/3 < 3/4< 4/5< 5/6 <1 ---> their squares' values are smaller than their original value ---> C< B
D= 1 - 1/3 + 4/5 - 3/4 = 2/3 + 4/5 -3/4 < B= 2/3 + 3/4 + 4/5 + 5/6 --> D< B
E= 1/4 + 4/5 + 1/3 < B= 2/3 + 3/4 + 4/5 + 5/6 ( this is obvious!)
--> E<B

Now compare A and B.
A= the sum of the squareroots of each term of B AND since those terms <1 ----> their squareroots < their values ----> B<A

Finally, conclude that A is the biggest!
SVP
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15 Mar 2006, 10:06
laxieqv wrote:
Which of the following represents the greatest value?

A) √2/√3 + √3/√4 + √4/√5 + √5/√6

B) 2/3 + 3/4 + 4/5 + 5/6

C) 2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2

D) 1 - 1/3 + 4/5 - 3/4

E) 1 - 3/4 + 4/5 + 1/3

The answer is pretty simple, but what I don't understand is how one can quickly determine which on of A and E is the greatest??

Notice that C= (2/3)^2 + (3/4)^2 + (4/5) ^2 + (5/6) ^2
because 2/3 < 3/4< 4/5< 5/6 <1 ---> their squares' values are smaller than their original value ---> C< B
D= 1 - 1/3 + 4/5 - 3/4 = 2/3 + 4/5 -3/4 < B= 2/3 + 3/4 + 4/5 + 5/6 --> D< B
E= 1/4 + 4/5 + 1/3 < B= 2/3 + 3/4 + 4/5 + 5/6 ( this is obvious!)
--> E<B

Now compare A and B.
A= the sum of the squareroots of each term of B AND since those terms <1 ----> their squareroots < their values ----> B<A

Finally, conclude that A is the biggest!

Finally, conclude that Laxie is the best!
VP
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16 Mar 2006, 22:26
Which of the following represents the greatest value?

A) √2/√3 + √3/√4 + √4/√5 + √5/√6
B) 2/3 + 3/4 + 4/5 + 5/6
C) 2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2
D) 1 - 1/3 + 4/5 - 3/4
E) 1 - 3/4 + 4/5 + 1/3

The answer is pretty simple, but what I don't understand is how one can quickly determine which on of A and E is the greatest??

A) √2/√3 + √3/√4 + √4/√5 + √5/√6

(√2/√3) is close to 1. similarly (√3/√4), (√4/√5), and (√5/√6), each, are close to 1. rest choices do not have components that are sclose to 1.
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17 Mar 2006, 06:53
Not sure if this is a sanctioned method, but try leveling the playing field. Square all the answer choices A-E and notice that the denominators get larger in B-E, hence making their values smaller. (A) remains.
17 Mar 2006, 06:53
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